Water (data page)#Water with dissolved NaCl

{{Short description|Chemical data page for water}}

This page provides supplementary data to the article properties of water.

Further comprehensive authoritative data can be found at the NIST Chemistry WebBook page on thermophysical properties of fluids.{{Cite web |title=Thermophysical Properties of Fluid Systems |url=https://webbook.nist.gov/chemistry/fluid/ |work=NIST Chemistry WebBook |id=NIST Standard Reference Database Number 69 |publisher=National Institute of Standards and Technology |doi=10.18434/T4D303}}

Structure and properties

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! {{chembox header}}|Structure and properties

Index of refraction, nD

| 1.333 at 20 °C

Dielectric constant{{sfn|Lide|2004|p=6-15}}

|

88.00 at 0 °C

86.04 at 5 °C

84.11 at 10 °C

82.22 at 15 °C

80.36 at 20 °C

78.54 at 25 °C

76.75 at 30 °C

75.00 at 35 °C

73.28 at 40 °C

71.59 at 45 °C

69.94 at 50 °C

66.74 at 60 °C

63.68 at 70 °C

60.76 at 80 °C

57.98 at 90 °C

55.33 at 100 °C

Bond strength

| 492.215 kJ/mol O–H bond dissociation energy{{cite journal|doi=10.1063/1.2387163|title=A direct measurement of the dissociation energy of water|year=2006|last1=Maksyutenko|first1=Pavlo|last2=Rizzo|first2=Thomas R.|last3=Boyarkin|first3=Oleg V.|journal=The Journal of Chemical Physics|volume=125|pages=181101|pmid=17115729|issue=18|bibcode=2006JChPh.125r1101M}}

Bond length

| 95.87 pm (equilibrium){{cite journal|doi=10.1016/0022-2852(74)90261-6|title=Molecular force field and structure of water: Recent microwave results|year=1974|last1=Cook|first1=R|last2=Delucia|first2=F|last3=Helminger|first3=P|journal=Journal of Molecular Spectroscopy|volume=53|issue=1|pages=62–76|bibcode=1974JMoSp..53...62C}}

Bond angle

| 104.48° (equilibrium) {{cite journal|year=1979|last1=Hoy|first1=AR|last2=Bunker|first2=PR|journal=Journal of Molecular Spectroscopy|volume=74|pages=1–8|doi=10.1016/0022-2852(79)90019-5|title=A precise solution of the rotation bending Schrödinger equation for a triatomic molecule with application to the water molecule|issue=1|bibcode=1979JMoSp..74....1H}}{{Cite web|url=http://cccbdb.nist.gov/expangle2.asp?descript=aHOH&all=0|title=List of experimental bond angles of type aHOH|website=Computational Chemistry Comparison and Benchmark DataBase}}

Magnetic susceptibility

| −9.04 × 10−6 volume SI units{{cite book|last=Griffiths|first=David Jeffery |title=Introduction to Electrodynamics|url=https://archive.org/details/introductiontoel00grif_0|url-access=registration|edition=3rd|year=1999|publisher=Prentice Hall|isbn=978-0-13-919960-8|page=[https://archive.org/details/introductiontoel00grif_0/page/275 275]}}

Thermodynamic properties

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! {{chembox header}}|Phase behavior

Triple point

| 273.16 K (0.01 °C), 611.73 Pa

Critical point

| 647 K (374 °C), 22.1 MPa

Enthalpy change
of fusion at 273.15 K
, ΔfusH

| 6.01 kJ/mol

Entropy change of fusion
at 273.15 K, 1 bar
, ΔfusS

| 22.0 J/(mol·K)

Std enthalpy change
of vaporization
, ΔvapHo

| 44.0 kJ/mol

Enthalpy change of
vaporization at 373.15 K
, ΔvapH

| 40.68 kJ/mol

Std entropy change
of vaporization
, ΔvapSo

| 118.89 J/(mol·K)

Entropy change of
vaporization at 373.15 K
, ΔvapS

| 109.02 J/(mol·K)

Enthalpy change of
sublimation at 273.15 K, ΔsubH

| 51.1 kJ/mol

Std entropy change of sublimation
at 273.15 K, 1 bar, ΔsubS

| ~144 J/(mol·K)

Molal freezing point constant

| −1.858 °C kg/mol

Molal boiling point constant

| 0.512 °C kg/mol

{{chembox header}}|Solid properties
Std enthalpy change
of formation
, ΔfHosolid

| −291.83 kJ/mol

Standard molar entropy,
Sosolid

| 41 J/(mol K)

