Talk:Vapour pressure of water

I think there is an error in the first equation. For example at a temperature of 25°C (298.15K) the calculated vapor pressure is 33.8mmHg. — Preceding unsigned comment added by 143.93.17.22 (talk) 15:13, 20 April 2016 (UTC)

The values of the Antoine equation do not match those given for water on the Antoine equation page. —Preceding unsigned comment added by 212.159.122.240 (talk) 14:03, 20 July 2009 (UTC)

Spelled vapour in the article title, can we fix this????? change it to the american spelling "vapor"

Please see Wikipedia:Manual_of_Style#National_varieties_of_English. SWAdair 06:17, 21 November 2006 (UTC)

• Wikipedia policy is to leave this as-is, although I admit that having the two articles with different spellings bugs me as well. C'est la vie! Msaunier (talk) 20:01, 20 February 2012 (UTC)

OK...so what does "exp" stand for in the simplified formula?

76.77.246.138 (talk) 18:56, 1 May 2009 (UTC)

{
Based on calculations that I have made, it seems that the "exp" in the first formula stand for e^x (exponentiation over base e), and that the "log" in the log(P)-vs-1/T graph in the accompanying figure stands for log base 10. I calculated the vapour pressure of water at 20°C = 293K, and got:
1) 2.35 kPa from the first formula by assuming e^x
2) 2.33 kPa from the Antoine equation by using the parameter values for water between 0°C and 100°C on the Antoine equation page
3) 2.2--2.5 kPa from the graph by assuming log base 10.
--Jason Pereira, 99.233.145.177 (talk) 01:11, 16 March 2010 (UTC).
}

Quibble about the definition

Dtprice (talk) 21:05, 26 November 2016 (UTC)

The opening statements are not really correct, as they confuse the vapo(u)r pressure with the vapour pressure at saturation. I would write the explanation/definition as something like:

• The vapor pressure of water is the pressure exerted by molecules of water vapor in gaseous form (whether pure or in a mixture of ideal gases such as air). With increasing pressure, or decreasing temperature, the water vapor content approaches saturation and at the saturation point it will be in thermodynamic equilibrium with its condensed state. At even higher pressures or lower temperatures some of the water condenses into liquid form, leaving the gaseous water vapor at or close to saturation.

I would also want to add something about vapour pressure over ice. Something like:

• At temperatures below the freezing point, condensation will generally result in ice formation. The form of the exponential relationship between temperature and water vapour over ice is similar to that for water vapour and liquid water at temperatures above freezing, but differs in the details, requiring different parameterisation. — Preceding unsigned comment added by Dtprice (talk • contribs) 21:17, 26 November 2016 (UTC)

This problem remains uncorrected, and for some purposes, it is more than a quibble. This article discusses the saturated vapour pressure without explicitly defining that

Modifying the preceding comments, perhaps: The vapor pressure of water is the pressure exerted by molecules of water vapor in gaseous form (whether pure or in a mixture with other gases such as air). This increases with increasing temperature of the liquid water. The maximum possible vapour pressure at steady state increases with the temperature of the gas phase. These are at equilibrium when the vapour pressure equals the saturated vapour pressure. The boiling point of water is the temperature at which the saturated vapour pressure equals the atmospheric pressure, and hence this decreases with decreasing atmospheric pressure.Jhunt29 (talk) 01:32, 9 October 2021 (UTC)

On reflection, alternatively, this page should be re-titled "Saturated vapor pressure of water". It is helpful to those who wish to understand why you cannot breath at 9000m altitude, or why there is a maximum height for a siphon, but not useful for understanding why your pool looses more water and gets colder when the wind blows on a hot day Jhunt29 (talk) 02:19, 9 October 2021 (UTC)

I changed the introduction, hopefully in a way that meets the various meanings of the phrase. If this is not just arbitrarily reversed, I will add some below freezing values to the vapour pressure table.Jhunt29 (talk) 07:22, 10 October 2021 (UTC)

Boiling point arrow on log graph is wrong

The log graph shows the boiling point with with an arrow at log P = 2.4 when it should be at log P = 2.01 — Preceding unsigned comment added by 64.118.100.243 (talk) 07:34, 12 September 2011 (UTC)

Units !!!!

OMG ! Who uses mmHg as units of pressure nowadays ! For goodness' sake get real and start using proper SI units that people will understand and can use. —Preceding unsigned comment added by G4oep (talk • contribs) 17:50, 15 October 2010 (UTC)

• Calm down, but I do agree; the metric world has more-or-less turned to SI units, but inHg is still used in the US, especially in aviation. Perhaps mmHg should be changed to inHg? Msaunier (talk) 19:51, 20 February 2012 (UTC)
• All that needs to happen is to add additional columns for SI units - and might as well include Imperial units and °F as well. Much of the work done in the U.S.A. is still in °F and psi. For instance public water utilities are interested in the vapor pressure of water for several types of engineering analyses.

