User:Karlhahn/oldSand

Material that has been retired from my main sandbox

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Castner-Kellner process

The Castner-Kellner process is a method of electrolysis on an aqueous alkali chloride solution (usually sodium chloride solution) to produce the corresponding alkali hydroxide.

Process details

Castner-Kellner aparatus

The aparatus shown is divided into two types of cells separated by slate walls. The first type, shown on the right and left of the diagram, uses an electrolyte of of sodium chloride solution, a graphite anode (A), and a mercury cathode (M). The other type of cell, shown in the center of the diagram, uses an electrolyte of sodium hydroxide solution, a mercury anode (M), and an iron cathode (D). Note that the mercury electrode is shared between the two cells. This is achieved by having the walls separating the cells dip below the level of the electrolytes but still allow the mercury to flow beneath them.

The reaction at anode (A) is:

2Cl^– → Cl₂ + 2e^–

The chlorine gas that results vents at the top of the outside cells where it is collected as a byproduct of the process. The reaction at the mercury cathode in the outer cells is

2Na⁺ + 2e^– → 2Na (amalgam)

The sodium metal formed by this reaction dissolves in the mercury to form an amalgam. The mercury conducts the current from the outside cells to the inside cell. In addition, a rocking mechanism (B shown by fulcrum on the left and rotating eccentric on the right) agitates the mercury to transport the dissolved sodium metal from the outside cells to the inside cell.

The anode reaction in the center cell takes place at the interface between the mercury and the sodium hydroxide solution.

2Na + 2e^– → 2Na⁺

Finally at the iron cathode (D) of the center cell the reaction is

2H₂O + 2e^– → 2OH^– + H₂

The net effect is that the concentration of sodium chloride in the outside cells decreases and the concentration of sodium hydroxide in the center cell increases.

Extraction of Copper from its Ores

Name	Formula	% Copper when pure
Chalcopyrite	CuFeS2	34.5
Chalcocite	CuS	79.8
Bornite	2Cu2S•CuS•FeS	63.3
Tetrahedrite	Cu3SbS3 + x(Fe,Zn)6Sb2S9	32-45
Malachite	CuCO3•Cu(OH)2	57.3
Azurite	2CuCO3•Cu(OH)2	55.1
Cuprite	Cu2O	88.8
Chrysocolla	CuO•SiO2•2H2O	37.9
Principal Copper-bearing Minerals

Most copper ores contain one or more of the copper-bearing minerals shown in the table. Ores containing as little as 1% copper can be economically exploited. Ores are crushed then concentrated a combination of gravity separation and froth floatation. The resulting concentrate is about 30% copper, having extracted 90% of the copper in the original ore.

Most copper ores contain large amounts of sulfides. These ores are roasted prior to smelting. The smelting is done by reverberatory furnace, although blast furnaces were used in the past. At around 1500°C the charge separates into layers of slag (silicates) and matte (sulfides). This also has the effect of separating much of the iron content of the ore because copper preferentially collects in the matte layer while iron preferentially collects in the slag.

Copper mattes from the reverberatory furnace are then separated from the remaining iron and converted to metal by heating them in an air blow, which effects the following reactions:

2FeS + 3O₂ → 2FeO + 2SO₂

2Cu₂S + 3O₂ → 2Cu₂O + 2SO₂

Cu₂S + 2Cu₂O → 6Cu + SO₂

The addition of silica absorbs the FeO into a silicate slag layer. The remaining metal layer is poured off and cast as impure blister copper. Impurities are primarily arsenic, antimony, bismuth, and precious metals. To obtain copper pure enough for electrical products, the blister copper must be electrolytically refined. Anodes are cast from blister copper. Cathodes are made of thin rolled sheets of pure copper. The electrolyte is a 10-16% aqueous sulfuric acid solution with 3-4% dissoved copper(II) ions. The cell requires only a 0.2-0.4 volt potential. At the anode, copper and less noble metals dissolve. More noble metals such as silver and gold settle to the bottom of the cell as anode mud, which form a saleable byproduct. At the cathode, copper metal plates out but less noble metals remain in solution. The process results in copper that is 99.9% pure.

Chlorine Compounds

Oxidation state	Name	Forumula	Example compounds
–1	chlorides	Cl–	ionic chlorides, organic chlorides, hydrochloric acid
0	chlorine	Cl2	elemental chlorine
+1	hypochlorites	ClO–	sodium and calcium hypochlorite
+3	chlorites	ClO2–	sodium chlorite
+5	chlorates	ClO3–	sodium chlorate, potassium chlorate
+7	perchlorates	ClO4–	potassium perchlorate, perchloric acid, organic perchlorates, ammonium perchlorate, magnesium perchlorate

Chlorine exists in all odd numbered oxidation states from –1 to +7, as well as the elemental state of zero. Progressing through the states, hydrogen chloride gas can be oxidized using manganese dioxide or catalytically by air to elemental chlorine gas. The solubility of chlorine in water is increased if the water contains dissolved alkali hydroxide. This is due to disproportionation:

Cl₂ + 2OH^– → Cl^– + ClO^– + H₂O

In hot concentrated alkali solution disproportionation continues:

2ClO^– → Cl^– + ClO₂^–

ClO^– + ClO₂^– → Cl^– + ClO₃^–

Potassium chlorate can be crystalized from solutions formed by the above reactions. If its crystals are heated, it undergoes the final disproportionation step.

ClO^– + ClO₃^– → Cl^– + ClO₄^–

This same progression from chloride to perchlorate can be accomplished by electrolysis. The anode reaction progression is:

Cl^– + H₂O → ClO^– + 2H⁺ + 2e^–

ClO^– + H₂O → ClO₂^– + 2H⁺ + 2e^–

ClO₂^– + H₂O → ClO₃^– + 2H⁺ + 2e^–

ClO₃^– + H₂O → ClO₄^– + 2H⁺ + 2e^–

Each step is accompanied at the cathode by

2H⁺ + 2e^– → H₂

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Ethanol Chemistry

Chemical formula of ethanol, (C is carbon, the dash is a single bond, H is hydrogen, O is oxygen)

The chemistry of ethanol is largely that of its hydroxyl group.

Acid-base chemistry

Ethanol's hydroxyl proton is weakly acidic, having a pK_a of only 15.9, compared to water's 15.7 (K_a of ethanol is a measure of $\scriptstyle {\frac {[C_{2}H_{5}O^{-}][H^{+}]}{[C_{2}H_{5}OH]}}$. Note that K_a of water is derived by dividing water's dissociation constant, $\scriptstyle [H^{+}][OH^{-}]=1.0\times 10^{-14}$ moles²/liter, by its molar density of 55.5 moles/liter). Ethanol can be quantitatively converted to its conjugate base, the ethoxide ion (CH₃CH₂O⁻), by reaction with an alkali metal such as sodium. This reaction evolves hydrogen gas:

2CH₃CH₂OH + 2Na → 2CH₃CH₂ONa + H₂

Nucleophilic substitution

In aprotic solvents, ethanol reacts with hydrogen halides to produce ethyl halides such as ethyl chloride and ethyl bromide via nucleophilic substitution:

CH₃CH₂OH + HCl → CH₃CH₂Cl + H₂O

CH₃CH₂OH + HBr → CH₃CH₂Br + H₂O

Ethyl halides can also be produced by reacting ethanol by more specialized halogenating agents, such as thionyl chloride for preparing ethyl chloride, or phosphorus tribromide for preparing ethyl bromide.

Esterification

Under acid-catalysed conditions, ethanol reacts with carboxylic acids to produce ethyl esters and water:

RCOOH + HOCH₂CH₃ → RCOOCH₂CH₃ + H₂O

The reverse reaction, hydrolysis of the resulting ester back to ethanol and the carboxylic acid, limits the extent of reaction, and high yields are unusual unless water can be removed from the reaction mixture as it is formed. Esterification can also be carried out using more a reactive derivative of the carboxylic acid, such as an acyl chloride or acid anhydride. A very common ester of ethanol is ethyl acetate, found in nailpolish remover.

Ethanol can also form esters with inorganic acids. Diethyl sulfate and triethyl phosphate, prepared by reacting ethanol with sulfuric and phosphoric acid, respectively, are both useful ethylating agents in organic synthesis. Ethyl nitrite, prepared from the reaction of ethanol with sodium nitrite and sulfuric acid, was formerly a widely-used diuretic.

Dehydration

Strong acids, such as sulfuric acid, can catalyse ethanol's dehydration to form either diethyl ether or ethylene:

2 CH₃CH₂OH → CH₃CH₂OCH₂CH₃ + H₂O

CH₃CH₂OH → H₂C=CH₂ + H₂O

Although sulfuric acid catalyses this reaction, the acid is diluted by the water that is formed, which makes the reaction inefficient. Which product, diethyl ether or ethylene, predominates depends on the precise reaction conditions.

Oxidation

Ethanol can be oxidized to acetaldehyde, and further oxidized to acetic acid. In the human body, these oxidation reactions are catalysed by enzymes. In the laboratory, aqueous solutions of strong oxidizing agents, such as chromic acid or potassium permanganate, oxidize ethanol to acetic acid, and it is difficult to stop the reaction at acetaldehyde at high yield. Ethanol can be oxidized to acetaldehyde, without overoxidation to acetic acid, by reacting it with pyridinium chromic chloride.

Combustion

Ethanol combusting in the confines of an evaporating dish

Combustion of ethanol forms carbon dioxide and water:

C₂H₅OH + 3 O₂ → 2 CO₂ + 3 H₂O

for Carbon dioxide (data page)

Liquid/vapor equilibrium thermodynamic data

The table below gives thermodynamic data of liquid CO₂ in equilibrium with its vapor at various temperatures. Heat content data, heat of vaporization, and entropy values are relative to the liquid state at 0°C temperature and 3483 kPa pressure. To convert heat values to molar values, multiply by 44.095 grams/mole. To convert densities to liters/mole, multiply by 22.678 liter-grams/cm³-mole. Data obtained from CRC Handbook of Chemistry and Physics, 44th ed. pages 2560-2561, except for critical temperature line (31.1°C) and temperatures –30°C and below, which are taken from Lange's Handbook of Chemistry, 10th ed. page 1463.

Carbon dioxide liquid/vapor equilibrium thermodynamic data
Temp. °C	Pvap Vapor pressure kPa	Hliq Heat content liquid J/gr	Hvap Heat content vapor J/gr	ΔvapHo Heat of vapor- ization J/gr	ρvap Density of vapor gr/cm3	ρliq Density of liquid gr/cm3	Sliq Entropy liquid J/mol-°C	Svap Entropy vapor J/mol-°C
–56.6	518.3					1.179
–56.0	531.8					1.177
–54.0	579.1					1.169
–52.0	629.6					1.162
–50.0	683.4					1.155
–48.0	740.6					1.147
–46.0	801.3					1.139
–44.0	865.6					1.131
–42.0	933.8					1.124
–40.0	1005.7					1.116
–38.0	1081.6					1.108
–36.0	1161.8					1.100
–34.0	1246.2					1.092
–32.0	1335.1					1.084
-30.0	1428.6					1.075
–28.89	1521	–55.69	237.1	292.9	0.03846	1.0306	–9.48	43.41
–27.78	1575	–53.76	237.3	291.0	0.03987	1.0276	–9.13	43.21
–26.67	1630	–51.84	237.6	289.4	0.04133	1.0242	–8.78	43.01
–25.56	1686	–49.87	237.6	287.5	0.04283	1.0209	–8.45	42.78
–24.44	1744	–47.91	237.8	285.7	0.04440	1.0170	–8.10	42.56
–23.33	1804	–45.94	237.8	283.6	0.04600	1.0132	–7.75	42.36
–22.22	1866	–43.93	237.8	281.7	0.04767	1.0093	–7.40	42.14
–21.11	1928	–41.92	237.8	279.6	0.04938	1.0053	–7.05	42.94
–20.00	1993	–39.91	237.8	277.8	0.05116	1.0011	–6.68	41.71
–18.89	2059	–37.86	237.8	275.7	0.05300	0.9968	–6.31	41.49
–17.78	2114	–35.82	237.6	273.6	0.05489	0.9923	–5.98	41.27
–16.67	2197	–33.73	237.6	271.2	0.05686	0.9875	–5.61	41.05
–15.56	2269	–31.64	237.3	269.2	0.05888	0.9829	–5.26	40.83
–14.44	2343	–29.54	237.3	266.9	0.06098	0.9782	–4.91	40.61
–13.33	2418	–27.41	237.1	264.5	0.06314	0.9734	–4.54	40.39
–12.22	2495	–25.27	236.9	262.2	0.06539	0.9665	–4.17	40.15
–11.11	2574	–23.09	236.7	259.7	0.06771	0.9639	–3.80	39.92
–10.00	2654	–20.90	236.4	257.3	0.07011	0.9592	–3.43	39.68
–8.89	2738	–18.69	235.9	254.8	0.07259	0.9543	–3.06	39.46
–7.78	2823	–16.45	235.7	252.2	0.07516	0.9494	–2.69	39.22
–6.67	2910	–14.18	235.2	249.4	0.07783	0.9443	–2.32	38.98
–5.56	2999	–11.90	234.8	246.6	0.08059	0.9393	–1.94	38.74
–4.44	3090	–9.977	234.3	243.8	0.08347	0.9340	–1.57	38.50
–3.89	3136	–8.410	234.1	242.4	0.08494	0.9313	–1.37	38.37
–2.78	3230	–6.046	233.6	239.7	0.08797	0.9260	–0.98	38.12
–1.67	3327	–3.648	232.9	236.6	0.09111	0.9206	–0.59	37.88
–0.56	3425	–1.222	232.4	233.6	0.09438	0.9150	–0.20	37.62
0.56	3526	1.234	231.7	230.5	0.09776	0.9094	0.20	37.36
1.67	3629	3.728	231.0	227.3	0.1013	0.9036	0.61	37.08
2.78	3735	6.268	230.4	224.0	0.1050	0.8975	1.01	36.83
3.89	3981	8.445	229.4	220.5	0.1088	0.8914	1.42	36.55
5.00	3953	11.46	228.5	217.0	0.1128	0.8850	1.83	36.25
6.11	4067	14.13	227.6	213.4	0.1169	0.8784	2.25	35.98
7.22	4182	16.85	226.5	209.7	0.1213	0.8716	2.69	35.68
8.33	4300	19.63	225.4	205.8	0.1258	0.8645	3.12	35.39
9.44	4420	22.46	224.3	201.8	0.1306	0.8571	3.56	35.07
10.56	4544	25.36	223.1	197.7	0.1355	0.8496	4.02	34.76
11.67	4670	28.33	221.8	193.4	0.1408	0.8418	4.48	34.45
12.78	4798	31.35	220.3	188.9	0.1463	0.8338	4.94	34.11
13.89	4929	34.49	218.8	184.3	0.1521	0.8254	5.42	33.76
15.00	5063	37.30	217.2	179.5	0.1583	0.8168	5.92	33.41
16.11	5200	41.03	215.1	174.4	0.1648	0.8076	6.42	33.02
17.22	5340	44.48	213.6	169.1	0.1717	0.7977	6.96	32.66
18.33	5482	48.03	211.5	163.5	0.1791	0.7871	7.49	32.25
19.44	5628	51.71	209.4	157.6	0.1869	0.7759	8.04	31.83
20.56	5776	55.61	207.0	151.4	0.1956	0.7639	8.63	31.38
21.67	5928	59.66	204.3	144.7	0.2054	0.7508	9.24	30.90
22.78	6083	63.97	201.5	137.5	0.2151	0.7367	9.89	30.39
23.89	6240	68.58	198.4	129.8	0.2263	0.7216	10.57	29.85
25.00	6401	73.51	194.8	121.3	0.2387	0.7058	11.31	29.24
26.11	6565	78.91	190.7	111.8	0.2532	0.6894	12.10	28.60
27.22	6733	84.94	186.0	101.1	0.2707	0.6720	12.99	27.84
28.33	6902	91.88	180.4	88.49	0.2923	0.6507	14.00	26.95
29.44	7081	100.4	173.1	72.72	0.3204	0.6209	15.24	25.85
30.00	7164	105.6	168.4	62.76	0.3378	0.5992	16.01	25.15
30.56	7253	112.3	162.3	50.04	0.3581	0.5661	16.99	24.24
31.1	7391			0.00	0.4641	0.4641
Temp. °C	Pvap Vapor pressure kPa	Hliq Heat content liquid J/gr	Hvap Heat content vapor J/gr	ΔvapHo Heat of vapor- ization J/gr	ρvap Density of vapor gr/cm3	ρliq Density of liquid gr/cm3	Sliq Entropy liquid J/mol-°C	Svap Entropy vapor J/mol-°C