Heat capacity, cp

| 12.2 J/(mol K) at −200 °C
15.0 J/(mol K) at −180 °C
17.3 J/(mol K) at −160 °C
19.8 J/(mol K) at −140 °C
24.8 J/(mol K) at −100 °C
29.6 J/(mol K) at −60 °C
32.77 J/(mol K) at −38.3 °C
33.84 J/(mol K) at −30.6 °C
35.20 J/(mol K) at −20.8 °C
36.66 J/(mol K) at −11.0 °C
37.19 J/(mol K) at −4.9 °C
37.84 J/(mol K) at −2.2 °C

{{chembox header}}|Liquid properties
Std enthalpy change
of formation
, ΔfHoliquid

| −285.83 kJ/mol

Standard molar entropy,
Soliquid

| 69.95 J/(mol K)

Heat capacity, cp

| 75.97 J/(mol K) and 4.2176 J/(g·K) at 0 °C
75.52 J/(mol K) and 4.1921 J/(g·K) at 10 °C
75.33 J/(mol K) and 4.1818 J/(g·K) at 20 °C
75.28 J/(mol K) and 4.1787 J/(g·K) at 25 °C
75.26 J/(mol K) and 4.1784 J/(g·K) at 30 °C
75.26 J/(mol K) and 4.1785 J/(g·K) at 40 °C
75.30 J/(mol K) and 4.1806 J/(g·K) at 50 °C
75.37 J/(mol K) and 4.1843 J/(g·K) at 60 °C
75.46 J/(mol K) and 4.1895 J/(g·K) at 70 °C
75.58 J/(mol K) and 4.1963 J/(g·K) at 80 °C
75.74 J/(mol K) and 4.2050 J/(g·K) at 90 °C
75.94 J/(mol K) and 4.2159 J/(g·K) at 100 °C

{{chembox header}}|Gas properties
Std enthalpy change
of formation
, ΔfHogas

| −241.83 kJ/mol

Standard molar entropy,
Sogas

| 188.84 J/(mol K)

Heat capacity, cp

| 36.5 J/(mol K) at 100 °C
36.1 J/(mol K) at 200 °C
36.2 J/(mol K) at 400 °C
37.9 J/(mol K) at 700 °C
41.4 J/(mol K) at 1000 °C

Heat capacity, cv

| 27.5 J/(mol K) at 100 °C
27.6 J/(mol K) at 200 °C
27.8 J/(mol K) at 400 °C
29.5 J/(mol K) at 700 °C
33.1 J/(mol K) at 1000 °C

Heat capacity ratio,
γ = cp/cv

| 1.324 at 100 °C
1.310 at 200 °C
1.301 at 400 °C
1.282 at 700 °C
1.252 at 1000 °C

van der Waals' constants

| a = 553.6 L2 kPa/mol2
b = 0.03049 L/mol

Liquid physical properties

File:Temperature dependence surface tension of water.svg

File:Density of ice and water (en).svg

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! {{chembox header}}|Velocity of sound in water

c in distilled water at 25 °C

| 1498 m/s

c at other temperatures{{cite web|url=http://www.engineeringtoolbox.com/sound-speed-water-d_598.html|title=Water and the Speed of Sound|publisher=www.engineeringtoolbox.com|access-date=2008-04-29}}

| 1403 m/s at 0 °C
1427 m/s at 5 °C
1447 m/s at 10 °C
1481 m/s at 20 °C
1507 m/s at 30 °C
1526 m/s at 40 °C
1541 m/s at 50 °C
1552 m/s at 60 °C
1555 m/s at 70 °C
1555 m/s at 80 °C
1550 m/s at 90 °C
1543 m/s at 100 °C

{{chembox header}}|Density{{sfn|Dean|Lange|1999|p=1199|ps=: Due to the old definition of liter used at the time, the data from the Handbook was converted from old g/ml to g/cm3, by multiplying by 0.999973}}{{sfn|Lide|2004|p=6-15}}{{page needed|date=June 2016}}
0.983854 g/cm3 at −30 °C

|0.99221 g/cm3 at 40 °C

0.993547 g/cm3 at −20 °C

|0.99022 g/cm3 at 45 °C

0.998117 g/cm3 at −10 °C

| 0.98804 g/cm3 at 50 °C

0.9998395 g/cm3 at 0 °C

| 0.98570 g/cm3 at 55 °C

0.999972 g/cm3 at 3.984 °C{{sfn|Franks|2012|p=376}}
0.9999720 g/cm3 at 4 °C

| 0.98321 g/cm3 at 60 °C

0.99996 g/cm3 at 5 °C

| 0.98056 g/cm3 at 65 °C

0.9997026 g/cm3 at 10 °C

| 0.97778 g/cm3 at 70 °C

0.9991026 g/cm3 at 15 °C

| 0.97486 g/cm3 at 75 °C

0.9982071 g/cm3 at 20 °C

| 0.97180 g/cm3 at 80 °C

0.9977735 g/cm3 at 22 °C

| 0.96862 g/cm3 at 85 °C

0.9970479 g/cm3 at 25 °C

| 0.96531 g/cm3 at 90 °C

0.9956502 g/cm3 at 30 °C

| 0.96189 g/cm3 at 95 °C

0.99403 g/cm3 at 35 °C

| 0.95835 g/cm3 at 100 °C

colspan=2| The values below 0 °C refer to supercooled water.
{{chembox header}}|Viscosity{{sfn|Lide|2004|p=6-201}}
1.7921 mPa·s (cP) at 0 °C

