Saturation vapor pressure

This article was registered in the quality assurance of the physics editorial team . If you are familiar with the topic, you are welcome to participate in the review and possible improvement of the article. The exchange of views about this is currently not taking place on the article discussion page , but on the quality assurance side of physics.

The saturation vapor pressure (also equilibrium vapor pressure ) of a substance is the pressure at which the gaseous state of aggregation is in equilibrium with the liquid or solid state of aggregation . The saturation vapor pressure depends on the temperature.

The saturation vapor pressure curve ( saturation vapor pressure line, vapor pressure curve, vapor pressure line ) describes the saturation vapor pressure as a function of temperature. It corresponds to the phase boundary line of the gaseous phase in the phase diagram .

Attention: In chemistry , the saturation vapor pressure is usually abbreviated as " vapor pressure ". There is a great risk here of confusing the concept of saturation vapor pressure with that of partial pressure . Therefore the term “vapor pressure” is not used here.

history

In the 19th century, John Dalton was concerned with the question of how much water vapor volume was necessary to bring the air to saturation. His first finding was that this volume is very dependent on temperature.

definition

The saturation vapor pressure of a pure substance in liquid or solid physical state at a given temperature , the pressure , of the thermodynamic equilibrium in an otherwise empty chamber via the liquid or solid phase is formed. In this state both phases coexist in a stable manner, neither grows at the expense of the other, because the evaporation of the liquid or sublimation of the solid is quantitatively equal to the condensation or resublimation of the gas. When the temperature or volume changes, so much of the substance evaporates or condenses until the saturation vapor pressure is reached again in equilibrium.

At temperatures above the triple point , the liquid phase is formed during condensation, below the triple point the solid, for example iodine at room temperature.

If there are several mutually insoluble liquid phases in the otherwise empty sample volume, a total pressure arises above them equal to the sum of the saturation vapor pressures of the individual substances. If, after heating or expansion, the saturation vapor pressure for one of the components is higher than the total pressure, this component begins to boil .

A solution made up of several components has a saturation vapor pressure that depends not only on the temperature but also on the composition of the solution. Each component contributes with a partial pressure that can differ from its own saturation vapor pressure. The composition of the steam depends on the temperature and does not generally match the composition of the solution.

Formula symbol and unit

The symbol E is usually used for the saturation vapor pressure, but other forms such as e _s and p _{s, max} , for liquid water especially e _w and p _{w, max} and for ice e _i and p _{i, max are also used} . The respective indices are also in uppercase E . Depending on the application, different pressure units are used, with hectopascal (hPa) and megapascal (MPa ) being the most common in the natural sciences, while bar (bar) is the most common in engineering .

The saturation vapor pressure in the phase diagram

Phase diagram of an "ordinary" substance and water ( density anomaly )

In the phase diagram , the saturation vapor pressure is the value of the pressure along the phase boundary line, marked here as black, between the gas phase and the corresponding solid or liquid phase. This phase boundary line is therefore also referred to as the vapor pressure curve or saturation vapor pressure curve. For the phase equilibrium of gas-solid bodies, the saturation vapor pressure is also called sublimation pressure and for the phase equilibrium of gas-liquid it is also called the boiling pressure . It should be noted here that at temperatures above the critical point there is no longer a liquid phase and therefore no saturation vapor pressure. Furthermore, the phase boundary line between solid and liquid, the so-called melting curve, does not play a role in the saturation vapor pressure.

Applications and meaning

The saturation vapor pressure is a measure of the proportion of those molecules or atoms that have enough energy to overcome the short-range and long-range order (the cohesive forces and the surface tension ) and to switch to the gaseous phase. The probability for this is given by the Boltzmann statistics . Therefore the vapor pressure curve is proportional to the Boltzmann factor :

{\ displaystyle \ exp \ left (- {\ frac {Q_ {d}} {k _ {\ mathrm {B}} \ cdot T}} \ right) \ ;,}

where is the energy of vaporization of a molecule or atom. ${\ displaystyle Q_ {d}}$

It follows from this that in the equilibrium state the number of particles in a specific gas volume is greater at higher temperatures than at lower temperatures, which means that the particle density increases with the temperature .