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from [Surface tension]]

Water Strider Physics

The photograph shows water striders standing on the surface of a pond. It is clearly visible that their feet cause indentations in the water's surface. It is intuitively evident that the surface with indentations has more surface area than a flat surface. If surface tension tends to minimize surface area, how is it that the water striders are increasing the surface area?

Recall that what nature really tries to minimize is potential energy. By increasing the surface area of the water, the water striders have increased the potential energy of that surface. But note also that the water striders' center of mass is lower than it would be if they were standing on a flat surface. So their potential energy is decreased. Indeed when you combine the two effects, the net potential energy is minimized. If the water striders depressed the surface any more, the increased surface energy would more than cancel the reduction in the decreased energy of lowering the insects' center of mass. If they depressed the surface any less, their higher center of mass would more than cancel the reduction in surface energy.

The photo of the water striders also illustrates the notion of surface tension being like having an elastic film over the surface of the liquid. In the surface depressions at their feet it is easy to see that the reaction of that imagined elastic film is exactly countering the weight of the insects.

Liquid in a Cylindrical Tube

Diagram of a Mercury Barometer

An old style mercury barometer consists of a vertical glass tube about 1 cm in diameter partially filled with mercury, and with a vacuum in the unfilled volume (see diagram to the left). Notice that the mercury level at the center of the tube is higher than at the at the edges, making the upper surface of the mercury dome-shaped. The center of mass of the entire column of mercury would be slightly lower if the top surface of the mercury were flat over the entire crossection of the tube. But the dome-shaped top gives slightly less surface area to the entire mass of mercury. Again the two effects combine to minimize the total potential energy. Such a surface shape is known as a convex meniscus.

The reason we consider the surface area of the entire mass of mercury, including the part of the surface that is in contact with the glass is because mercury does not adhere at all to glass. So the surface tension of the mercury acts over its entire surface area, including where it is in contact with the glass. If instead of glass, the tube were made out of copper, the situation would be very different. Mercury aggressively adheres to copper. So in a copper tube, the level of mercury at the center of the tube will be lower rather than higher than at the edges (that is, it would be a concave meniscus). In a situation where the liquid adheres to the walls of its container, we consider the part of the fluid's surface area that is in contact with the container to have negative surface tension. The fluid then works to maximize the contact surface area. So in this case increasing the area in contact with the container decreases rather than increases the potential energy. That decrease is enough compensate for the increase potential energy associated with the lifting of the fluid near the walls of the container.

Pool of Liquid on a Nonadhesive Surface

Pouring mercury onto a horizontal flat sheet of glass results in a puddle that has a perceptible thickness (do not try this except under a fume hood. Mercury vapor is a toxic hazard). The puddle will only spread out only to the point where it is a little under a centimeter thick, and no thinner. Again this is the action of mercury's strong surface tension. The liquid mass flattens out because that brings as much of the mercury to as low a level as possible. But the surface tension, at the same time, is acting to reduce the total surface area. The result is the compromise of a puddle of a nearly fixed thickness.

The same surface tension demonstration can be done with water, but only on a surface made of a substance that the water does not adhere to. Candle wax is such a substance. Water poured onto a smooth, flat, horizontal wax surface will behave similarly to the mercury poured onto glass.

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end of surface tension material

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Descriptive chemistry (lead)

Various oxidized forms of lead are easily reduced to the metal. An example is heating PbO with mild organic reducing agents such as glucose. A mixuture of the oxide and the sulfide heated together without any reducing agent will also form the metal.

2PbO + PbS   →   3 Pb + SO₂

Metallic lead is attacked only superficially by air, forming a thin layer of oxide that protects it from further oxidation. The metal is not attacked by sulfuric or hydrochloric acids. It does, however, dissovle in nitric acid with the evolution of nitric oxide gas to form dissolved Pb(NO₃)₂.

3 Pb + 8 H⁺ + 8 NO₃^–   →   3 Pb²⁺ + 6 NO₃^– + 2 NO + 4H₂O

When heated with nitrates of alkali metals, metallic lead oxidizes to form PbO (also known as litharge), leaving the corresponding alkali nitrite. PbO is representative of lead's II oxidation state. It is soluble in nitric and acetic acids, from which solutions it is possible to preciptate halide, sulfate, and basic carbonate salts of lead. The sulfide can also be precipitated from acetate solutions. These salts are all poorly soluble in water. Among the halides, the iodide is less soluble than the bromide, which, in turn, is less soluble than the chloride.

The II oxide is also soluble in alkali hydroxide solutions to form the corresponding plumbite salt.

PbO + 2OH^– + H₂O   →   Pb(OH)₄^2–

Chlorination of plumbite solutions causes the formation of lead's IV oxidation state. Lead dioxide is representative of the IV state, and is a powerful oxidizing agent. The chloride of this oxidation state is formed only with difficulty and decomposes readily into the II chloride and chlorine gas. The bromide and iodide of IV lead are not known to exist. Lead dioxide dissolves in alkali hydroxide solutions to form the corresponding plumbates.

PbO₂ + 2 OH^– + 2 H₂O   →   Pb(OH)₆^2–

Rewrite Project

for calcium carbonate water solubility section:

Original version

Calcium carbonate is not rigorously insoluble in water. For the following equilibrium reaction

• CaC0₃(solid) ↔ Ca²⁺ + CO₃²⁻, we take a solubility product $\scriptstyle K_{sp}=[Ca^{2+}][CO_{3}^{2-}]=4.47\times 10^{-9}$ at 25°C (K_sp=3.8 x 10⁻⁹ is given in

Considering a saturated pure CaCO₃ solution, the calculation of the Ca²⁺ concentration must take into account the equilibria between the three different carbonate forms (H₂CO₃, HCO₃⁻ and CO₃²⁻) as well as the equilibrium between H₂CO₃ and the dissolved CO₂ and the equilibrium between the dissolved CO₂ and the gaseous CO₂ above the solution. The reactions involved are the following (see carbonic acid):

• CO₂(gas) ↔ CO₂(dissolved) with $\scriptstyle {\frac {[CO_{2}]}{p_{CO_{2}}}}={\frac {1}{k'_{c}}}$ where k'_c=29.76 atm/(mol/L) at 25°C (Henry constant), $\scriptstyle p_{CO_{2}}$ being the CO₂ partial pressure.

• CO₂(dissolved) + H₂O ↔ H₂CO₃ with $\scriptstyle K_{h}={\frac {[H_{2}CO_{3}]}{[CO_{2}]}}=1.70\times 10^{-3}$ at 25°C

• H₂CO₃ ↔ H⁺ + HCO₃⁻ with $\scriptstyle K_{a1}={\frac {[H^{+}][HCO_{3}^{-}]}{[H_{2}CO_{3}]}}=2.5\times 10^{-4}$ at 25°C

• HCO₃⁻ ↔ H⁺ + CO₃²⁻ with $\scriptstyle K_{a2}={\frac {[H^{+}][CO_{3}^{2-}]}{[HCO_{3}^{-}]}}=5.61\times 10^{-11}$ at 25°C

The above relations (together with the $\scriptstyle [H^{+}][OH^{-}]=10^{-14}$ relation and the neutrality condition $\scriptstyle 2[Ca^{2+}]+[H^{+}]=[HCO_{3}^{-}]+2[CO_{3}^{2-}]+[OH^{-}]$, i.e. 7 equations for 7 unknowns) allow the numerical calculation of the pH and of the Ca²⁺ concentration as a function of $\scriptstyle p_{CO_{2}}$. The result is given in the table below:

$\scriptstyle p_{CO_{2}}$ (atm)	pH	[Ca2+] (mol/L)
10−12	12.0	5.19 x 10−3
10−10	11.3	1.12 x 10−3
10−8	10.7	2.55 x 10−4
10−6	9.83	1.20 x 10−4
10−4	8.62	3.16 x 10−4
3.5 x 10−4	8.27	4.70 x 10−4
10−3	7.96	6.62 x 10−4
10−2	7.30	1.42 x 10−3
10−1	6.63	3.05 x 10−3
1	5.96	6.58 x 10−3
10	5.30	1.42 x 10−2

We see that for normal atmospheric conditions ($\scriptstyle p_{CO_{2}}=3.5\times 10^{-4}$ atm), we get a slightly basic solution (pH = 8.3) with a low Ca²⁺ concentration (4.7 x 10⁻⁴ mol/L i.e. 0.019 g/L of Ca). Increasing the CO₂ pressure makes the solution slightly acid with a better Ca solubility (0.57 g/L of Ca at 10 atm). For decreasing CO₂ pressure values, the solubility goes to a minimum for $\scriptstyle p_{CO_{2}}=10^{-6}$ atm and then increases again as the solution gets strongly basic.

Remark: For $\scriptstyle p_{CO_{2}}$ > 10⁻⁴ atm, CO₃²⁻, H⁺ and OH⁻ concentrations can be neglected in the neutrality condition. This means physically that we have essentially a calcium bicarbonate solution. In this case, the system can be solved analytically, giving (with a very good precision)

$\scriptstyle [H^{+}]\simeq \left({\frac {K_{a1}^{2}K_{a2}K_{h}^{2}}{2K_{sp}k_{c}^{\prime 2}}}\right)^{1/3}p_{CO_{2}}^{2/3}\;\;\;,\;\;\;[Ca^{2+}]\simeq \left({\frac {K_{a1}K_{sp}K_{h}}{4K_{a2}k_{c}^{\prime }}}\right)^{1/3}p_{CO_{2}}^{1/3}$

Current state of rewritten version

Calcium carbonate is poorly soluble in water. The equilibrium of its solution is given by the equation (with dissolved calcium carbonate on the right):

CaCO3 ⇋ Ca2+ + CO32–

Ksp = 3.7×10–9 to 8.7×10–9 at 25 °C

where the solubility product for [Ca²⁺][CO₃^2–] is given as anywhere from K_sp = 3.7×10^–9 to K_sp = 8.7×10^–9 at 25 °C, depending upon the data source. What the equation means is that the product of number of moles of dissolved Ca²⁺ with the number of moles of dissolved CO₃^2– cannot exceed the value of K_sp. This seemingly simple solubility equation, however, must be taken along with the more complicated equilibrium of carbon dioxide with water. Some of the CO₃^2– combines with H⁺ in the solution according to:

HCO3– ⇋ H+ + CO32–

Ka2 = 5.61×10–11 at 25 °C

HCO₃^– is known as the bicarbonate ion. Calcium bicarbonate is many times more soluble in water than calcium carbonate -- indeed it exists only in solution.

Some of the HCO₃^– combines with H⁺ in solution according to:

H2CO3 ⇋ H+ + HCO3–

Ka1 = 2.5×10–4 at 25 °C

Some of the H₂CO₃ breaks up into water and dissolved carbon dioxide according to:

H2O + CO2(dissolved) ⇋ H2CO3

Kh = 1.70×10–3 at 25 °C

And dissolved carbon dioxide is in equilibrium with atmospheric carbon dioxide according to:

${\frac {P_{\mathrm {CO} _{2}}}{[\mathrm {CO} _{2}]}}\ =\ k'_{c}$

where k'c = 29.76 atm/(mol/L) at 25°C (Henry constant), $\scriptstyle P_{\mathrm {CO} _{2}}$ being the CO2 partial pressure.