| 0.5494 mPa·s at 50 °C

1.5188 mPa·s at 5 °C

| 0.5064 mPa·s at 55 °C

1.3077 mPa·s at 10 °C

| 0.4688 mPa·s at 60 °C

1.1404 mPa·s at 15 °C

| 0.4355 mPa·s at 65 °C

1.0050 mPa·s at 20 °C

| 0.4061 mPa·s at 70 °C

0.8937 mPa·s at 25 °C

| 0.3799 mPa·s at 75 °C

0.8007 mPa·s at 30 °C

| 0.3635 mPa·s at 80 °C

0.7225 mPa·s at 35 °C

| 0.3355 mPa·s at 85 °C

0.6560 mPa·s at 40 °C

| 0.3165 mPa·s at 90 °C

0.5988 mPa·s at 45 °C

| 0.2994 mPa·s at 95 °C

| 0.2838 mPa·s at 100 °C
{{chembox header}}|Surface tension{{sfn|Dean|Lange|1999|p=1663}}
75.64 dyn/cm at 0 °C

| 69.56 dyn/cm at 40 °C

74.92 dyn/cm at 5 °C

| 68.74 dyn/cm at 45 °C

74.22 dyn/cm at 10 °C

| 67.91 dyn/cm at 50 °C

73.49 dyn/cm at 15 °C

| 66.18 dyn/cm at 60 °C

72.75 dyn/cm at 20 °C

| 64.42 dyn/cm at 70 °C

71.97 dyn/cm at 25 °C

| 62.61 dyn/cm at 80 °C

71.18 dyn/cm at 30 °C

| 60.75 dyn/cm at 90 °C

70.38 dyn/cm at 35 °C

| 58.85 dyn/cm at 100 °C

class="wikitable"

|+ Electrical conductivity of highly purified water at saturation pressure[http://www.iapws.org/relguide/TransD2O-2007.pdf Revised Release on Viscosity and Thermal Conductivity of Heavy Water Substance], The International Association for the Properties of Water and Steam Lucerne, Switzerland, August 2007.

Temperature, °CConductivity, μS/m
0.011.15
255.50
10076.5
200299
300241

Water/steam equilibrium properties

Vapor pressure formula for steam in equilibrium with liquid water:{{sfn|Dean|Lange|1999|p=1436}}

: \log_{10} P = A - \frac{B}{T - C},

where P is equilibrium vapor pressure in kPa, and T is temperature in kelvins.

For T = 273 K to 333 K: A = 7.2326; B = 1750.286; C = 38.1.

For T = 333 K to 423 K: A = 7.0917; B = 1668.21; C = 45.1.

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! {{chembox header}} align="center" colspan="6"| Steam table{{sfn|Dean|Lange|1999|p=1476}}

bgcolor="E0E0E0" align="center"|Temperature
(°C)

| bgcolor="E0E0E0" align="center"|Pressure
(kPa)

| bgcolor="E0E0E0" align="center"|H of liquid
(J/g)

| bgcolor="E0E0E0" align="center"|ΔvapH
(J/g)

| bgcolor="E0E0E0" align="center"|Wvap
(J/g)

| bgcolor="E0E0E0" align="center"|ρ of vapor
(kg/m3)