Categorization

Why is this categorized under "Chemical properties". I don't see any chemistry here. Shouldn't this rather be in a subcategory of "Physics", say "Thermodynamics"? Philip Trueman 14:43, 12 March 2007 (UTC)

Philip, you raise a good point. It would seem that such a thing might be better categorized under physics or thermodynamics. However, the vapor pressure of water, and partial pressures of gases in general, has long been a topic of physical chemistry. So, I'd say it's properly categorized. For example, the combined gas law (PV=nRT) comes from chemistry, not physics. The vapor pressure of water at various temperatures is frequently used in chemistry when performing gas-phase chemical reactions.

But, what bothers me about this entry is that there is not a single reference to an acceptable scientific source for the numbers. Sure, there is a reference to a High School text book. Also, the table seems a bit incomplete. One would like the similar numbers in different units, say mmHg (ie: Torr), atm. Both these units are more common in the chemistry laboratory than are Pascal (which are more likely used in a physics lab).

I'd like to see external references to other sources of physical chemistry, like a textbook (e.g.: any of Atkins' books on physical chemistry), a good reference manual (e.g.: CRC Handbook of Chemistry and Physics), and a scientific paper from a refereed journal (e.g.: something relevant from J. Phys. Chem.) Such referencing can buttruss the information in such a scientific entry and help to dispell the notion that Wikipedia is not a reference to be used for "scientific" information. Patrick 02:45, 9 October 2007 (UTC)

This is just wrong. Water has many chemical properties, but the vapour pressure is a thermodynamic property. Sure it is often used in chemistry - so is it's mass. Anyway, the category "Thermodynamic properties", is a subcategory of both "Thermodynamics" and "Chemical properties" (the current category), and must be correct for this article.

Btw: Using mmHg instead of SI-units, in an article like this, seems contrary to Wiki-guidelines, unless the article was i.e. "vapour pressure of water in chemistry", and someone could document, that the usual unit of preference in that sector was mmHg. However I'm not a w-lawyer, and so I'll leave it to someone else to judge and correct that. 83.92.159.225 (talk) 00:02, 6 December 2010 (UTC)

I love the first sentence: 'The vapour pressure of water is the vapour pressure of water'. God job buddy. —Preceding unsigned comment added by 123.3.79.202 (talk) 15:06, 4 May 2010 (UTC)

Accuracy?

Dtprice (talk) 16:51, 26 November 2016 (UTC)

I came to this page to find a decent approximation formula, being too lazy to look it up in a book. But after I tried both formulae I was concerned (not to say surprised) that neither of them gives an accurate calculation of saturation vapo(u)r pressure (P) at 0 °C!!!

The table shows a value of 0.6113 kPa at °C, which seems to be commonly agreed. The first formulation (least accurate and unattributed) gives me 0.6593 kPa! Antoine's formula gives me 0.6056 kPa. I then went to one of my reliable sources: Monteith and Unsworth (2008). P. 13 provides Tetens' formula (published in 1930!) for temperatures above 0 °C, but cites Murray (1967):

$P=0.61078\exp \left({\frac {17.27T}{T+237.3}}\right),$

where temperature T is in degrees Celsius (°C) and saturation vapor pressure P is in kilopascals (kPa) [NOTE: I have simplified the published equation slightly to make it easier to code.] According to Monteith and Unsworth, "Values of saturation vapour pressure from Tetens' formula are within 1 Pa of exact values up to 35 °C."

Murray also provides Tetens' equation for temperatures below 0 °C [again I have simplified slightly]:

$P=0.61078\exp \left({\frac {21.875T}{T+265.5}}\right).$

I also investigated the Buck formulation. This is rather more complicated than Tetens, but much more accurate, and reportedly superior to the Goff-Gratch equation. Pursuing this further, I calculated values at six temperatures and their % error from the table values (which I am assuming are accurate, given the source is cited as ). I get the following results:

T (°C)	P (Table)	P (Eq 1)	P (Antoine)	P (Tetens)	P (Buck)
0	0.6113	0.6593 (+7.85%)	0.6056 (-0.93%)	0.6108 (-0.09%)	0.6112 (-0.01%)
20	2.3388	2.3755 (+1.57%)	2.3296 (-0.39%)	2.3399 (+0.05%)	2.3383 (-0.02%)
35	5.6267	5.5696 (-1.01%)	5.6090 (-0.31%)	5.6289 (+0.04%)	5.6268 (+0.00%)
50	12.344	12.065 (-2.26%)	12.306 (-0.31%)	12.354 (+0.08%)	12.349 (+0.04%)
75	38.563	37.738 (-2.14%)	38.463 (-0.26%)	38.718 (+0.40%)	38.595 (+0.08%)
100	101.32	101.31 (-0.01%)	101.34 (+0.02%)	102.43 (+1.10%)	101.31 (-0.01%)