Calcium Ion Solubility as a function of CO2 partial pressure
$\scriptstyle P_{\mathrm {CO} _{2}}$ (atm)	pH	[Ca2+] (mol/L)
10−12	12.0	5.19 × 10−3
10−10	11.3	1.12 × 10−3
10−8	10.7	2.55 × 10−4
10−6	9.83	1.20 × 10−4
10−4	8.62	3.16 × 10−4
3.5 × 10−4	8.27	4.70 × 10−4
10−3	7.96	6.62 × 10−4
10−2	7.30	1.42 × 10−3
10−1	6.63	3.05 × 10−3
1	5.96	6.58 × 10−3
10	5.30	1.42 × 10−2

For ambient air, $\scriptstyle P_{\mathrm {CO} _{2}}$ is around 3.5×10^–4 atmospheres (or equivalently 35 Pa). The last equation above fixes the concentration of dissolved CO₂ as a function of $\scriptstyle P_{\mathrm {CO} _{2}}$, independent of the concentration of dissolved CaCO₃. At atmospheric partial pressure of CO₂, dissolved CO₂ concentration is 1.2×10^–5 moles/liter. The equation before that fixes the concentration of H₂CO₃ as a function of [CO₂]. For [CO₂]=1.2×10^–5, it results in [H₂CO₃]=2.0×10^–8 moles per liter. When [H₂CO₃] is known, the remaining three equations together with

H2O ⇋ H+ + OH–

K = 10–14 at 25 °C

(which is true for all aqueous solutions), and the fact that the solution must be electrically neutral,

2[Ca²⁺] + [H⁺] = [HCO₃^–] + 2[CO₃^2–] + [OH^–]

make it possible to solve simultaneously for the remaining five unknown concentrations. The table on the right shows the solution for [Ca²⁺] and [H⁺] (in the form of pH) as a function of ambient partial pressure of CO₂. At atmopheric levels of ambient CO₂ the table indicates the solution will be slightly alkaline. The trends the table shows are

1) As ambient CO₂ partial pressure is reduced below atmospheric levels, the solution becomes more and more alkaline. At extremly low $\scriptstyle P_{\mathrm {CO} _{2}}$, dissolved CO₂, bicarbonate ion, and carbonate ion largely evaporate from the solution, leaving a highly alkaline solution of calcium hydroxide, which is more soluble than CaCO₃.

2) As ambient CO₂ partial pressure increases to levels above atmospheric, pH drops, and much of the carbonate ion is converted to bicarbonate ion, which results in higher solubility of Ca²⁺.

The effect of the latter is especially evident in day to day life of people who have hard water. Water in aquifers underground can be exposed to levels of CO₂ much higher than atmospheric. As such water perculates through calcium carbonate rock, the CaCO₃ dissolves according to the second trend. When that same water then water emerges from the tap, in time it comes into equilibrium with CO₂ levels in the air by outgassing its excess CO₂. The calcium carbonate becomes less soluble as a result and the excess precipitates as lime scale. This same process is responsible for the formation of stalactites and stalagmites in limestone caves.

Liquid/Vapor Equilibrium Data

Vapor over Anhydrous Ammonia
Temp.	Pressure	ρ of liquid	ρ of vapor	ΔvapH
–78 °C	5.90 kPa
–75 °C	7.93 kPa	0.73094 g/cm3	7.8241×10–5 g/cm3
–70 °C	10.92 kPa	0.72527 g/cm3	1.1141×10–4 g/cm3
–65 °C	15.61 kPa	0.71953 g/cm3	1.5552×10–4 g/cm3
–60 °C	21.90 kPa	0.71378 g/cm3	2.1321×10–4 g/cm3
–55 °C	30.16 kPa	0.70791 g/cm3	2.8596×10–4 g/cm3
–50 °C	40.87 kPa	0.70200 g/cm3	3.8158×10–4 g/cm3	1417 J/g
–45 °C	54.54 kPa	0.69604 g/cm3	4.9940×10–4 g/cm3	1404 J/g
–40 °C	71.77 kPa	0.68999 g/cm3	6.4508×10–4 g/cm3	1390 J/g
–35 °C	93.19 kPa	0.68385 g/cm3	8.2318×10–4 g/cm3	1375 J/g
–30 °C	119.6 kPa	0.67764 g/cm3	1.0386×10–3 g/cm3	1361 J/g
–25 °C	151.6 kPa	0.67137 g/cm3	1.2969×10–3 g/cm3	1345 J/g
–20 °C	190.2 kPa	0.66503 g/cm3	1.6039×10–3 g/cm3	1330 J/g
–15 °C	236.3 kPa	0.65854 g/cm3	1.9659×10–3 g/cm3	1314 J/g
–10 °C	290.8 kPa	0.65198 g/cm3	2.3874×10–3 g/cm3	1297 J/g
–5 °C	354.8 kPa	0.64533 g/cm3	2.8827×10–3 g/cm3	1280 J/g
0 °C	429.4 kPa	0.63857 g/cm3	3.4528×10–3 g/cm3	1263 J/g
5 °C	515.7 kPa	0.63167 g/cm3	4.1086×10–3 g/cm3	1245 J/g
10 °C	614.9 kPa	0.62469 g/cm3	4.8593×10–3 g/cm3	1226 J/g
15 °C	728.3 kPa	0.61755 g/cm3	5.7153×10–3 g/cm3	1207 J/g
20 °C	857.1 kPa	0.61028 g/cm3	6.6876×10–3 g/cm3	1187 J/g
25 °C	1003 kPa	0.60285 g/cm3	7.7882×10–3 g/cm3	1167 J/g
30 °C	1166 kPa	0.59524 g/cm3	9.0310×10–3 g/cm3	1146 J/g
35 °C	1350 kPa	0.58816 g/cm3	1.0431×10–2 g/cm3	1124 J/g
40 °C	1554 kPa	0.57948 g/cm3	1.2006×10–2 g/cm3	1101 J/g
45 °C	1781 kPa	0.57130 g/cm3	1.3775×10–2 g/cm3	1083 J/g
50 °C	2032 kPa	0.56287 g/cm3	1.5761×10–2 g/cm3	1052 J/g
55 °C	2310 kPa	0.55420 g/cm3
60 °C	2613 kPa	0.54523 g/cm3	2.05×10–2 g/cm3
65 °C	2947 kPa	0.53596 g/cm3
70 °C	3312 kPa	0.52632 g/cm3	2.65×10–2 g/cm3
75 °C	3711 kPa	0.51626 g/cm3
80 °C	4144 kPa	0.50571 g/cm3	3.41×10–2 g/cm3
85 °C	4614 kPa	0.49463 g/cm3
90 °C	5123 kPa	0.48290 g/cm3	4.39×10–2 g/cm3
95 °C	5672 kPa	0.47041 g/cm3
100 °C	6264 kPa	0.45693 g/cm3	5.68×10–2 g/cm3

The table above gives properties of the vapor/liquid equilibrium of anhydrous ammonia at various temperatures. The second column is vapor pressure in kPa. The third column is the density of the liquid phase. The fourth column is the density of the vapor. The fifth column is the heat of vaporization needed to convert one gram of liquid to vapor.

Equilibrium of vapor over aqueous solution

Vapor over Aqueous Ammonia Solution
Temp.	%wt NH3	Partial Pressure NH3	Partial Pressure H2O
0 °C	4.72	1.52 kPa	0.68 kPa
	9.15	3.31 kPa	0.71 kPa
	14.73	6.84 kPa	0.55 kPa
	19.62	11.0 kPa	0.40 kPa
	22.90	14.9 kPa	0.37 kPa
10 °C	4.16	2.20 kPa	1.21 kPa
	8.26	4.96 kPa	1.17 kPa
	12.32	8.56 kPa	1.01 kPa
	15.88	12.68 kPa	0.93 kPa
	20.54	19.89 kPa	0.83 kPa
	21.83	22.64 kPa	0.73 kPa
19.9 °C	4.18	3.65 kPa	2.19 kPa
	6.50	6.11 kPa	2.15 kPa
	6.55	6.13 kPa	2.13 kPa
	7.72	7.49 kPa	2.08 kPa
	10.15	10.75 kPa	2.01 kPa
	10.75	11.51 kPa	1.96 kPa
	16.64	22.14 kPa	1.72 kPa
	19.40	28.74 kPa	1.64 kPa
	23.37	40.32 kPa	1.37 kPa
30.09 °C	3.93	5.49 kPa	4.15 kPa
	7.43	11.51 kPa	3.89 kPa
	9.75	16.00 kPa	3.80 kPa
	12.77	23.33 kPa	3.55 kPa
	17.76	38.69 kPa	3.31 kPa
	17.84	38.81 kPa	3.24 kPa
	21.47	53.94 kPa	2.95 kPa
40 °C	3.79	8.15 kPa	7.13 kPa
	7.36	17.73 kPa	6.76 kPa
	11.06	29.13 kPa	6.55 kPa
	15.55	47.14 kPa	5.52 kPa
	17.33	57.02 kPa
	20.85	76.81 kPa	5.04 kPa
50 °C	3.29	10.54 kPa	11.95 kPa
	5.90	20.17 kPa	11.61 kPa
	8.91	32.88 kPa	11.07 kPa
	11.57	45.56 kPa	10.75 kPa
	14.15	60.18 kPa	10.27 kPa
	14.94	64.94 kPa	10.03 kPa
60 °C	3.86	18.25 kPa	19.21 kPa
	5.77	28.78 kPa
	7.78	40.05 kPa	18.47 kPa
	9.37	50.09 kPa	18.07 kPa
	9.37	63.43 kPa	17.39 kPa

---

Hebrew Calendar

Summary of Calendar Calculations

The audience for this section is computer programmers who wish to write software that accurately computes dates in the Hebrew calendar. The following details are sufficient to generate such software.

1) The Hebrew calendar is computed by lunations. One lunation is reckoned at 29 days, 12 hours, 44 minutes, 3⅓ seconds, or equivalently 765433 halakim = 29 days, 13753 halakim.

2) A common year must be either 353, 354, or 355 days; a leap year must be 383, 384, or 385 days. A 353 or 383 day year is called kesidrah. A 354 or 384 day year is shelemah. A 355 or 385 day year is haserah.

3) Leap years follow a 19 year schedule in which years 3, 6, 8, 11, 14, 17, and 19 are leap years. The Jewish year 5752 (which starts in Gregorian year 1991) is the first year of a cycle.

4) 19 years is the same as 235 lunations.

5) The months are Tishri, Heshvan, Kislev, Tebeth, Shebhat, Adar, Nisan, Iyyar, Sivan, Tammuz, Av, and Elul. In addition, a second Adar (also called Veadar, Adar II, or Adar Sheni) is added in leap years. When added, it follows Adar.

6) Each month has either 29 or 30 days. A 30 day month is male, a 29 day month is haser.

Nisan, Sivan, Av, Tishri, and Shebhat are always male.

Iyyar, Tammuz, Elul, Tebeth, and Adar II are always haser.

Adar is male in leap years, haser in common years.

Heshvan and Kislev vary, but when they differ, Heshvan is haser and Kislev is male.

7) Tishri 1st (Rosh Hashana) is the day of a molad (new moon) unless certain conditions (dahiyyah sing; dahiyyot pl) exist.

a) This dahiyyah exists whenever Tishri 10 (Yom Kippur) would fall on a Friday or a Sunday, or if Tishri 21 (7th day of Sukkot) would fall on a Saturday. This is equivalent to the molad being on Sunday, Wednesday, or Friday. Whenever this happens, Tishri 1 is delayed by 1 day.

b) This dahiyyah exists whenever the molad occurs on or after noon. When this dahiyyah exists, Tishri 1 is delayed by 1 day. If this causes dahiyyah A to exist, Tishri 1 is delayed an additional day.

c) If the year is to be a common year and the molad falls on a Tuesday on or after 3:11:20 am (3 hours 204 halakim) Jerusalem time, Tishri 1 is delayed by 2 days. This is because if it weren't delayed, the resulting year would be 356 days long.

d) If the new year follows a leap year and the molad is on a Monday on or after 9:32:43 and one third seconds (9 hours 589 halakim), Tishri 1 is delayed 1 day. This is because if it weren't, the preceding year would have only 382 days.

8) Delays are implemented by adding a day to Kislev of the preceding year, making it male. If Kislev is already male, the day is added to Heshvan of the preceding year, making it male also. If a delay of 2 days is called for, both Heshvan and Kislev of the preceding year become male.

9) The molad of 08-Sep-1991, which is Rosh Hashana of Hebrew yer, 5752, is Julian day, 2448509 plus 3294 halakim.

Future Project: Tide Prediction

Plan to explain the method of harmonic constituents as detailed in U.S. Govt. Special Publication 92.

Reorganize Heat Capacity Ratio Table

Heat Capacity Ratio for various gases
Temp.	Gas	γ		Temp.	Gas	γ		Temp.	Gas	γ
–181°C	H2	1.597		–76°C	H2	1.453		20°C	H2	1.41
100°C	H2	1.404		400°C	H2	1.387		1000°C	H2	1.358
2000°C	H2	1.318		20°C	He	1.66		20°C	H2O	1.33
100°C	H2O	1.324		200°C	H2O	1.310		–180°C	Ar	1.76
20°C	Ar	1.67		0°C	Dry Air	1.403		20°C	Dry Air	1.40
100°C	Dry Air	1.401		200°C	Dry Air	1.398		400°C	Dry Air	1.393
1000°C	Dry Air	1.365		1400°C	Dry Air	1.341		2000°C	Dry Air	1.088
0°C	CO2	1.310		20°C	CO2	1.30		100°C	CO2	1.281
400°C	CO2	1.235		1000°C	CO2	1.195		20°C	CO	1.40
–181°C	O2	1.45		–76°C	O2	1.415		20°C	O2	1.40
100°C	O2	1.399		200°C	O2	1.397		400°C	O2	1.394
20°C	NO	1.40		20°C	N2O	1.31		–181°C	N2	1.47
15°C	N2	1.404		20°C	Cl2	1.34		–115°C	CH4	1.41
–74°C	CH4	1.35		20°C	CH4	1.32		19°C	Ne	1.64
19°C	Kr	1.68		19°C	Xe	1.66		15°C	SO2	1.29
360°C	Hg	1.67

Heat Capacity Ratio for various gases
Temp.	Gas	γ		Temp.	Gas	γ		Temp.	Gas	γ
–181°C	H2	1.597		200°C	Dry Air	1.398		20°C	NO	1.40
–76°C		1.453		400°C		1.393		20°C	N2O	1.31
20°C		1.41		1000°C		1.365		–181°C	N2	1.47
100°C		1.404		2000°C		1.088		15°C		1.404
400°C		1.387		0°C	CO2	1.310		20°C	Cl2	1.34
1000°C		1.358		20°C		1.30		–115°C	CH4	1.41
2000°C		1.318		100°C		1.281		–74°C		1.35
20°C	He	1.66		400°C		1.235		20°C		1.32
20°C	H2O	1.33		1000°C		1.195		15°C	NH3	1.310
100°C		1.324		20°C	CO	1.40		19°C	Ne	1.64
200°C		1.310		–181°C	O2	1.45		19°C	Xe	1.66
–180°C	Ar	1.76		–76°C		1.415		19°C	Kr	1.68
20°C		1.67		20°C		1.40		15°C	SO2	1.29
0°C	Dry Air	1.403		100°C		1.399		360°C	Hg	1.67
20°C		1.40		200°C		1.397		15°C	C2H6	1.22
100°C		1.401		400°C		1.394		16°C	C3H8	1.13

---

Translating Water (data page) equivalent from German

Physical and Thermodynamic Tables

In the following tables, values are temperature dependent and to a lesser degree pressure dependent, and are arranged by state of aggregation (s=solid, lq=liquid, g=gas), which are clearly a function of temperature and pressure. All of the data were computed from data given in "Formulation of the Thermodynamic Properties of Ordinary Water Substance for Scientific and General Use" (1984). This applies to:

• T - temperature in degrees celsius
• V - specific volume in decimeter³ per kilogram
• H - specific enthalpy in kJ per kilogram
• U - internal energy in kJ per kilogram
• S - specific entropy in kJ per kilogram-Kelvin
• c_p - specific (constant pressure) heat capacity in kJ per kilogram-Kelvin
• γ - Thermal expansion coefficient as 10^–3 per Kelvin
• λ - Heat conductivity in milliwatt per meter-Kelvin
• η - Viscosity in μPa-seconds
• σ - Surface Tension millinewtons per meter

Standard conditions

In the following table, material data is given for standard pressure of 0.1 MPa (equivalent to 1 bar). Up to 99.63 °C (the boiling point of water), at this pressure water exists as a liquid. Above that, it exists as water vapor.