0

| 0.612

| 0.00

| 2496.5

| 126.0

| 0.004855

10

| 1.227

| 42.0

| 2473.5

| 130.5

| 0.009498

20

| 2.336

| 83.8

| 2450.9

| 135.1

| 0.01728

30

| 4.242

| 125.6

| 2427.9

| 139.7

| 0.03037

40

| 7.370

| 167.2

| 2404.9

| 144.2

| 0.05107

50

| 12.33

| 209.0

| 2381.4

| 148.7

| 0.08275

60

| 19.90

| 250.8

| 2357.6

| 153.0

| 0.1300

70

| 31.15

| 292.7

| 2332.9

| 157.3

| 0.1979

80

| 46.12

| 334.6

| 2307.7

| 161.5

| 0.2930

90

| 70.10

| 376.6

| 2282.6

| 165.5

| 0.4232

100

| 101.32

| 419.0

| 2256.3

| 169.4

| 0.5974

110

| 143.27

| 460.8

| 2229.5

| 173.1

| 0.8264

120

| 198.50

| 503.2

| 2201.4

| 176.7

| 1.121

130

| 270.13

| 545.8

| 2172.5

| 180.2

| 1.497

140

| 361.4

| 588.5

| 2142.8

| 183.2

| 1.967

150

| 476.0

| 631.5

| 2111.8

| 186.1

| 2.548

160

| 618.1

| 674.7

| 2080.0

| 188.7

| 3.263

170

| 792.0

| 718.5

| 2047.0

| 190.6

| 4.023

180

| 1002.7

| 762.5

| 2012.2

| 192.8

| 5.165

190

| 1254.9

| 807.0

| 1975.8

| 194.5

| 6.402

200

| 1554.3

| 851.9

| 1937.3

| 195.6

| 7.868

210

| 1907.9

| 897.5

| 1897.5

| 196.3

| 9.606

221.1

| 2369.8

| 948.5

| 1850.2

| 196.6

| 11.88

229.4

| 2769.6

| 987.9

| 1812.5

| 196.2

| 13.87

240.6

| 3381.1

| 1040.6

| 1759.4

| 195.1

| 16.96

248.9

| 3904.1

| 1080.3

| 1715.8

| 193.7

| 19.66

260.0

| 4695.9

| 1134.8

| 1653.9

| 190.8

| 23.84

271.1

| 5603.4

| 1195.9

| 1586.5

| 186.9

| 28.83

279.4

| 6366.5

| 1240.7

| 1532.5

| 183.3

| 33.18

290.6

| 7506.2

| 1302.3

| 1456.3

| 177.4

| 39.95

298.9

| 8463.9

| 1350.0

| 1394.8

| 172.2

| 45.93

310.0

| 9878.0

| 1415.7

| 1307.7

| 164.2

| 55.25

321.1

| 11461

| 1483.9

| 1212.7

| 154.5

| 66.58

329.4

| 12785

| 1537.9

| 1133.2

| 145.6

| 76.92

340.6

| 14727

| 1617.9

| 1007.6

| 130.9

| 94.25

348.9

| 16331

| 1687.0

| 892.0

| 117.0

| 111.5

360.0

| 18682

| 1797.0

| 694.0

| 91.0

| 145.3

371.1

| 21349

| 1968.3

| 365.0

| 47.0

| 214.5

374.4

| 22242

| 2151.2

| 0

| 0

| 306.8

bgcolor="E0E0E0" align="center"|Temperature
(°C)

| bgcolor="E0E0E0" align="center"|Pressure
(kPa)

| bgcolor="E0E0E0" align="center"|H of liquid
(J/g)

| bgcolor="E0E0E0" align="center"|ΔvapH
(J/g)

| bgcolor="E0E0E0" align="center"|Wvap
(J/g)

| bgcolor="E0E0E0" align="center"|ρ of vapor
(kg/m3)

{{clear|left}}

Data in the table above is given for water–steam equilibria at various temperatures over the entire temperature range at which liquid water can exist. Pressure of the equilibrium is given in the second column in kPa. The third column is the heat content of each gram of the liquid phase relative to water at 0 °C. The fourth column is the heat of vaporization of each gram of liquid that changes to vapor. The fifth column is the work PΔV done by each gram of liquid that changes to vapor. The sixth column is the density of the vapor.

Melting point of ice at various pressures

Data obtained from CRC Handbook of Chemistry and Physics 44th ed., p. 2390.

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{{chembox header}}

| Pressure kPa

Temp. °C
101.3250.0
32950−2.5
60311−5.0
87279−7.5
113267−10.0
138274−12.5
159358−15.0
179952−17.5
200251−20.0
215746−22.1

Table of various forms of ice

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! align="center" bgcolor="F8EABA" colspan="6"|Properties of various forms of ice{{cite web|url=https://water.lsbu.ac.uk/water/water_phase_diagram.html|title=Water Phase Diagram|publisher=London South Bank University|author=Martin Chaplin|access-date=2022-05-27}}

Ice
form
Density
g/cm3
Crystal
structure
Triple
points
TP temp °CTP pressure
MPa
rowspan=3|Ih