So the simple formulas presented in the wikipedia article are reasonably accurate at 100 °C, but quite poor for most of the temperature range below boiling point. Tetens, as reported by Murray and Monteith and Unsworth, beats both the empirical equations presented in the wikipedia article over the range from 0 to 50 °C (and I'd guess, probably for some way above 50 °C as well), but Antoine's is superior at 75 °C and above. The unattributed formula must have zero error at around 26 °C, but is of very poor accuracy outside a very narrow range. Tetens' equations are generally much more accurate and arguably simpler for use at everyday temperatures (e.g., in meteorology). However, I don't have reliable information on the performance of Tetens' equation for T < 0 °C. As expected, Buck's equation for T > 0 °C is significantly more accurate than Tetens, and its superiority increases markedly above 50 °C, though it is more complicated to use. For completeness, here are Buck's (1981) equations for P(T) for T both above and below freezing:

$P=0.61121\exp \left(\left(18.678-{\frac {T}{234.5}}\right)\left({\frac {T}{257.14+T}}\right)\right)$, over liquid water, T > 0 °C

$P=0.61115\exp \left(\left(23.036-{\frac {T}{333.7}}\right)\left({\frac {T}{279.82+T}}\right)\right)$, over ice, T < 0 °C

For serious computation, my preferred formulation has been Lowe (1977). Lowe developed two pairs of equations for temperatures above and below freezing, with different levels of accuracy. They are all very accurate (compared to Clausius-Clapeyron and the Goff-Gratch) but use nested polynomials for very efficient computation. However, there are more recent reviews of possibly superior formulations, notably Wexler (1976, 1977), reported by Flatau et al. (1992).

---

You say Goff-Gratch is less accurate than Buck but you fail to present the corrected numbers for this equation. The numbers quoted in the article are incorrect according to my verified calculations using the Goff-Gratch. Specifically, I've calculated:

Table of Buck vs. Goff-Gratch values at 5 Centigrade-Degree intervals

Temperature (℃)	Measured (kPa)	Goff-Gratch (kPa)	Buck (kPa)	Goff-Gratch offset (kPa)	Buck offset (kPa)
0	0.6113	0.6107	0.6112	-0.0008	-0.0001
5	0.8726	0.8718	0.8724	-0.0008	-0.0002
10	1.2281	1.2270	1.2279	-0.0011	-0.0002
15	1.7056	1.7041	1.7052	-0.0015	-0.0004
20	2.3388	2.3370	2.3383	-0.0018	-0.0005
25	3.1690	3.1667	3.1685	-0.0023	-0.0005
30	4.2455	4.2426	4.2451	-0.0029	-0.0004
35	5.6267	5.6231	5.6268	-0.0036	+0.0001
40	7.3814	7.3771	7.3824	-0.0043	+0.0010
45	9.5898	9.5848	9.5923	-0.0050	+0.0025
50	12.3440	12.3387	12.3494	-0.0053	+0.0054
55	15.7520	15.7452	15.7600	-0.0068	+0.0080
60	19.9320	19.9251	19.9451	-0.0069	+0.0131
65	25.0220	25.0149	25.0412	-0.0071	+0.0192
70	31.1760	31.1680	31.2010	-0.0080	+0.0250
75	38.5630	38.5551	38.5947	-0.0079	+0.0317
80	47.3730	47.3657	47.4103	-0.0073	+0.0373
85	57.8150	57.8086	57.8543	-0.0064	+0.0393
90	70.1170	70.1127	70.1521	-0.0043	+0.0351
95	84.5290	84.5278	84.5486	-0.0012	+0.0196
100	101.3200	101.3250	101.3078	+0.0050	-0.0122

Basically, yes, Buck is better lower than 50℃ but above that Goff-Gratch does much better. However, for most uses of the formula, such as humidity calculations, temperatures less than 50℃ are much more common than above so Buck probably is better for most applications. However, it would be useful to consider sub-0 vapour pressures to get the full picture.

TimeHorse (talk) TimeHorse (talk) 18:40, 18 October 2022 (UTC)

---

I looked up the Vapour Pressure of Ice I calculated the vapour pressure below 0℃ using both the above Buck algorithm for below freezing and the Goff-Gratch algorithm below freezing. Analyzing these results, I found Goff-Gratch to be the more accurate from 0℃ to -100℃, though they are close from -50℃ to 0℃ which again are common temperatures meteorologically.