 

Water/Steam Data Table at Standard Pressure (0.1 MPa)
T °C		V dm³/kg	H kJ/kg	U kJ/kg	S kJ/(kg·K)	cp kJ/(kg·K)	γ 10–3/K	λ mW / (m·K)	η μPa·s	σ1 mN/m
0	lq	1.0002	0.06	-0.04	-0.0001	4.228	-0.080	561.0	1792	75.65
5		1.0000	21.1	21.0	0.076	4.200	0.011	570.6	1518	74.95
10		1.0003	42.1	42.0	0.151	4.188	0.087	580.0	1306	74.22
15		1.0009	63.0	62.9	0.224	4.184	0.152	589.4	1137	73.49
20		1.0018	83.9	83.8	0.296	4.183	0.209	598.4	1001	72.74
25		1.0029	104.8	104.7	0.367	4.183	0.259	607.2	890.4	71.98
30		1.0044	125.8	125.7	0.437	4.183	0.305	615.5	797.7	71.20
35		1.0060	146.7	146.6	0.505	4.183	0.347	623.3	719.6	70.41
40		1.0079	167.6	167.5	0.572	4.182	0.386	630.6	653.3	69.60
45		1.0099	188.5	188.4	0.638	4.182	0.423	637.3	596.3	68.78
50		1.0121	209.4	209.3	0.704	4.181	0.457	643.6	547.1	67.95
60		1.0171	251.2	251.1	0.831	4.183	0.522	654.4	466.6	66.24
70		1.0227	293.1	293.0	0.955	4.187	0.583	663.1	404.1	64.49
80		1.0290	335.0	334.9	1.075	4.194	0.640	670.0	354.5	62.68
90		1.0359	377.0	376.9	1.193	4.204	0.696	675.3	314.6	60.82
99.63	lq	1.0431	417.5	417.4	1.303	4.217	0.748	679.0	283.0	58.99
	g	1694.3	2675	2505	7.359	2.043	2.885	25.05	12.26	–
100	g	1696.1	2675	2506	7.361	2.042	2.881	25.08	12.27	58.92
200		2172.3	2874	2657	7.833	1.975	2.100	33.28	16.18	37.68
300		2638.8	3073	2810	8.215	2.013	1.761	43.42	20.29	14.37
500		3565.5	3488	3131	8.834	2.135	1.297	66.970	28.57	–
750		4721.0	4043	3571	9.455	2.308	0.978	100.30	38.48	–
1000		5875.5	4642	4054	9.978	2.478	0.786	136.3	47.66	–
1 The values for surface tension for the liquid section of the table are for a liquid/air interface. Values for the gas section of the table are for a liquid/saturated steam interface.

Triple Point

In the following table, material data is given with a pressure of 0.0006117 MPa (equivalent to 0.006117 bar). Up to a temperature of 0.01 °C, the triple point of water, water normally exists as ice, except for supercooled water, for which one data point is tabulated here. At the triple point ice can exist together with both liquid water and vapor. At higher temperatures the data is for water vapor only.

 

Water/Steam Data Table at Triple Point Pressure (0.0006117 MPa)
T °C		V dm³/kg	H kJ/kg	U kJ/kg	S kJ/(kg·K)	cp kJ/(kg·K)	γ 10–3/K	λ mW / (m·K)	η μPa·s
0	lq	1.0002	–0.04	–0.04	–0.0002	4.339	–0.081	561.0	1792
0.1	s	1.0908	–333.4	–333.4	–1.221	1.93	0.1	2.2	–
	lq	1.0002	0.0	0	0	4.229	–0.080	561.0	1791
	g	205986	2500	2374	9.154	1.868	3.672	17.07	9.22
5	g	209913	2509	2381	9.188	1.867	3.605	17.33	9.34
10		213695	2519	2388	9.222	1.867	3.540	17.60	9.46
15		217477	2528	2395	9.254	1.868	3.478	17.88	9.59
20		221258	2537	2402	9.286	1.868	3.417	18.17	9.73
25		225039	2547	2409	9.318	1.869	3.359	18.47	9.87
30		228819	2556	2416	9.349	1.869	3.304	18.78	10.02
35		232598	2565	2423	9.380	1.870	3.249	19.10	10.17
40		236377	2575	2430	9.410	1.871	3.197	19.43	10.32
45		240155	2584	2437	9.439	1.872	3.147	19.77	10.47
50		243933	2593	2444	9.469	1.874	3.098	20.11	10.63
60		251489	2612	2459	9.526	1.876	3.004	20.82	10.96
70		259043	2631	2473	9.581	1.880	2.916	21.56	11.29
80		266597	2650	2487	9.635	1.883	2.833	22.31	11.64
90		274150	2669	2501	9.688	1.887	2.755	23.10	11.99
100		281703	2688	2515	9.739	1.891	2.681	23.90	12.53
200		357216	2879	2661	10.194	1.940	2.114	32.89	16.21
300		432721	3076	2811	10.571	2.000	1.745	43.26	20.30
500		583725	3489	3132	11.188	2.131	1.293	66.90	28.57
750		772477	4043	3571	11.808	2.307	0.977	100.20	38.47
1000		961227	4642	4054	12.331	2.478	0.785	136.30	47.66

Saturated Vapor Pressure

The following table is based on different, complementary sources and approximation formulas, whose values are of various quality and accuracy. The values in the temperature range of –100 °C to 100 °C were inferred from D. Sunday (1982) and are quite uniform and exact. The values in the temperature range of the boiling point of the water up to the critical point (100 °C to 374 °C), are drawn from different sources and are substantially less accurate, hence they should be understood and used also only as approximate values.

To use the values corrctly, consider the following points:

• The values apply only to smooth interfaces and in the absence other gases or gas mixtures such as air. Hence they apply only to pure phases and need a correction factor for systems in which air is present.
• The values were not computed according formulas widely used in the US, but using somewhat more exact formulas (see below), which can also also be used to compute further values in the appropriate temperature ranges.
• The saturated steam pressure over water in the temperature range of –100 °C to –50 °C is only extrapolated.
• The values have various units (Pa, hPa or bar), which must be considered when reading them.

Formulas

The table values for –100 °C to 100 °C were computed by the following formulas, where T is in Kelvins and vapor pressures, P_w and P_i are in Pa.

Over Liquid Water

log_e(P_w)  =  –6094.4642 T^–1 + 21.1249952 – 2.724552×10^–2 T + 1.6853396×10^–5 T² + 2.4575506 log_e(T)

For Temperature Range: 173.15 K to 373.15 K or equivalently –100 °C to 100 °C

Over Ice

log_e(P_i)  =  –5504.4088 T^–1 – 3.5704628 – 1.7337458×10^–2 T + 6.5204209×10^–6 T² + 6.1295027 log_e(T)

For temperature range: 173.15 K to 273.15 K or equivalently –100 °C to 0 °C

Triple point

An important basic value, which is not registered in the table, is the saturated vapor pressure at the triple point of water. The internationally accepted value according to measurements of Guildner, Johnson and Jones (1976) amounts to:

P_w(t_tp  =  0.01 °C)  =  611.657 Pa ± 0.010 Pa at (1-α)  =  99%

 

Values of Saturated Vapor Pressure of Water
Temp. t in °C	Pi(t) over ice in Pa	Pw(t) over water in Pa	Temp. t in °C	Pw(t) over water in hPa	Temp. t in °C	P(t) in bar	Temp. t in °C	P(t) in bar	Temp. t in °C	P(t) in bar
-100	0.0013957	0.0036309	0	6.11213	100	1.01	200	15.55	300	85.88
-99	0.0017094	0.0044121	1	6.57069	101	1.05	201	15.88	301	87.09
-98	0.0020889	0.0053487	2	7.05949	102	1.09	202	16.21	302	88.32
-97	0.002547	0.0064692	3	7.58023	103	1.13	203	16.55	303	89.57
-96	0.0030987	0.0078067	4	8.13467	104	1.17	204	16.89	304	90.82
-95	0.0037617	0.0093996	5	8.72469	105	1.21	205	17.24	305	92.09
-94	0.0045569	0.011293	6	9.35222	106	1.25	206	17.60	306	93.38
-93	0.0055087	0.013538	7	10.0193	107	1.30	207	17.96	307	94.67
-92	0.0066455	0.016195	8	10.728	108	1.34	208	18.32	308	95.98
-91	0.0080008	0.019333	9	11.4806	109	1.39	209	18.70	309	97.31
-90	0.0096132	0.023031	10	12.2794	110	1.43	210	19.07	310	98.65
-89	0.011528	0.027381	11	13.1267	111	1.48	211	19.46	311	100
-88	0.013797	0.032489	12	14.0251	112	1.53	212	19.85	312	101.37
-87	0.016482	0.038474	13	14.9772	113	1.58	213	20.25	313	102.75
-86	0.019653	0.045473	14	15.9856	114	1.64	214	20.65	314	104.15
-85	0.02339	0.053645	15	17.0532	115	1.69	215	21.06	315	105.56
-84	0.027788	0.063166	16	18.1829	116	1.75	216	21.47	316	106.98
-83	0.032954	0.074241	17	19.3778	117	1.81	217	21.89	317	108.43
-82	0.039011	0.087101	18	20.6409	118	1.86	218	22.32	318	109.88
-81	0.046102	0.10201	19	21.9757	119	1.93	219	22.75	319	111.35
-80	0.054388	0.11925	20	23.3854	120	1.99	220	23.19	320	112.84
-79	0.064057	0.13918	21	24.8737	121	2.05	221	23.64	321	114.34
-78	0.07532	0.16215	22	26.4442	122	2.12	222	24.09	322	115.86
-77	0.088419	0.1886	23	28.1006	123	2.18	223	24.55	323	117.39
-76	0.10363	0.21901	24	29.847	124	2.25	224	25.02	324	118.94
-75	0.12127	0.25391	25	31.6874	125	2.32	225	25.49	325	120.51
-74	0.14168	0.29390	26	33.6260	126	2.4	226	25.98	326	122.09
-73	0.16528	0.33966	27	35.6671	127	2.47	227	26.46	327	123.68
-72	0.19252	0.39193	28	37.8154	128	2.55	228	26.96	328	125.30
-71	0.22391	0.45156	29	40.0754	129	2.62	229	27.46	329	126.93
-70	0.26004	0.51948	30	42.452	130	2.7	230	27.97	330	128.58
-69	0.30156	0.59672	31	44.9502	131	2.78	231	28.48	331	130.24
-68	0.34921	0.68446	32	47.5752	132	2.87	232	29.01	332	131.92
-67	0.40383	0.78397	33	50.3322	133	2.95	233	29.54	333	133.62
-66	0.46633	0.89668	34	53.2267	134	3.04	234	30.08	334	135.33
-65	0.53778	1.0242	35	56.2645	135	3.13	235	30.62	335	137.07
-64	0.61933	1.1682	36	59.4513	136	3.22	236	31.18	336	138.82
-63	0.71231	1.3306	37	62.7933	137	3.32	237	31.74	337	140.59
-62	0.81817	1.5136	38	66.2956	138	3.42	238	32.31	338	142.37
-61	0.93854	1.71950	39	69.9675	139	3.51	239	32.88	339	144.18
-60	1.0753	1.9509	40	73.8127	140	3.62	240	33.47	340	146.00
-59	1.2303	2.2106	41	77.8319	141	3.72	241	34.06	341	147.84
-58	1.4060	2.5018	42	82.0536	142	3.82	242	34.66	342	149.71
-57	1.6049	2.8277	43	86.4633	143	3.93	243	35.27	343	151.58
-56	1.8296	3.1922	44	91.0757	144	4.04	244	35.88	344	153.48
-55	2.0833	3.5993	45	95.8984	145	4.16	245	36.51	345	155.40
-54	2.3694	4.0535	46	100.939	146	4.27	246	37.14	346	157.34
-53	2.6917	4.5597	47	106.206	147	4.39	247	37.78	347	159.30
-52	3.0542	5.1231	48	111.708	148	4.51	248	38.43	348	161.28
-51	3.4618	5.7496	49	117.452	149	4.64	249	39.09	349	163.27
-50	3.9193	6.4454	50	123.4478	150	4.76	250	39.76	350	165.29
-49	4.4324	7.2174	51	129.7042	151	4.89	251	40.44	351	167.33
-48	5.0073	8.0729	52	136.2304	152	5.02	252	41.12	352	169.39
-47	5.6506	9.0201	53	143.0357	153	5.16	253	41.81	353	171.47
-46	6.3699	10.068	54	150.1298	154	5.29	254	42.52	354	173.58
-45	7.1732	11.225	55	157.5226	155	5.43	255	43.23	355	175.70
-44	8.0695	12.503	56	165.2243	156	5.58	256	43.95	356	177.85
-43	9.0685	13.911	57	173.2451	157	5.72	257	44.68	357	180.02
-42	10.181	15.463	58	181.5959	158	5.87	258	45.42	358	182.21
-41	11.419	17.17	59	190.2874	159	6.03	259	46.16	359	184.43
-40	12.794	19.048	60	199.3309	160	6.18	260	46.92	360	186.66
-39	14.321	21.11	61	208.7378	161	6.34	261	47.69	361	188.93
-38	16.016	23.372	62	218.5198	162	6.50	262	48.46	362	191.21
-37	17.893	25.853	63	228.6888	163	6.67	263	49.25	363	193.52
-36	19.973	28.57	64	239.2572	164	6.84	264	50.05	364	195.86
-35	22.273	31.544	65	250.2373	165	7.01	265	50.85	365	198.22
-34	24.816	34.795	66	261.6421	166	7.18	266	51.67	366	200.61
-33	27.624	38.347	67	273.4845	167	7.36	267	52.49	367	203.02
-32	30.723	42.225	68	285.7781	168	7.55	268	53.33	368	205.47
-31	34.140	46.453	69	298.5363	169	7.73	269	54.17	369	207.93
-30	37.903	51.060	70	311.7731	170	7.92	270	55.03	370	210.43
-29	42.046	56.077	71	325.5029	171	8.11	271	55.89	371	212.96
-28	46.601	61.534	72	339.7401	172	8.31	272	56.77	372	215.53
-27	51.607	67.466	73	354.4995	173	8.51	273	57.66	373	218.13
-26	57.104	73.909	74	369.7963	174	8.72	274	58.56	374	220.64
-25	63.134	80.902	75	385.6459	175	8.92	275	59.46	374.15	221.20
-24	69.745	88.485	76	402.0641	176	9.14	276	60.38
-23	76.987	96.701	77	419.0669	177	9.35	277	61.31
-22	84.914	105.60	78	436.6708	178	9.57	278	62.25
-21	93.584	115.22	79	454.8923	179	9.80	279	63.20
-20	103.06	125.63	80	473.7485	180	10.03	280	64.17
-19	113.41	136.88	81	493.2567	181	10.26	281	65.14
-18	124.70	149.01	82	513.4345	182	10.50	282	66.12
-17	137.02	162.11	83	534.3000	183	10.74	283	67.12
-16	150.44	176.23	84	555.8714	184	10.98	284	68.13
-15	165.06	191.44	85	578.1673	185	11.23	285	69.15
-14	180.97	207.81	86	601.2068	186	11.49	286	70.18
-13	198.27	225.43	87	625.009	187	11.75	287	71.22
-12	217.07	244.37	88	649.5936	188	12.01	288	72.27
-11	237.49	264.72	89	674.9806	189	12.28	289	73.34
-10	259.66	286.57	90	701.1904	190	12.55	290	74.42
-9	283.69	310.02	91	728.2434	191	12.83	291	75.51
-8	309.75	335.16	92	756.1608	192	13.11	292	76.61
-7	337.97	362.10	93	784.9639	193	13.40	293	77.72
-6	368.52	390.95	94	814.6743	194	13.69	294	78.85
-5	401.58	421.84	95	845.3141	195	13.99	295	79.99
-4	437.31	454.88	96	876.9057	196	14.29	296	81.14
-3	475.92	490.19	97	909.4718	197	14.60	297	82.31
-2	517.62	527.93	98	943.0355	198	14.91	298	83.48
-1	562.62	568.22	99	977.6203	199	15.22	299	84.67
0	611.153	611.213	100	1013.25	200	15.55	300	85.88
Temp. t in °C	Pi(t) over ice in Pa	Pw(t) over water in Pa	Temp. t in °C	Pw(t) over water in hPa	Temp. t in °C	P(t) in bar	Temp. t in °C	P(t) in bar	Temp. t in °C	P(t) in barbar