| rowspan=3|0.92

| rowspan=3|hexagonal

| Lq, Vap, Ih || 0.01 || 0.000612

Lq, Ih, III−22.0207.5
Ih, II, III−34.7212.9
rowspan=1|Ic

| rowspan=1|0.92

| rowspan=1|cubic

| || ||

rowspan=3|II

| rowspan=3|1.17

| rowspan=3 |rhombohedral

| Ih, II, III || −34.7 || 212.9

II, III, V−24.3344.3
II, V, VI−55 (est)620
rowspan=4|III

| rowspan=4|1.14

| rowspan=4|tetragonal

| Lq, Ih, III || −22.0 || 207.5

Lq, III, V−17346.3
Ih, II, III−34.7212.9
II, III, V−24.3344.3
rowspan=1|IV

| rowspan=1|1.27

| rowspan=1|rhombohedral

| || ||

rowspan=4|V

| rowspan=4|1.23

| rowspan=4|monoclinic

| Lq, III, V || −17 || 346.3

Lq, V, VI0.16625.9
II, III, V−24.3344.3
II, V, VI−55 (est)620
rowspan=4|VI

| rowspan=4|1.31

| rowspan=4|tetragonal

| Lq, V, VI || 0.16 || 625.9

Lq, VI, VII81.62200
II, V, VI−55 (est)620
VI, VII, VIII≈52100
rowspan=3|VII

| rowspan=3|1.50

| rowspan=3|cubic

| Lq, VI, VII || 81.6 || 2200

VI, VII, VIII≈52100
VII, VIII, X−17362000
rowspan=2|VIII

| rowspan=2|1.46

| rowspan=2|tetragonal

| VI, VII, VIII || ≈5 || 2100

VII, VIII, X−17362000
rowspan=1|IX

| rowspan=1|1.16

| rowspan=1|tetragonal

| || ||

rowspan=1|X

| rowspan=1|2.46

| rowspan=1|cubic

| VII, VIII, X || −173 || 62000

rowspan=1|XI

| rowspan=1|0.92

| rowspan=1|orthorhombic

| Vap, Ih, XI || −201.5 || 0 (expected)

rowspan=1|XII

| rowspan=1|1.29

| rowspan=1|tetragonal

| || ||

rowspan=1|XIII

| rowspan=1|1.23

| rowspan=1|monoclinic

| || ||

rowspan=1|XIV

| rowspan=1|1.29

| rowspan=1|orthorhombic

| || ||

Ice XI triple point is theoretical and has never been obtained

Phase diagram

File:Phase diagram of water.svg pressure–temperature phase diagram of water. The Roman numerals indicate various ice phases.]]

Water with dissolved NaCl

File:WatNaCl.png

class="wikitable" style="text-align:center"

|+ Properties of water–NaCl mixtures {{RubberBible86th|pages=8–71, 8–116}}

NaCl, wt%Teq, °Cρ, g/cm3nη, mPa·s
000.999841.3331.002
0.5−0.31.00181.33391.011
1−0.591.00531.33471.02
2−1.191.01251.33651.036
3−1.791.01961.33831.052
4−2.411.02681.341.068
5−3.051.0341.34181.085
6−3.71.04131.34351.104
7−4.381.04861.34531.124
8−5.081.05591.3471.145
9−5.811.06331.34881.168
10−6.561.07071.35051.193
12−8.181.08571.35411.25
14−9.941.10081.35761.317
16−11.891.11621.36121.388
18−14.041.13191.36481.463
20−16.461.14781.36841.557
22−19.181.1641.37211.676
23.3−21.1
23.7−17.3
24.9−11.1
26.1−2.7
26.280
26.3210
26.4120
26.4525
26.5230
26.6740
26.8450
27.0360
27.2570
27.580
27.7890
28.05100

Note: ρ is density, n is refractive index at 589 nm,{{clarify|date=May 2018}} and η is viscosity, all at 20 °C; Teq is the equilibrium temperature between two phases: ice/liquid solution for Teq < 0–0.1 °C and NaCl/liquid solution for Teq above 0.1 °C.

Self-ionization

{{Main article|Self-ionization of water}}

File:Temperature dependence water ionization.svg

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! {{chembox header}}|°C

|  −35 

 0  25  60  300 (~50 MPa)
{{chembox header}}|pKw{{cite web|url=https://water.lsbu.ac.uk/water/water_dissociation.html|title=Water ionization |access-date=2022-05-27|author=Martin Chaplin|publisher=London South Bank University}}

|  17  ||  14.9  ||  14.0  ||  13.0  ||  12 

:pK_w = -\log ( [\mathrm{H}^+] [\mathrm{OH}^-] )

Spectral data

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! {{chembox header}}|UV-Vis

λmax

| ? nm

Extinction coefficient, ε

| ?