Specifically:

Table of Buck vs. Goff-Gratch values for ice vapour pressure

Temperature (℃)	Measured (Pa)	Goff-Gratch (Pa)	Buck (Pa)	Goff-Gratch offset (Pa)	Buck offset (Pa)
0	610.8	611.2	611.1	+0.4	+0.4
-1	562.3	562.7	562.7	+0.4	+0.4
-2	517.3	517.8	517.7	+0.5	+0.4
-3	475.7	476.1	476.1	+0.4	+0.4
-4	437.2	437.5	437.5	+0.3	+0.3
-5	401.5	401.8	401.8	+0.3	+0.3
-6	368.5	368.8	368.8	+0.3	+0.3
-7	337.9	338.2	338.2	+0.3	+0.3
-8	309.7	310.0	310.0	+0.3	+0.3
-9	283.7	283.9	284.0	+0.2	+0.3
-10	259.7	259.9	259.9	+0.2	+0.2
-15	165.2	165.3	165.3	+0.1	+0.1
-20	103.2	103.2	103.3	+0.0	+0.1
-25	63.23	63.28	63.31	+0.05	+0.08
-30	37.98	38.00	38.02	+0.02	+0.04
-35	22.33	22.34	22.36	+0.01	+0.03
-40	12.83	12.84	12.85	+0.01	+0.02
-45	7.198	7.202	7.206	+0.004	+0.008
-50	3.935	3.936	3.939	+0.001	+0.004
-55	2.092	2.093	2.095	+0.001	+0.003
-60	1.080	1.081	1.082	+0.001	+0.002
-65	0.5406	0.5407	0.5413	+0.0001	+0.0007
-70	0.2615	0.2615	0.2619	+0.0000	+0.0004
-80	0.05470	0.05472	0.05484	+0.00002	+0.00014
-90	0.009670	0.009670	0.009709	+0.000000	+0.000039
-100	0.001400	0.001403	0.001413	+0.000003	+0.000013

Also, I wanted to show the Python code I used to calculate these values; code uses the Pint library to ensure dimensionality:

from pint import UnitRegistry

ureg = UnitRegistry()
_Q = ureg.Quantity
T100C = _Q(100, ureg.degC)
TTPC = 273.16 * ureg.K
atm = _Q(1, ureg.atm)

def get_vapour_pressure_water_goff_gratch(T):
    K = ureg.K
    Tst = T100C.to(K).magnitude
    TK = T.to(K).magnitude
    esst = atm.to(ureg.hPa)

    return (10**(-7.90298*(Tst/TK-1)) * (Tst/TK)**5.02808 / \
            10**(1.3816e-7*(10**(11.344*(1-TK/Tst)) - 1)) * \
            10**(8.1328e-3*(10**(-3.49149*(Tst/TK - 1)) - 1)) * \
            esst).to(ureg.kPa)

def get_vapour_pressure_water_buck(T):
    TC = T.to(ureg.degC).magnitude
    return 0.61121*np.exp((18.678-TC/234.5) * TC / (257.14 + TC)) * \
           ureg.kPa

def get_vapour_pressure_ice_goff_gratch(T):
    K = ureg.K
    T0 = TTPC.to(K).magnitude
    TK = T.to(K).magnitude
    esi0 = 6.1173 * ureg.hPa
    return (10**(-9.09718*(T0/TK-1)) / (T0/TK)**3.56654 * \
            10**(0.876793*(1-TK/T0)) * esi0).to(ureg.Pa)

def get_vapour_pressure_ice_buck(T):
    TC = T.to(ureg.degC).magnitude
    return 0.61115*np.exp((23.036-TC/333.7) * TC / (279.82 + TC)) * \
           ureg.Pa

TimeHorse (talk) 19:20, 19 October 2022 (UTC)

Vapor pressure graph appears to be labeled wrong

This logarithmic graph: https://en.wikipedia.org/wiki/Vapour_pressure_of_water#/media/File:Vapor_Pressure_of_Water.png looks like the label for "Normal Boiling Point" is pointing to the incorrect log(pressure)/perk. Water normally boils at 373 K, so 1000/373 = 2.68, moreover, the vapor pressure would be 101 kPa, and the logarithm of that is ~2 (I can tell it's base ten because where the arrow's pointing bases 2 and e aren't anywhere close, being ~5.28 and ~11, respectively). The graph DOES intersect perk of 2.68 (mT)-1 and 2 log(kPa) exactly, which is where the "Normal Boiling Point" label should point. Someone should fix it but I won't do anything until I get consensus and I'm too busy to commit to fixing. — Preceding unsigned comment added by 71.45.76.116 (talk) 05:08, 11 February 2022 (UTC)

Actually I see that this issue has been raised farther up in the talk page over ten years ago lol. — Preceding unsigned comment added by 71.45.76.116 (talk) 05:09, 11 February 2022 (UTC)

References

— Preceding unsigned comment added by talk 00:18, 26 November 2016 (UTC) Comment was added and now updated by Dtprice (talk) 16:51, 26 November 2016 (UTC)