Material is copied in from

Drucktabellen

Die in der folgenden Tabelle dargestellten Größen sind temperatur- und teilweise auch druckabhängig, richten sich aber in jedem Fall nach dem Aggregatzustand des Wassers (hier s = fest; l = flüssig; g = gasförmig). Dieser wird durch Druck und Temperatur eindeutig bestimmt. Alle Daten wurden Grigull et. al. (1990) entnommen, welche sie nach der Vorgabe durch die "Formulation of the Thermodynamic Properties of Ordinary Water Substance for Scientific and General Use" (1984) der IAPWS mit einer verringerten Iterationsschranke berechneten. Es handelt sich um:

• $\vartheta$ - die Celsius-Temperatur in Grad Celsius
• v – das spezifische Volumen in Kubikdezimeter je Kilogramm
• h – die spezifische Enthalpie in Kilojoule je Kilogramm
• u – die spezifische Innere Energie in Kilojoule je Kilogramm
• s – die spezifische Entropie in Kilojoule je Kilogramm mal Kelvin
• c_p - die spezifische Wärmekapazität bei konstantem Druck in Kilojoule je Kilogramm mal Kelvin
• γ – Volumenausdehnungskoeffzient in 10^-3 durch Kelvin
• λ – Wärmeleitfähigkeit in Milliwatt je Meter mal Kelvin
• η – Viskosität in Mikropascal mal Sekunde
• σ – Oberflächenspannung in Millinewton je Meter

Standardbedingungen

In der folgenden Tabelle handelt es sich um die Stoffdaten bei Standarddruck (SATP), also 0,1 Megapascal (entspricht einem bar). Bis zu einer Temperatur von 99,63 °C, dem Siedepunkt des Wasser bei diesem Druck, liegt das Wasser als Flüssigkeit vor, darüber als Wasserdampf.

$\vartheta$ °C		v dm³/kg	h kJ/kg	u kJ/kg	s kJ/(kg·K)	cp kJ/(kg·K)	γ 10-3/K	λ mW / (m·K)	η μPa·s	σ1 mN/m
0		1,0002	0,06	-0,04	-0,0001	4,228	-0,080	561,0	1792	75,65
5		1,0000	21,1	21,0	0,076	4,200	0,011	570,6	1518	74,95
10		1,0003	42,1	42,0	0,151	4,188	0,087	580,0	1306	74,22
15		1,0009	63,0	62,9	0,224	4,184	0,152	589,4	1137	73,49
20		1,0018	83,9	83,8	0,296	4,183	0,209	598,4	1001	72,74
25		1,0029	104,8	104,7	0,367	4,183	0,259	607,2	890,4	71,98
30		1,0044	125,8	125,7	0,437	4,183	0,305	615,5	797,7	71,20
35		1,0060	146,7	146,6	0,505	4,183	0,347	623,3	719,6	70,41
40		1,0079	167,6	167,5	0,572	4,182	0,386	630,6	653,3	69,60
45		1,0099	188,5	188,4	0,638	4,182	0,423	637,3	596,3	68,78
50		1,0121	209,4	209,3	0,704	4,181	0,457	643,6	547,1	67,95
60		1,0171	251,2	251,1	0,831	4,183	0,522	654,4	466,6	66,24
70		1,0227	293,1	293,0	0,955	4,187	0,583	663,1	404,1	64,49
80		1,0290	335,0	334,9	1,075	4,194	0,640	670,0	354,5	62,68
90		1,0359	377,0	376,9	1,193	4,204	0,696	675,3	314,6	60,82
99,63	l	1,0431	417,5	417,4	1,303	4,217	0,748	679,0	283,0	58,99
	g	1694,3	2675	2505	7,359	2,043	2,885	25,05	12,26	–
100		1696,1	2675	2506	7,361	2,042	2,881	25,08	12,27	58,92
200		2172,3	2874	2657	7,833	1,975	2,100	33,28	16,18	37,68
300		2638,8	3073	2810	8,215	2,013	1,761	43,42	20,29	14,37
500		3565,5	3488	3131	8,834	2,135	1,297	66,970	28,57	–
750		4721,0	4043	3571	9,455	2,308	0,978	100,30	38,48	–
1000		5875,5	4642	4054	9,978	2,478	0,786	136,3	47,66	–
1 Die Werte der Oberflächenspannung gelten nicht für den Normaldruck, sondern für den zur jeweiligen Temperatur gehörigen Sättigungsdampfdruck.

Tripelpunkt

In der folgenden Tabelle handelt es sich um die Stoffdaten bei einem Druck von 0,0006117 Megapascal (entspricht 0,006117 bar). Bis zu einer Temperatur von 0,01 °C, dem Tripelpunkt des Wassers, liegt das Wasser normalerweise als Eis vor, wurde jedoch hier für unterkühltes Wasser tabelliert. Am Tripelpunkt selbst kann es sowohl als Eis als auch Flüssigkeit oder Wasserdampf vorliegen, bei höheren Temperaturen handelt es sich jedoch wiederum um Wasserdampf.

$\vartheta$ °C		v dm³/kg	h kJ/kg	u kJ/kg	s kJ/(kg·K)	cp kJ/(kg·K)	γ 10-3/K	λ mW / (m·K)	η μPa·s	σ1 mN/m
0		1,0002	-0,04	-0,04	-0,0002	4,339	-0,081	561,0	1792	–
0,1	s	1,0908	-333,4	-333,4	-1,221	1,93	0,1	2,2	–	–
	l	1,0002	0,0	0	0	4,229	-0,080	561,0	1791	–
	g	205986	2500	2374	9,154	1,868	3,672	17,07	9,22	–
5		209913	2509	2381	9,188	1,867	3,605	17,33	9,34	–
10		213695	2519	2388	9,222	1,867	3,540	17,60	9,46	–
15		217477	2528	2395	9,254	1,868	3,478	17,88	9,59	–
20		221258	2537	2402	9,286	1,868	3,417	18,17	9,73	–
25		225039	2547	2409	9,318	1,869	3,359	18,47	9,87	–
30		228819	2556	2416	9,349	1,869	3,304	18,78	10,02	–
35		232598	2565	2423	9,380	1,870	3,249	19,10	10,17	–
40		236377	2575	2430	9,410	1,871	3,197	19,43	10,32	–
45		240155	2584	2437	9,439	1,872	3,147	19,77	10,47	–
50		243933	2593	2444	9,469	1,874	3,098	20,11	10,63	–
60		251489	2612	2459	9,526	1,876	3,004	20,82	10,96	–
70		259043	2631	2473	9,581	1,880	2,916	21,56	11,29	–
80		266597	2650	2487	9,635	1,883	2,833	22,31	11,64	–
90		274150	2669	2501	9,688	1,887	2,755	23,10	11,99	–
100		281703	2688	2515	9,739	1,891	2,681	23,90	12,53	–
200		357216	2879	2661	10,194	1,940	2,114	32,89	16,21	–
300		432721	3076	2811	10,571	2,000	1,745	43,26	20,30	–
500		583725	3489	3132	11,188	2,131	1,293	66,90	28,57	–
750		772477	4043	3571	11,808	2,307	0,977	100,20	38,47	–
1000		961227	4642	4054	12,331	2,478	0,785	136,30	47,66	–
1 Die Werte der Oberflächenspannung sind hier identisch zur ersten Tabelle, wobei in gleicherweise der Sättigungsdampfdruck angewendet werden muss.

Sättigungsdampfdruck

Folgende Tabelle basiert auf verschiedenen, sich gegenseitig ergänzenden Quellen bzw. Näherungsformeln, was jedoch auch nach sich zieht, dass die Werte von unterschiedlicher Güte und Genauigkeit sind. Die Werte des Temperaturbereichs von -100 °C bis 100 °C wurden aus D. Sonntag (1982) entnommen und sind daher recht einheitlich und genau, wenn auch nicht auf dem neuesten Stand. Die Werte des Temperaturbereichs vom Siedepunkt des Wassers bis zum kritischen Punkt, also von 100 °C bis 374 °C, stammen jedoch aus unterschiedlichen Quellen und sind daher wesentlich ungenauer, folglich sollten sie auch nur als Orientierungswerte verstanden und genutzt werden.

Zur richtigen Nutzung der Werte sind folgende Punkte zu beachten:

• Die Werte gelten nur für ebene Oberflächen und in der Abwesenheit anderer Gase bzw. Gasgemische wie Luft. Sie gelten also lediglich für reine Phasen und benötigen einen Korrekturfaktor bei der Anwesenheit von Luft.
• Die Werte wurden nicht nach der Magnus-Formel berechnet, sondern nach etwas genaueren Formeln (siehe unten), mit deren Hilfe sich auch weitere Werte in den entsprechenden Temperaturintervallen berechnen lassen.
• Die Sättigungsdampfdrücke über Wasser im Temperaturintervall von -100 °C bis -50 °C wurden lediglich extrapoliert.
• Die Werte haben unterschiedliche Einheiten (Pa, hPa oder bar), was es beim ablesen zu beachten gilt.

Formeln

Berechnet wurden die Tabellenwerte von -100 °C bis 100 °C durch folgende Formeln:

Über Wasser:

$E_{w}(T)=\exp \left(-6094{,}4642\cdot T^{-1}+21{,}1249952-2{,}724552\cdot 10^{-2}\cdot T+1{,}6853396\cdot 10^{-5}\cdot T^{2}+2{,}4575506\cdot \ln T\right)$

Temperaturintervall:

$173{,}15\ \mathrm {K} \leq T\leq 373{,}15\ \mathrm {K}$, entspricht $-100\,^{\circ }\mathrm {C} \leq t\leq 100\,^{\circ }\mathrm {C}$

Über Eis:

$E_{i}(T)=\exp \left(-5504{,}4088\cdot T^{-1}-3{,}5704628-1{,}7337458\cdot 10^{-2}\cdot T+6{,}5204209\cdot 10^{-6}\cdot T^{2}+6{,}1295027\cdot \ln T\right)$

Temperaturintervall:

$173{,}15\ \mathrm {K} \leq T\leq 273{,}15\ \mathrm {K}$, entspricht $-100\,^{\circ }\mathrm {C} \leq t\leq 0\,^{\circ }\mathrm {C}$

Werden die Temperaturen in Kelvin eingesetzt, so ergibt sich der jeweilige Sättigungsdampfdruck E(T) in Pa.