{{chembox header}}|IR
Major absorption bands{{cite web|url=https://water.lsbu.ac.uk/water/water_vibrational_spectrum.html|title=Water Absorption Spectrum|author=Martin Chaplin|publisher=London South Bank University|access-date=2022-05-27}}

|

{|

| vapor:

ν1 = 3657.05,ν2 = 1594.75,ν3 = 3755.93cm−1
liquid:ν1 = 3280,ν2 = 1644,ν3 = 3490cm−1
hexagonal ice:ν1 = 3085,ν2 = 1650,ν3 = 3220cm−1

|-

! {{chembox header}}|NMR

|-

| Proton NMR

|  4.79 ppm in D2O ; 1.56 ppm in CDCl3 ; 0.40 ppm in C6D6 ; 4.87 in CD3OD{{cite journal|last1=Fulmer|first1=Gregory R.|last2=Miller|first2=Alexander J. M.|last3=Sherden|first3=Nathaniel H.|last4=Gottlieb|first4=Hugo E.|last5=Nudelman|first5=Abraham|last6=Stoltz|first6=Brian M.|last7=Bercaw|first7=John E.|last8=Goldberg|first8=Karen I.|title=NMR Chemical Shifts of Trace Impurities: Common Laboratory Solvents, Organics, and Gases in Deuterated Solvents Relevant to the Organometallic Chemist|journal=Organometallics|volume=29|issue=9|year=2010|pages=2176–2179|issn=0276-7333|doi=10.1021/om100106e|url=https://authors.library.caltech.edu/18475/2/om100106e_si_001.pdf}}

|-

| Carbon-13 NMR

|  N/A

|-

| Other NMR data

|  

|-

! {{chembox header}}|MS

|-

| Masses of
main fragments

|  

|-

|}

Self-diffusion coefficients

border="1" cellspacing="0" cellpadding="6" style="margin: 0 0 0 0.5em; background: white; border-collapse: collapse; border-color: #C0C090;"
{{chembox header}} colspan=11|Experimental self-diffusion coefficients at various temperatures{{Cite journal|last1=Holz|first1=Manfred|last2=Heil|first2=Stefan R.|last3=Sacco|first3=Antonio|date=2000|title=Temperature-dependent self-diffusion coefficients of water and six selected molecular liquids for calibration in accurate {{chem|1|H}} NMR PFG measurements|url=http://xlink.rsc.org/?DOI=b005319h|journal=Physical Chemistry Chemical Physics|language=en|volume=2|issue=20|pages=4740–4742|bibcode=2000PCCP....2.4740H|doi=10.1039/b005319h|issn=1463-9084}}
style="text-align: center" bgcolor="#E0E0E0"

|Temperature in {{formatnum:}}°C

|Coefficients in {{10^

9}} m2/s
0

|1.099

1

|1.138

4

|1.261

5

|1.303

10

|1.525

15

|1.765

20

|2.023

25

|2.299

30

|2.594

35

|2.907

40

|3.238

45

|3.588

50

|3.956

56

|4.423

60

|4.748

70

|5.615

80

|6.557

90

|7.574

100

|8.667

Additional data translated from German "Wasser (Stoffdaten)" page

The data that follows was copied and translated from the German language Wikipedia version of this page (which has moved to [http://de.wikibooks.org/wiki/Tabellensammlung_Chemie/_Stoffdaten_Wasser here]). It provides supplementary physical, thermodynamic, and vapor pressure data, some of which is redundant with data in the tables above, and some of which is additional.

=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" (IAPWS , 1984) (obsolete as of 1995).{{cite web |title=IAPWS |url=http://iapws.org/newform.html |website=Main IAPWS Thermodynamic Property Formulations |access-date=4 May 2023 |quote=In 1995, IAPWS approved a new formulation of the thermodynamic properties of water and steam for general and scientific use. This replaced the 1984 formulation of Haar, Gallagher and Kell, and now serves as the international standard for water's thermodynamic properties.}} This applies to:

==Standard conditions==

In the following table, material data are given for standard pressure of 0.1 MPa (equivalent to 1 bar). Up to 99.63 °C (the boiling point of water at 0.1 MPa), at this pressure water exists as a liquid. Above that, it exists as water vapor. Note that the boiling point of 100.0 °C is at a pressure of 0.101325 MPa (1 atm), which is the average atmospheric pressure.

:: 

border="1" cellspacing="0" cellpadding="6" style="margin: 0 0 0 0.5em; background: white; border-collapse: collapse; border-color: #C0C090;"
{{chembox header}} colspan=11|Water/steam data table at standard pressure (0.1 MPa)
style="text-align: center" bgcolor="#E0E0E0"

| width="10%" colspan="2"|T °C

| width="10%"|V
dm3/kg

| width="10%"|H
kJ/kg

| width="10%"|U
kJ/kg

| width="10%"|S
kJ/(kg·K)

| width="10%"|cp
kJ/(kg·K)

| width="10%"|γ
10−3/K

| width="10%"|λ
mW / (m·K)

| width="10%"|η
μPa·s

| width="10%"|σ   
mN/m

0

| rowspan="15"|lq

1.00020.06−0.04−0.00014.228−0.080561.0179275.65
51.000021.121.00.0764.2000.011570.6151874.95
101.000342.142.00.1514.1880.087580.0130674.22
151.000963.062.90.2244.1840.152589.4113773.49
201.001883.983.80.2964.1830.209598.4100172.74
251.0029104.8104.70.3674.1830.259607.2890.471.98
301.0044125.8125.70.4374.1830.305615.5797.771.20
351.0060146.7146.60.5054.1830.347623.3719.670.41
401.0079167.6167.50.5724.1820.386630.6653.369.60
451.0099188.5188.40.6384.1820.423637.3596.368.78
501.0121209.4209.30.7044.1810.457643.6547.167.95
601.0171251.2251.10.8314.1830.522654.4466.666.24
701.0227293.1293.00.9554.1870.583663.1404.164.49
801.0290335.0334.91.0754.1940.640670.0354.562.68
901.0359377.0376.91.1934.2040.696675.3314.660.82
rowspan="2"|99.63lq1.0431417.5417.41.3034.2170.748679.0283.058.99
g1694.3267525057.3592.0432.88525.0512.26align="center"|–
100

| rowspan="6"|g

1696.1267525067.3612.0422.88125.0812.2758.92
2002172.3287426577.8331.9752.10033.2816.1837.68
3002638.8307328108.2152.0131.76143.4220.2914.37
5003565.5348831318.8342.1351.29766.97028.57align="center"|–
7504721.0404335719.4552.3080.978100.3038.48align="center"|–
10005875.5464240549.9782.4780.786136.347.66align="center"|–
bgcolor="#ffebad"

| colspan="11" align="left"| 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.

{{clear|right}}

==Triple point==

In the following table, material data are given with a pressure of 611.7 Pa (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 are for water vapor only.

:: 

border="1" cellspacing="0" cellpadding="6" style="margin: 0 0 0 0.5em; background: white; border-collapse: collapse; border-color: #C0C090;"
{{chembox header}} colspan=10|Water/steam data table at triple point pressure (0.0006117 MPa)
style="text-align: center" bgcolor="#E0E0E0"

| width="10%" colspan="2"|T °C

| width="10%"|V
dm3/kg

| width="10%"|H
kJ/kg

| width="10%"|U
kJ/kg

| width="10%"|S
kJ/(kg·K)

| width="10%"|cp
kJ/(kg·K)

| width="10%"|γ
10−3/K

| width="10%"|λ
mW / (m·K)

| width="10%"|η
μPa·s

0

| lq

1.0002−0.04−0.04−0.00024.339−0.081561.01792
rowspan="3"|0.01s1.0908−333.4−333.4−1.2211.930.12180align="center"|–
lq1.00020.0004.229−0.080561.01791
g205986250023749.1541.8683.67217.079.22
5

| rowspan="20"|g

209913250923819.1881.8673.60517.339.34
10213695251923889.2221.8673.54017.609.46
15217477252823959.2541.8683.47817.889.59
20221258253724029.2861.8683.41718.179.73
25225039254724099.3181.8693.35918.479.87
30228819255624169.3491.8693.30418.7810.02
35232598256524239.3801.8703.24919.1010.17
40236377257524309.4101.8713.19719.4310.32
45240155258424379.4391.8723.14719.7710.47
50243933259324449.4691.8743.09820.1110.63
60251489261224599.5261.8763.00420.8210.96
70259043263124739.5811.8802.91621.5611.29
80266597265024879.6351.8832.83322.3111.64
90274150266925019.6881.8872.75523.1011.99
100281703268825159.7391.8912.68123.9012.53
2003572162879266110.1941.9402.11432.8916.21
3004327213076281110.5712.0001.74543.2620.30
5005837253489313211.1882.1311.29366.9028.57
7507724774043357111.8082.3070.977100.2038.47
10009612274642405412.3312.4780.785136.3047.66
{{clear|right}}

=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 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 used only as approximate values.{{cite journal|doi=10.1126/science.191.4233.1261|title=Vapor Pressure of Water at Its Triple Point: Highly Accurate Value|year=1976|last1=Guildner|first1=L. A.|last2=Johnson|first2=D. P.|last3=Jones|first3=F. E.|journal=Science|volume=191|pages=1261|pmid=17737716|issue=4233|bibcode=1976Sci...191.1261G|s2cid=37399612}}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|3-540-10930-7}}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 GrundstoffindustrieUlrich Grigull, Johannes Staub, Peter Schiebener (1990): Steam Tables in SI-Units – Wasserdampftafeln. Springer-Verlagdima gmbh

To use the values correctly, 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 be used to compute further values in the appropriate temperature ranges.
  • The saturated vapor pressure over water in the temperature range of −100 °C to −50 °C is only extrapolated [Translator's note: Supercooled liquid water is not known to exist below −42 °C].
  • 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, Pw and Pi, are in pascals.