Tripelpunkt

Ein wichtiger Grundwert, der nicht in die Tabelle eingetragen wurde, ist der Sättigungsdampfdruck beim Tripelpunkt des Wassers. Der international akzeptierte Bestwert nach Messungen von Guildner, Johnson und Jones (1976) beträgt:

$E_{w}(t_{tr}=0{,}01\,^{\circ }\mathrm {C} )=611{,}657\ \mathrm {Pa} \ \pm 0{,}010\ \mathrm {Pa} \ \mathrm {bei} \ (1-\alpha )=99\mathrm {\%}$

Tabelle

Beispielwerte des Sättigungsdampfdrucks von Wasser

Temperatur t in °C	$E_{i}$(t) über Eis p in Pa	$E_{w}$(t) über Wasser p in Pa	Temperatur t in °C	E(t) über Wasser p in hPa	Temperatur t in °C	E(t) p in bar	Temperatur t in °C	E(t) p in bar	Temperatur t in °C	E(t) p in bar
-100	0,0013957	0,0036309	0	6,11213	100	1,01	200	15,55	300	85,88
-99	0,0017094	0,0044121	1	6,57069	101	1,05	201	15,88	301	87,09
-98	0,0020889	0,0053487	2	7,05949	102	1,09	202	16,21	302	88,32
-97	0,002547	0,0064692	3	7,58023	103	1,13	203	16,55	303	89,57
-96	0,0030987	0,0078067	4	8,13467	104	1,17	204	16,89	304	90,82
-95	0,0037617	0,0093996	5	8,72469	105	1,21	205	17,24	305	92,09
-94	0,0045569	0,011293	6	9,35222	106	1,25	206	17,6	306	93,38
-93	0,0055087	0,013538	7	10,0193	107	1,3	207	17,96	307	94,67
-92	0,0066455	0,016195	8	10,728	108	1,34	208	18,32	308	95,98
-91	0,0080008	0,019333	9	11,4806	109	1,39	209	18,7	309	97,31
-90	0,0096132	0,023031	10	12,2794	110	1,43	210	19,07	310	98,65
-89	0,011528	0,027381	11	13,1267	111	1,48	211	19,46	311	100
-88	0,013797	0,032489	12	14,0251	112	1,53	212	19,85	312	101,37
-87	0,016482	0,038474	13	14,9772	113	1,58	213	20,25	313	102,75
-86	0,019653	0,045473	14	15,9856	114	1,64	214	20,65	314	104,15
-85	0,02339	0,053645	15	17,0532	115	1,69	215	21,06	315	105,56
-84	0,027788	0,063166	16	18,1829	116	1,75	216	21,47	316	106,98
-83	0,032954	0,074241	17	19,3778	117	1,81	217	21,89	317	108,43
-82	0,039011	0,087101	18	20,6409	118	1,86	218	22,32	318	109,88
-81	0,046102	0,10201	19	21,9757	119	1,93	219	22,75	319	111,35
-80	0,054388	0,11925	20	23,3854	120	1,99	220	23,19	320	112,84
-79	0,064057	0,13918	21	24,8737	121	2,05	221	23,64	321	114,34
-78	0,07532	0,16215	22	26,4442	122	2,12	222	24,09	322	115,86
-77	0,088419	0,1886	23	28,1006	123	2,18	223	24,55	323	117,39
-76	0,10363	0,21901	24	29,847	124	2,25	224	25,02	324	118,94
-75	0,12127	0,25391	25	31,6874	125	2,32	225	25,49	325	120,51
-74	0,14168	0,2939	26	33,626	126	2,4	226	25,98	326	122,09
-73	0,16528	0,33966	27	35,6671	127	2,47	227	26,46	327	123,68
-72	0,19252	0,39193	28	37,8154	128	2,55	228	26,96	328	125,3
-71	0,22391	0,45156	29	40,0754	129	2,62	229	27,46	329	126,93
-70	0,26004	0,51948	30	42,452	130	2,7	230	27,97	330	128,58
-69	0,30156	0,59672	31	44,9502	131	2,78	231	28,48	331	130,24
-68	0,34921	0,68446	32	47,5752	132	2,87	232	29,01	332	131,92
-67	0,40383	0,78397	33	50,3322	133	2,95	233	29,54	333	133,62
-66	0,46633	0,89668	34	53,2267	134	3,04	234	30,08	334	135,33
-65	0,53778	1,0242	35	56,2645	135	3,13	235	30,62	335	137,07
-64	0,61933	1,1682	36	59,4513	136	3,22	236	31,18	336	138,82
-63	0,71231	1,3306	37	62,7933	137	3,32	237	31,74	337	140,59
-62	0,81817	1,5136	38	66,2956	138	3,42	238	32,31	338	142,37
-61	0,93854	1,7195	39	69,9675	139	3,51	239	32,88	339	144,18
-60	1,0753	1,9509	40	73,8127	140	3,62	240	33,47	340	146
-59	1,2303	2,2106	41	77,8319	141	3,72	241	34,06	341	147,84
-58	1,406	2,5018	42	82,0536	142	3,82	242	34,66	342	149,71
-57	1,6049	2,8277	43	86,4633	143	3,93	243	35,27	343	151,58
-56	1,8296	3,1922	44	91,0757	144	4,04	244	35,88	344	153,48
-55	2,0833	3,5993	45	95,8984	145	4,16	245	36,51	345	155,4
-54	2,3694	4,0535	46	100,939	146	4,27	246	37,14	346	157,34
-53	2,6917	4,5597	47	106,206	147	4,39	247	37,78	347	159,3
-52	3,0542	5,1231	48	111,708	148	4,51	248	38,43	348	161,28
-51	3,4618	5,7496	49	117,452	149	4,64	249	39,09	349	163,27
-50	3,9193	6,4454	50	123,4478	150	4,76	250	39,76	350	165,29
-49	4,4324	7,2174	51	129,7042	151	4,89	251	40,44	351	167,33
-48	5,0073	8,0729	52	136,2304	152	5,02	252	41,12	352	169,39
-47	5,6506	9,0201	53	143,0357	153	5,16	253	41,81	353	171,47
-46	6,3699	10,068	54	150,1298	154	5,29	254	42,52	354	173,58
-45	7,1732	11,225	55	157,5226	155	5,43	255	43,23	355	175,7
-44	8,0695	12,503	56	165,2243	156	5,58	256	43,95	356	177,85
-43	9,0685	13,911	57	173,2451	157	5,72	257	44,68	357	180,02
-42	10,181	15,463	58	181,5959	158	5,87	258	45,42	358	182,21
-41	11,419	17,17	59	190,2874	159	6,03	259	46,16	359	184,43
-40	12,794	19,048	60	199,3309	160	6,18	260	46,92	360	186,66
-39	14,321	21,11	61	208,7378	161	6,34	261	47,69	361	188,93
-38	16,016	23,372	62	218,5198	162	6,5	262	48,46	362	191,21
-37	17,893	25,853	63	228,6888	163	6,67	263	49,25	363	193,52
-36	19,973	28,57	64	239,2572	164	6,84	264	50,05	364	195,86
-35	22,273	31,544	65	250,2373	165	7,01	265	50,85	365	198,22
-34	24,816	34,795	66	261,6421	166	7,18	266	51,67	366	200,61
-33	27,624	38,347	67	273,4845	167	7,36	267	52,49	367	203,02
-32	30,723	42,225	68	285,7781	168	7,55	268	53,33	368	205,47
-31	34,14	46,453	69	298,5363	169	7,73	269	54,17	369	207,93
-30	37,903	51,06	70	311,7731	170	7,92	270	55,03	370	210,43
-29	42,046	56,077	71	325,5029	171	8,11	271	55,89	371	212,96
-28	46,601	61,534	72	339,7401	172	8,31	272	56,77	372	215,53
-27	51,607	67,466	73	354,4995	173	8,51	273	57,66	373	218,13
-26	57,104	73,909	74	369,7963	174	8,72	274	58,56	374	220,64
-25	63,134	80,902	75	385,6459	175	8,92	275	59,46	374,15	221,2
-24	69,745	88,485	76	402,0641	176	9,14	276	60,38
-23	76,987	96,701	77	419,0669	177	9,35	277	61,31
-22	84,914	105,6	78	436,6708	178	9,57	278	62,25
-21	93,584	115,22	79	454,8923	179	9,8	279	63,2
-20	103,06	125,63	80	473,7485	180	10,03	280	64,17
-19	113,41	136,88	81	493,2567	181	10,26	281	65,14
-18	124,7	149,01	82	513,4345	182	10,5	282	66,12
-17	137,02	162,11	83	534,3	183	10,74	283	67,12
-16	150,44	176,23	84	555,8714	184	10,98	284	68,13
-15	165,06	191,44	85	578,1673	185	11,23	285	69,15
-14	180,97	207,81	86	601,2068	186	11,49	286	70,18
-13	198,27	225,43	87	625,009	187	11,75	287	71,22
-12	217,07	244,37	88	649,5936	188	12,01	288	72,27
-11	237,49	264,72	89	674,9806	189	12,28	289	73,34
-10	259,66	286,57	90	701,1904	190	12,55	290	74,42
-9	283,69	310,02	91	728,2434	191	12,83	291	75,51
-8	309,75	335,16	92	756,1608	192	13,11	292	76,61
-7	337,97	362,1	93	784,9639	193	13,4	293	77,72
-6	368,52	390,95	94	814,6743	194	13,69	294	78,85
-5	401,58	421,84	95	845,3141	195	13,99	295	79,99
-4	437,31	454,88	96	876,9057	196	14,29	296	81,14
-3	475,92	490,19	97	909,4718	197	14,6	297	82,31
-2	517,62	527,93	98	943,0355	198	14,91	298	83,48
-1	562,62	568,22	99	977,6203	199	15,22	299	84,67
0	611,153	611,213	100	1013,25	200	15,55	300	85,88

Literatur

• L.A. Guildner, D.P. Johnson und F.E. Jones (1976): Vapor pressure of Water at Its Triple Point. J. Res. NBS - A, Vol. 80A, No. 3, p. 505 - 521
• Klaus Scheffler (1981): Wasserdampftafeln: thermodynam. Eigenschaften von Wasser u. Wasserdampf bis 800°C u. 800 bar (Water Vapor Tables: Thermodynamic Characteristics of Water and Water Vapor to 800°C and 800 bar), Berlin [u.a.] ISBN 3540109307
• D. Sonntag und D. Heinze (1982): Sättigungsdampfdruck- und Sättigungsdampfdichtetafeln für Wasser und Eis. (Saturated Vapor Pressure and Saturated Vapor Density Tables for Water and Ice)(1. Aufl.), VEB Deutscher Verlag für Grundstoffindustrie
• Ulrich Grigull, Johannes Staub, Peter Schiebener (1990): Steam Tables in SI-Units - Wasserdampftafeln. Springer-Verlagdima gmbh

---

Original draft of Frederick Jacobi article

Frederick Jacobi (born May 4,1891 in San Francisco, California; died October 24, 1952 in New York City of heart failure) was a prolific American composer, whose works include symphonies, concerti, chamber music, works for solo piano and for solo organ, lieder, and one opera. Besides composing, his career included teaching at Juilliard School of Music and serving as the director of the American section of the International Society for Contemporary Music.

Early life

Frederick Jacobi was the son of San Francisco wholesale wine merchant, Frederick Jacobi Sr. and Flora Brandenstein, whom Frederick Sr. had married in 1875. During the composer's childhood years, he demonstrated his musical talent, composing short pieces at the piano and playing tunes from contemporary musical comedies by ear. In these years the family traveled each summer to visit relatives in New York City. The scenery of those cross-country train rides later provided the themes of a number of his nature-inspired compositions.

Musical Training and Career

When Frederick Sr. died in 1911, Frederick Jr. inherited the estate, which provided him enough wealth that he could devote his entire livelihood to music. In his twenties Jacobi studied music and composition under such masters as Isidore Philipp of the Paris Conservatory, Ernest Bloch and Rubin Goldmark in New York, and Paul Juon in Berlin.

In 1917, while working as a vocal coach and assistant conductor at the Metropolitan Opera, he met and married Irene Schwarcz, who, at the time, was studying piano at the New York Institute of Musical Art (which later became Juilliard). Irene would go on to become an accomplished concert pianist, and played piano parts in many performances and recordings of Jacobi's works.

Jacobi enlisted in the army shortly after marrying Irene, where he served as a saxaphone player in the Alcatraz Army Band. He was discharged in 1919, at which time he moved to New York to be in closer contact with the American composers of the time. For the remainder of his life he published and performed new works nearly every year -- sometimes several in the same year (see compositions section). Major American orchestras such as the New York Philharmonic, the Philadelphia Orchestra, and the Boston, Chicago, and San Francisco symphonies performed Jacobi's orchestral compositions during the years of his life.

In works from what has become known as Jacobi's Indian period (late 1920's and early 1930's), he incorporated rhythms and other elements from indigenous Native American music he had heard in his travels through the American southwest. Indeed he spent the winter of 1927 with the Navajo and Pueblo of New Mexico studying their music.

In 1942-1944 Jacobi collaborated with playwright and librettist, Herman Voaden, to produce the opera, The Prodigal Son, which debuted at the American Opera Society of Chicago in May of 1945.

Jacobi is also known as a composer of works with Judaic themes. His interest in this genre began with a 1930 commission from Temple Emanu-El of New York for a sabbath evening service. This soon led to other works with biblical titles that explored the musical traditions of Judaism. Although little of Jacobi's secular work is performed today, his liturgical works continue to enjoy performaces in synagogues.

Jacobi's work largely rejects the polytonality and atonality that was popular with the avante-garde composers of his time. Instead he finds his influence in the classical and romantic periods. New York Times critic Olin Downes described the aesthetics of Jacobi's music as "not so much of the 20th as of the 19th century."

Frederick Jacobi quotes on musical composition

"I am a great believer in melody; a believer, too, that music should give pleasure and not try to solve philosophical problems."

"The surest way to kill whatever originality one possesses within himself is to try to be original!"