Over liquid water

:loge(Pw) = −6094.4642 T−1 + 21.1249952 − 2.724552×10−2 T + 1.6853396×10−5 T2 + 2.4575506 loge(T)

For temperature range: 173.15 K to 373.15 K or equivalently −100 °C to 100 °C

Over ice

:loge(Pi) = −5504.4088 T−1 − 3.5704628 − 1.7337458×10−2 T + 6.5204209×10−6 T2 + 6.1295027 loge(T)

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

At 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:

:Pw(ttp = 0.01 °C) = 611.657 Pa ± 0.010 Pa at (1 − α) = 99%

border="1" cellspacing="0" cellpadding="6" style="margin: 0 0 0 0.5em; background: white; border-collapse: collapse; border-color: #C0C090;"

! {{chembox header}} colspan="15"|Values of saturated vapor pressure of water

style="text-align: center" bgcolor="#E0E0E0" width="100%"

| width="8%"|Temp.
T in °C

| width="8%"|Pi(T) over ice
in Pa

| width="8%"|Pw(T) over water
in Pa

| width="10px" rowspan="103" |

| width="8%"|Temp.
T in °C

| width="8%"|Pw(T) over water
in hPa

| width="10px" rowspan="103" |

| width="8%"|Temp.
T in °C

| width="8%"|P(T)
in bar

| width="10px" rowspan="103" |

| width="8%"|Temp.
T in °C

| width="8%"|P(T)
in bar

| width="10px" rowspan="103" |

| width="8%"|Temp.
T in °C

| width="8%"|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

|0.0025470

|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

|10.7280

|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

|100.00

−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

|0.075320

|0.16215

|22

|26.4442

|122

|2.12

|222

|24.09

|322

|115.86

−77

|0.088419

|0.18860

|23

|28.1006

|123

|2.18

|223

|24.55

|323

|117.39

−76

|0.10363

|0.21901

|24

|29.8470

|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

|2.40

|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

|42.4520

|130

|2.70

|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

|146.00

−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

|17.170

|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

|21.110

|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

|28.570

|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

|625.0090

|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

|

|

style="text-align: center" bgcolor="#E0E0E0" width="100%"

| width="9%"|Temp.
T in °C

| width="9%"|Pi(T) over ice
in Pa

| width="9%"|Pw(T) over water
in Pa

| width="9%"|Temp.
T in °C

| width="9%"|Pw(T) over water
in hPa

| width="9%"|Temp.
T in °C

| width="9%"|P(T)
in bar

| width="9%"|Temp.
T in °C

| width="9%"|P(T)
in bar

| width="9%"|Temp.
T in °C

| width="9%"|P(T)
in bar

Magnetic susceptibility

Accepted standardized value of the magnetic susceptibility of water at 20 °C (room temperature) is −12.97 cm3/mol.{{Cite book|title=CRC, Handbook of Chemistry and Physics 64th edition|last=Weast|first=Robert|publisher=CRC publishing|year=1983–1984|isbn=0-8493-0464-4|location=Boca Raton, Florida|pages=E-119}}

Accepted standardized value of the magnetic susceptibility of water at 20 °C (room temperature) is −0.702 cm3/g.

class="wikitable"

|+ Magnetic susceptibility of water at different temperatures

Isotopolog,
state

!Temperature
in K

!Magnetic susceptibiliy
in cm3/mol

H2O(g)

|>373

| −13.1

H2O(l)

|373

| −13.09

H2O(l)

|293

| −12.97

H2O(l)

|273

| −12.93

H2O(s)

|273

| −12.65

H2O(s)

|223

| −12.31

DHO(l)

|302

| −12.97

D2O(l)

|293

| −12.76

D2O(l)

|276.8

| −12.66

D2O(s)

|276.8

| −12.54

D2O(s)

|213

| −12.41

{{Chemical data page general note}}

See also

{{Portal|Water}}

References

{{Reflist|30em}}

Bibliography

{{refbegin}}

  • {{cite book|last1=Dean|first1=John Aurie |last2=Lange|first2=Norbert Adolph |title=Lange's Handbook of Chemistry|url=https://books.google.com/books?id=56KPMQEACAAJ|edition=15th|year=1999|publisher=McGraw-Hill|isbn=978-0-07-016384-3}}
  • {{cite book|last=Franks|first=Felix |title=The Physics and Physical Chemistry of Water|url=https://books.google.com/books?id=5f_xBwAAQBAJ&pg=PA376|year=2012|publisher=Springer |isbn=978-1-4684-8334-5}}
  • {{nist}}
  • {{cite book|last=Lide|first=David R. |title=CRC Handbook of Chemistry and Physics|url=https://books.google.com/books?id=WDll8hA006AC&pg=SA6-15|edition=85th|year=2004|publisher=CRC Press|isbn=978-0-8493-0485-9}}

{{refend}}