Links

• Milken Archive: American Jewish Music
• Frederick Jacobi and Herman Voaden: The Prodigal Son
• Hear audio sample of Frederick Jacobi's work

Compositions

• 1915 The Pied Piper, Symphonic Poem

• 1916 Three Songs to Poems by Sarojini Naidu (“The Faery Isle of Janjira,” “Love and Death,” “In the Night,” for high voice and piano)

• 1917 A California Suite (for orchestra)

• 1918 Nocturne, for string quartet

• 1918 Psalmody (piano vocal score)

• 1920 Three Songs, for high voice with piano (words by Sarojini Naidu; “Palanquin-Bearers,” “In a Time of Flowers,” “From a Latticed Balcony”)

• 1920 The Eve of Saint Agnes (25 min. Symphonic prelude after the poem of John Keats)

• 1921 Three Preludes for Violin and Piano

• 1921 Morning and Evening at Blue Hill (for two violins and string orchestra with piano)

• 1921 A Festival Prelude (for orchestra)

• 1922 Symphony No. 1 (Subtitled Assyrian, 22 min.)

• 1922 Three Songs to Poems by Chaucer (for voice and piano) “Roundel” and “Ballade” published as Two Poems by Geoffrey Chaucer

• 1923 Two Assyrian Prayers (piano vocal score)

• 1923 Two Assyrian Prayers (Soprano or Tenor and chamber orchestra, 12 min. French text by Rebecca Godchaux. “To Ishtar” and “To Bel-Marduk”)

• 1924 Three Preludes for Violin, with orchestral accompaniment

• 1924 String Quartet (Based) on (American) Indian Themes (18 min.)

• 1925 The Poet in the Desert (after the poem by C.E.S. Wood, for orchestra, chorus and baritone solo)

• 1926 Nocturne (for flute and small orchestra; 5 min.) Rewritten second movement of Symphony No. 1, 1922)

• 1926 Marsyas (for violin and piano)

• 1927-28 Indian Dances/Danses Indiennes/Indianische Tänze (16 ½ min.) ( Buffalo Dance, Butterfly Dance, War Dance, Corn Dance; Suite for Orchestra)

• 1930-31 Sabbath Evening Service According to the Union Prayer Book (Friday Evening Service, baritone solo/cantor, mixed chorus, a capella; 20 min.)

• 1932 Concerto (Three Psalms) for Cello and Orchestra (16 min.) Reduction for Piano and Cello,

• 1933 String Quartet No. 2 (23 min.)

• 1933 Six Pieces for the Organ for Use in the Synagogue. One piece published as Prelude.

• 1933 Three Preludes for Organ.

• 1934-35 Concerto for Piano and Orchestra (26 min.)

• 1934 Piano Pieces for Children (includes A Lovely Little Movie Actress, Once Upon a Time, A Charming Prince, There Was a Wicked Fairy and Six Caprices) A Lovely Little Movie Actress and Once Upon a Time published separately.

• 1936 Scherzo for Flute, Oboe, Clarinet, Bassoon and Horn (5 min.) (Scherzo for Wind Instruments)

• 1936-37 Concerto for Violin and Orchestra (16 min.)

• 1937 Cadenza to Mozart’s Rondo for Piano and Orchestra (Kochel No. 386)

• 1937 Swing Boy (violin and piano)

• 1938 Hagiographa: Three Biblical Narratives for String Quartet and Piano (26 min.)

• 1938 Preludes on Traditional Melodies

• 1939 Ave Rota: (Hail to the Wheel [of Fortune]) Three Pieces in Multiple Style for Small Orchestra and Piano (“The Swing” [“La Balançoire”], “The Merman” and “May-Dance;” written for the Juilliard Alumni). (14 min. The same for large orchestra and piano)

• 1939 Dunam Po (“A Dunam Here”) Palestinian folk song arrangement published in Hans Nathan, ed. Folk Songs of the New Palestine.

• 194? Variations on a Theme by Moussorgsky (for cello and piano)

• 1940 Shemesh (based on a Palestinian Folk Song) Cello and Piano

• 1940 Rhapsody for Harp and String Orchestra (8 min.)

• 1941 Fantasy for Viola and Piano (9 min.)

• 1941 Ode for Orchestra (12 min.)

• 1941 Cadenza for Mozart’s Concerto for Piano and Orchestra in C Minor (Kochel No. 491)

• 1941 Night Piece for Flute and Small Orchestra (5 min.) (Rewritten Nocturne in Niniveh, 1926)

• 1941 Night Piece and Dance, for flute and piano.

• 1942 Ballade for Violin and Piano (11 min.)

• 1942 Hymn for Men’s Chorus (text by Saadia Gaon; 5 min.)

• 1942 From the Prophet Nehemiah: Three Excerpts for Voice and Two Pianos (5, 4 and 6 minutes respectively)

• 1942-44 The Prodigal Son: Opera in Three Acts based on Four Early American Prints. Text by Herman Voaden. (Full orchestra, 2 ½ hours). [Act I of first version inscribed “ July 18, 1943, Riverdale, N.Y.”; Act II “ Nov. 17, 1943” and Act III “ Sept. 9, 1944”]

• 1943 Penelope (arrangement for viola and piano from the 1921 Vocalises.)

• 1944 Dances From The Prodigal Son Arranged for Two Pianos, Four Hands (10 min.) [polka, polonaise, waltz, tarantella]

• 1944 Night Piece for Flute, Oboe, Clarinet, String Quintet and Piano

• 1944 Music for Monticello (Trio for Flute, Cello and Piano, 20 min.)

• 1945 String Quartet No. 3 (26 min.)

• 1945 Ahavas Olom (Ahavat Olam; 3 min.) (For tenor solo/cantor mixed voices and organ)

• 1945 Kaddish (for organ)

• 1945 Toccata (for organ)

• 1945 Toccata for piano solo. From Prelude and Toccata.

• 1945 Prelude in E Minor, for piano From Prelude and Toccata.

• 1945 Impressions from the Odyssey (three pieces for violin and piano; “Ulysses,” “Penelope,” “The Return”)

• 1945 Fantasy Sonata for Piano (9 min.)

• 1945 Four Dances From The Prodigal Son (orchestra, 18 min.)

• 1946 Concertino for Piano and String Orchestra (17 min.)

• 1946 Kaddish (for cantor, chorus and organ)

• 1946 Two Pieces in Sabbath Mood (Kaddish and Oneg Shabbat) (for orchestra, 2 min. and 9 min. Originally composed as two separate works for organ solo: Kaddish and Toccata; transcribed for small orchestra, 1946)

• 1946 Moods (for piano)

• 1946 Introduction and Toccata, for piano solo

• 1946 Prelude in E Minor for piano solo

• 1946 Contemplation (to a poem by William Blake, for mixed voices with piano accompaniment; 5:30 min.)

• 1946 Toccata (for organ)

• 1947 Symphony in C (Symphony No. 2, 21 min.)

• 1947 Meditation for Trombone and Piano

• 1947 Suite Fantasque (for piano)

• 1948 Three Songs to Words by Philip Freneau (for medium voice and piano). (“On the Sleep of Plants” [1790], “Elegy” [1786], “Ode to Freedom” [1795])

• 1948 Ode to Zion (text by Jehuda Halevi) for mixed voices and two harps

• 1948 Two Dances From The Prodigal Son (arranged for piano, four hands by the composer) [waltz, polka]

• 1948 Music Hall: Overture for Orchestra (6 min.)

• 1949 Yeibichai (Yébiché): Variations for Orchestra on an American Indian Theme (9 min.)

• 1949? Tuari: Nocturne for String Orchestra (“From the [Lento movement of] the String Quartet on Indian Themes”)

• 1949 Music Hall Suite

• 1949 Fanfare, in Memory of James Whitcomb Riley: Born 1849 (wind instruments and percussion)

• 1949 Ashrey Haish (arrangement for mixed voices and string orchestra of a Zionist song by Mordecai Zaira)

• 1950 Three Quiet Preludes (for organ)

• 1950 Ballade Concertante for two pianos

• 1950 Ballade Concertante (Symphonie Concertante) for piano and orchestra

• 1950-51 Sonata for Cello and Piano

• 1951 Two Pieces for Flute and Orchestra: Night Piece and Dance (Nocturne in Nineveh and Dance

• 1951 Capriccio for Violin and Piano

• 1951 Violin Pieces (with piano; “Alpha,” “Ad Astram,” “Bärentanz”)

• 1951 Night Piece and Dancefor Flute and Piano (Nocturne in Niniveh, for flute and piano)

• 1951-52 Arvit L’Shabbat (Friday Evening Service No. 2) for organ, baritone solo/cantor, mixed voices

• 1952 O May the Words for organ and mixed voices

• 1952 Serenade (Revised Ballade/Symphonie Concertante; arrangement for two pianos by the composer)

• 1952 Serenade for Piano and Orchestra (Revised Ballade/Symphonie Concertante)

Density of ethanol at various temperatures

Data obtained from Lange's Handbook of Chemistry, 10th ed.

Temp.	Density		Temp.	Density		Temp.	Density
0°C	0.80625		13°C	0.79535		26°C	0.78437
1°C	0.80541		14°C	0.79451		27°C	0.78352
2°C	0.80457		15°C	0.79367		28°C	0.78267
3°C	0.80374		16°C	0.79283		29°C	0.78182
4°C	0.80290		17°C	0.79198		30°C	0.78097
5°C	0.80207		18°C	0.79114		31°C	0.78012
6°C	0.80123		19°C	0.79029		32°C	0.77927
7°C	0.80039		20°C	0.78945		33°C	0.77841
8°C	0.79956		21°C	0.78860		34°C	0.77756
9°C	0.79872		22°C	0.78775		35°C	0.77671
10°C	0.79788		23°C	0.78691		36°C	0.77585
11°C	0.79704		24°C	0.78606		37°C	0.77500
12°C	0.79620		25°C	0.78522		38°C	0.77414
						39°C	0.77329

Properties of aqueous ethanol solutions

Data obtained from Lange's Handbook of Chemistry, 10th ed. The annotation, d a°C/b°C, indicates density of solution at temperature a divided by density of pure water at temperature b.

% wt ethanol	% vol ethanol	grams ethanol per 100 cc 15.56°C	d 10°C/4°C	d 20°C/4°C	d 25°C/4°C	d 30°C/4°C	d 20°C/20°C	d 25°C/25°C	freezing temp.
0.0	0.0	0.0	0.99973	0.99823	0.99708	0.99568	1.00000	1.00000	0°C
1.0			0.99785	0.99636	0.99520	0.99379	0.99813	0.99811
2.0			0.99602	0.99453	0.99336	0.99194	0.99629	0.99627
2.5	3.13			0.99363					–1°C
3.0			0.99426	0.99275	0.99157	0.99014	0.99451	0.99447
4.0	5.00	3.97	0.99258	0.99103	0.98984	0.98839	0.99279	0.99274
4.8	6.00	4.76		0.98971					–2°C
5.0			0.99098	0.98938	0.98817	0.98670	0.99113	0.99106
5.05	6.30	5.00		0.98930
6.0			0.98946	0.98780	0.98656	0.98507	0.98955	0.98945
6.8	8.47			0.98658					–3°C
7.0			0.98801	0.98627	0.98500	0.98347	0.98802	0.98788
8.0			0.98660	0.98478	0.98346	0.98189	0.98653	0.98634
9.0			0.98524	0.98331	0.98193	0.98031	0.98505	0.98481
10.0	12.40	9.84	0.98393	0.98187	0.98043	0.97575	0.98361	0.98330
11.0			0.98267	0.98047	0.97897	0.97723	0.98221	0.98184
11.3	14.0	11.11		0.98006					–5°C
12.0			0.98145	0.97910	0.97753	0.97573	0.98084	0.98039
13.0			0.98026	0.97775	0.97611	0.97424	0.97948	0.97897
13.78	17.00	13.49		0.98658					–6.1°C
14.0			0.97911	0.97643	0.97472	0.97278	0.97816	0.97757
15.0			0.97800	0.97514	0.97334	0.97133	0.97687	0.97619
15.02	18.50	14.68		0.97511
16.0			0.97692	0.97387	0.97199	0.96990	0.97560	0.97484
16.4	20.2			0.97336					–7.5°C
17.0			0.97583	0.97259	0.97062	0.96844	0.97431	0.97346
17.5	21.5			0.97194					–8.7°C
18.0	22.10	17.54	0.97473	0.97129	0.96923	0.96697	0.97301	0.97207
18.8	23.1			0.97024					–9.4°C
19.0			0.97363	0.96997	0.96782	0.96547	0.97169	0.97065
20.0			0.97252	0.96864	0.96639	0.96395	0.97036	0.96922
20.01	24.50	19.44		0.96863
20.3	24.8			0.96823					–10.6°C
21.0			0.97139	0.96729	0.96495	0.96242	0.96901	0.96778
22.0			0.97024	0.96592	0.96348	0.96087	0.96763	0.96630
22.11	27.00	21.43		0.96578					–12.2°C
23.0			0.96907	0.96453	0.96199	0.95929	0.96624	0.96481
24.0			0.96787	0.96312	0.96048	0.95769	0.96483	0.96329
24.2	29.5			0.96283					–14.0°C
25.0	30.40	24.12	0.96665	0.96168	0.95895	0.95607	0.96339	0.96176
26.0			0.96539	0.96020	0.95738	0.95422	0.96190	0.96018
26.7	32.4			0.95914					–16.0°C
27.0			0.96406	0.95867	0.95576	0.95272	0.96037	0.95856
28.0	33.90	26.90	0.96268	0.95710	0.95410	0.95098	0.95880	0.95689
29.0			0.96125	0.95548	0.95241	0.94922	0.95717	0.95520
29.9	36.1			0.95400					–18.9°C
30.0	36.20	28.73	0.95977	0.95382	0.95067	0.94741	0.95551	0.95345
31.0			0.95823	0.95212	0.94890	0.94557	0.95381	0.95168
32.0			0.95665	0.95038	0.94709	0.94370	0.95207	0.94986
33.0			0.95502	0.94860	0.94525	0.94180	0.95028	0.94802
33.8	40.5			0.94715					–23.6°C
34.0			0.95334	0.94679	0.94337	0.93986	0.94847	0.94613
35.0			0.95162	0.94494	0.94146	0.93790	0.94662	0.94422
35.04	41.90	33.25		0.94486
36.0			0.94986	0.94306	0.93952	0.93591	0.94473	0.94227
37.0			0.94805	0.94114	0.93756	0.93390	0.94281	0.94031
38.0			0.94620	0.93919	0.93556	0.93186	0.94086	0.93830
39.0	46.3		0.94431	0.93720	0.93353	0.92979	0.93886	0.93626	–28.7°C
40.0			0.94238	0.93518	0.93148	0.92770	0.93684	0.93421
40.04	47.40	37.61		0.93510
41.0			0.94042	0.93314	0.92940	0.92558	0.93479	0.93212
42.0			0.93842	0.93107	0.92729	0.92344	0.93272	0.93001
43.0			0.93639	0.92897	0.92516	0.92128	0.93062	0.92787
44.0			0.93433	0.92685	0.92301	0.91910	0.92849	0.92571
45.0			0.93226	0.92472	0.92085	0.91692	0.92636	0.92355
45.31	53.00	42.07		0.92406
46.0			0.93017	0.92257	0.91868	0.91472	0.92421	0.92137
46.3	53.8			0.92193					–33.9°C
47.0			0.92806	0.92041	0.91649	0.91250	0.92204	0.91917
48.0			0.92593	0.91823	0.91429	0.91028	0.91986	0.91697
49.0			0.92379	0.91604	0.91208	0.90805	0.91766	0.91475
50.0			0.92162	0.91384	0.90985	0.90580	0.91546	0.91251
50.16	58.0	46.04		0.91349
51.0			0.91943	0.91160	0.90760	0.90353	0.91322	0.91026
52.0			0.91723	0.90936	0.90524	0.90125	0.91097	0.90799
53.0			0.91502	0.90711	0.90307	0.89896	0.90872	0.90571
54.0			0.91279	0.90485	0.90079	0.89667	0.90645	0.90343
55.0			0.91055	0.90258	0.89850	0.89437	0.90418	0.90113
55.16	63.0	50.00		0.90220
56.0			0.90831	0.90031	0.89621	0.89206	0.90191	0.89833
56.1	63.6			0.90008					–41.0°C
57.0			0.90607	0.89803	0.89392	0.88975	0.89962	0.89654
58.0			0.90381	0.89574	0.89162	0.88744	0.89733	0.89423
59.0			0.90154	0.89344	0.88931	0.88512	0.89502	0.89191
60.0			0.89927	0.89113	0.88699	0.88278	0.89271	0.88959
60.33	68.0	53.98		0.89038
61.0			0.89898	0.88882	0.88466	0.88044	0.89040	0.88725
62.0			0.89468	0.88650	0.88233	0.87809	0.88807	0.88491
63.0			0.89237	0.88417	0.87998	0.87574	0.88574	0.88256
64.0			0.89006	0.88183	0.87763	0.87337	0.88339	0.88020
65.0			0.88774	0.87948	0.87527	0.87100	0.88104	0.87783
66.0			0.88541	0.87713	0.87291	0.86863	0.87869	0.87547
67.0			0.88308	0.87477	0.87054	0.86625	0.87632	0.87309
68.0			0.88071	0.87241	0.86817	0.86387	0.87396	0.87071
69.0			0.87839	0.87004	0.86579	0.86148	0.87158	0.86833
70.0			0.87602	0.86766	0.86340	0.85908	0.86920	0.86593
71.0			0.87365	0.86527	0.86100	0.85667	0.86680	0.86352
71.9	78.3			0.86311					–51.3°C
72.0			0.87127	0.86287	0.85859	0.85426	0.86440	0.86110
73.0			0.86888	0.86047	0.85618	0.85184	0.86200	0.85869
74.0			0.86648	0.85806	0.85376	0.84941	0.85958	0.85626
75.0			0.86408	0.85564	0.85135	0.84698	0.85716	0.85383
76.0			0.86168	0.85322	0.84891	0.84455	0.85473	0.85140
77.0			0.85927	0.85079	0.84647	0.84211	0.85230	0.84895
78.0			0.85685	0.84835	0.84403	0.83966	0.84985	0.84650
79.0			0.85422	0.84590	0.84158	0.83720	0.84740	0.84404
80.0			0.85197	0.84344	0.83911	0.83473	0.84494	0.84157
81.0			0.84950	0.84096	0.83664	0.83224	0.84245	0.83909
82.0			0.84702	0.83848	0.83415	0.82974	0.83997	0.83659
83.0			0.84453	0.83599	0.83164	0.82724	0.83747	0.83408
84.0			0.84203	0.83348	0.82913	0.82473	0.83496	0.83156
85.0			0.83951	0.83095	0.82660	0.82220	0.83242	0.82902
86.0			0.83697	0.82840	0.82405	0.81965	0.82987	0.82646
87.0			0.83441	0.82323	0.82148	0.81708	0.82729	0.82389
88.0			0.83181	0.82323	0.81888	0.81448	0.82469	0.82128
89.0			0.82919	0.82062	0.81626	0.81186	0.82207	0.81865
90.0			0.82654	0.81797	0.81362	0.80922	0.81942	0.81600
91.00	94.00	74.62	0.82386	0.81529	0.81094	0.80655	0.81674	0.81331
92.0			0.82114	0.81257	0.80823	0.80384	0.81401	0.81060
93.0			0.81839	0.80983	0.80549	0.80111	0.81127	0.80785
94.0			0.81561	0.80705	0.80272	0.79835	0.80848	0.80507
95.0			0.81278	0.80424	0.79991	0.79555	0.80567	0.80225
96.0			0.80991	0.80138	0.79706	0.79271	0.80280	0.79939
97.0			0.80698	0.79846	0.79415	0.78981	0.79988	0.79648
98.0			0.80399	0.79547	0.79117	0.78684	0.79688	0.79349
99.0			0.80094	0.79243	0.78814	0.78382	0.79383	0.79045
100.0	100.0	79.39	0.79784	0.78934	0.78506	0.78075	0.79074	0.78736	−114.3 °C
% wt ethanol	% vol ethanol	grams ethanol per 100 cc 15.56°C	d 10°C/4°C	d 20°C/4°C	d 25°C/4°C	d 30°C/4°C	d 20°C/20°C	d 25°C/25°C	freezing temp.

Properties of aqueous methanol solutions

% wt methanol	% vol methanol	d 15.6°C/4°C	d 0°C/4°C	d 10°C/4°C	d 20°C/4°C	freezing temp °C
0	0	0.99908	0.99984	0.99970	0.99820	0.0
1	1.25	0.99728	0.9981	0.9980	0.9965
2	2.50	0.99543	0.9963	0.9962	0.9943
3	3.75	0.99370	0.9946	0.9945	0.9931
3.9	5	0.9938				–2.2
4	4.99	0.99198	0.9930	0.9929	0.9914
5	6.22	0.99029	0.9914	0.9912	0.9896
6	7.45	0.98864	0.9899	0.9896	0.9880
7	8.68	0.98701	0.9884	0.9881	0.9863
8	9.91	0.98547	0.9870	0.9865	0.9847
8.1	10	0.9872				–5.0
9	11.13	0.98547	0.9856	0.9849	0.9831
10	12.35	0.98241	0.9842	0.9834	0.9815
11	13.56	0.98093	0.9829	0.9820	0.9799
12	14.77	0.97945	0.9816	0.9805	0.9784
12.2	15	0.9810				–8.3
13	15.98	0.97802	0.9804	0.9791	0.9768
14	17.18	0.97660	0.9792	0.9778	0.9754
15	18.38	0.97518	0.9780	0.9764	0.9740
16	19.58	0.97377	0.9769	0.9751	0.9725
16.4	20	0.975				–11.7
17	20.77	0.97237	0.9758	0.9739	0.9710
18	21.96	0.97096	0.9747	0.9726	0.9696
19	23.15	0.96955	0.9736	0.9713	0.9681
20	24.33	0.96814	0.9725	0.9700	0.9666
20.6	25	0.968				–15.6
21	25.51	0.96673	0.9714	0.9687	0.9651
22	26.69	0.96533	0.9702	0.9673	0.9636
23	27.86	0.96392	0.9690	0.9660	0.9622
24	29.03	0.96251	0.9678	0.9646	0.9607
24.9	30	0.964				–20.0
25	30.19	0.96108	0.9666	0.9632	0.9592
26	31.35	0.95963	0.9654	0.9628	0.9576
27	32.51	0.95817	0.9642	0.9604	0.9562
28	33.66	0.95668	0.9629	0.9590	0.9546
29	34.81	0.95518	0.9616	0.9575	0.9531
29.2	35	0.957				–25.0
30	35.95	0.95366	0.9604	0.9560	0.9515
31	37.09	0.95213	0.9590	0.9546	0.9499
32	38.22	0.95056	0.9576	0.9531	0.9483
33	39.35	0.94896	0.9563	0.9516	0.9466
33.6	40	0.950				–30.0
34	40.48	0.94734	0.9549	0.9500	0.9450
35	41.59	0.94570	0.9534	0.9484	0.9433
36	42.71	0.94404	0.9520	0.9469	0.9416
37	43.82	0.94237	0.9505	0.9453	0.9398
38	44.92	0.94067	0.9490	0.9437	0.9381	–35.6
39	46.02	0.93894	0.9475	0.9420	0.9363
40	47.11	0.93720	0.9459	0.9403	0.9345
41	48.20	0.93543	0.9443	0.9387	0.9327
42	49.28	0.93365	0.9427	0.9370	0.9309
43	50.35	0.93185	0.9411	0.9352	0.9290
44	51.42	0.93001	0.9395	0.9334	0.9272
45	52.49	0.92815	0.9377	0.9316	0.9252
46	53.54	0.92627	0.9360	0.9298	0.9234
47	54.60	0.92436	0.9342	0.9279	0.9214
48	55.64	0.92242	0.9324	0.9260	0.9196
49	56.68	0.92048	0.9306	0.9240	0.9176
50	57.71	0.91852	0.9287	0.9221	0.9156
51	58.74	0.91653	0.9269	0.9202	0.9135
52	59.76	0.91451	0.9250	0.9182	0.9114
53	60.77	0.91248	0.9230	0.9162	0.9094
54	61.78	0.91044	0.9211	0.9142	0.9073
55	62.78	0.90839	0.9191	0.9122	0.9052
56	63.78	0.90631	0.9172	0.9101	0.9032
57	64.77	0.90421	0.9151	0.9080	0.9010
58	65.75	0.90210	0.9131	0.9060	0.8988
59	66.73	0.89996	0.9111	0.9039	0.8968
60	67.69	0.89781	0.9090	0.9018	0.8946
61	68.65	0.89563	0.9068	0.8998	0.8924
62	69.61	0.89341	0.9046	0.8977	0.8902
63	70.55	0.89117	0.9024	0.8955	0.8879
64	71.49	0.88890	0.9002	0.8933	0.8856
65	72.42	0.88662	0.8980	0.8911	0.8834
66	73.34	0.88433	0.8958	0.8888	0.8811
67	74.26	0.88203	0.8935	0.8865	0.8787
68	75.17	0.87971	0.8913	0.8842	0.8763
69	76.08	0.87739	0.8891	0.8818	0.8738
70	76.98	0.87507	0.8869	0.8794	0.8715
71	77.86	0.87271	0.8847	0.8770	0.8690
72	78.75	0.87033	0.8824	0.8747	0.8665
73	79.62	0.86792	0.8801	0.8724	0.8641
74	80.48	0.86546	0.8778	0.8699	0.8616
75	81.34	0.86300	0.8754	0.8676	0.8592
76	82.18	0.86051	0.8729	0.8651	0.8567
77	83.02	0.85801	0.8705	0.8626	0.8542
78	83.86	0.85551	0.8680	0.8602	0.8518
79	84.68	0.85300	0.8657	0.8577	0.8494
80	85.50	0.85048	0.8634	0.8551	0.8469
81	86.31	0.84794	0.8610	0.8527	0.8446
82	87.11	0.84536	0.8585	0.8501	0.8420
83	87.90	0.84274	0.8560	0.8475	0.8394
84	88.68	0.84009	0.8535	0.8449	0.8366
85	89.45	0.83742	0.8510	0.8422	0.8340
86	90.21	0.83475	0.8483	0.8394	0.8314
87	90.97	0.83207	0.8456	0.8367	0.8286
88	91.72	0.82937	0.8428	0.8340	0.8258
89	92.46	0.82667	0.8400	0.8314	0.8230
90	93.19	0.82396	0.8374	0.8287	0.8202
91	93.92	0.82124	0.8347	0.8261	0.8174
92	94.63	0.81849	0.8320	0.8234	0.8146
93	95.33	0.81568	0.8293	0.8208	0.8118
94	96.02	0.81285	0.8266	0.8180	0.8090
95	96.70	0.80999	0.8240	0.8152	0.8062
96	97.37	0.80713	0.8212	0.8124	0.8034
97	98.04	0.80428	0.8186	0.8096	0.8005
98	98.70	0.80143	0.8158	0.8068	0.7976
99	99.35	0.79859	0.8130	0.8040	0.7948
100	100	0.79577	0.8102	0.8009	0.7917	–97.8
% wt methanol	% vol methanol	d 15.6°C/4°C	d 0°C/4°C	d 10°C/4°C	d 20°C/4°C	freezing temp °C

Solubility in water at various temperatures

Aqueous Solubility of CO2 at 760 mm Hg pressure
Temperature	Dissolved CO2 volume at 0 °C, 760 mm Hg per volume H2O	grams/100 ml H2O
0 °C	1.713	0.3346
1 °C	1.646	0.3213
2 °C	1.527	0.3091
3 °C	1.527	0.2978
4 °C	1.473	0.2871
5 °C	1.424	0.2774
6 °C	1.377	0.2681
7 °C	1.331	0.2589
8 °C	1.282	0.2492
9 °C	1.237	0.2403
10 °C	1.194	0.2318
11 °C	1.154	0.2239
12 °C	1.117	0.2165
13 °C	1.083	0.2098
14 °C	1.050	0.2032
15 °C	1.019	0.1970
16 °C	0.985	0.1903
17 °C	0.956	0.1845
18 °C	0.928	0.1789
19 °C	0.902	0.1737
20 °C	0.878	0.1688
21 °C	0.854	0.1640
22 °C	0.829	0.1590
23 °C	0.804	0.1540
24 °C	0.781	0.1493
25 °C	0.759	0.1449
26 °C	0.738	0.1406
27 °C	0.718	0.1366
28 °C	0.699	0.1327
29 °C	0.682	0.1292
30 °C	0.655	0.1257
35 °C	0.592	0.1105
40 °C	0.530	0.0973
45 °C	0.479	0.0860
50 °C	0.436	0.0761
60 °C	0.359	0.0576