Important examples are water vapor and humidity . Many humidity measures are defined or calculated using vapor pressure and saturation vapor pressure, especially in connection with the relative humidity , the saturation deficit and the dew point .

One example of an application of saturation vapor pressure in technology is freeze drying , another is pressure cooking (see pressure cooker ). In building physics, the Glaser method (a comparison of saturated steam pressures according to the temperature profile and the respectively theoretically prevailing partial vapor pressures at the layer boundaries of the component) is used to assess whether a component is at risk from condensation.

Calculation and influencing factors

The Clapeyron equation can be used to calculate the saturation vapor pressure or the Clausius-Clapeyron equation , especially for the phase transition from liquid to gas . Applied to the saturation vapor pressure this reads:

{\ displaystyle \ quad {\ frac {\ mathrm {d} E_ {s}} {\ mathrm {d} T}} = {\ frac {q_ {v} E_ {s}} {R_ {w} T ^ { 2}}}}

The individual symbols stand for the following quantities :

E _s - saturation vapor pressure
q _v - specific heat of vaporization ( heat of vaporization per mass )
R _w - specific gas constant
T - temperature

However, this equation is fraught with practical problems because it is difficult to integrate (temperature dependence of the heat of vaporization). If one assumes that (the heat of evaporation) would be constant, the result for the saturation vapor pressure is: ${\ displaystyle q_ {v}}$

{\ displaystyle E_ {s} = E_ {0} \ cdot \ exp \ left ({\ frac {q_ {v}} {R_ {w}}} \ cdot \ left ({\ frac {1} {T_ {0 }}} - {\ frac {1} {T}} \ right) \ right)}

In the case of the saturation vapor pressure of water, which is very important for many applications, various approximation equations have therefore been developed, the simplest of which are the Magnus formulas. The currently most exact equation for calculating the vapor pressure above water is the Goff-Gratch equation - a polynomial of the sixth degree in logarithms of the temperature - which is also recommended by the World Meteorological Organization . The formula given in VDI / VDE 3514 Part 1 is more precise.

Calculation of the saturation vapor pressure of water using the Magnus formula

The saturation vapor pressure for water vapor can be calculated using the Magnus formula (here the internationally recognized formula according to Sonntag 1990, see literature ).

Over level water surfaces

{\ displaystyle E_ {w} (t) = 6 {,} 112 \, \ mathrm {hPa} \ cdot \ exp \ left ({\ frac {17 {,} 62 \ cdot t} {243 {,} 12 \ ; ^ {\ circ} \ mathrm {C} + t}} \ right) \ qquad {\ text {for}} \ quad -45 \, ^ {\ circ} \ mathrm {C} \ leq t \ leq 60 \ , ^ {\ circ} \ mathrm {C}}

Over flat ice surfaces

{\ displaystyle E_ {i} (t) = 6 {,} 112 \, \ mathrm {hPa} \ cdot \ exp \ left ({\ frac {22 {,} 46 \ cdot t} {272 {,} 62 \ , ^ {\ circ} \ mathrm {C} + t}} \ right) \ qquad {\ text {for}} \ quad -65 \, ^ {\ circ} \ mathrm {C} \ leq t \ leq 0 { ,} 01 \, ^ {\ circ} \ mathrm {C}}

Hints

Wikibooks: data table with more precise formulas - learning and teaching materials

In the Magnus formulas it should be noted that for t the temperature is to be entered in degrees Celsius and not in Kelvin . The resulting saturation vapor pressure has the unit of the pre-factor , i.e. hPa for the values given here . Beyond the naturally occurring temperature values on earth, the deviation of the empirically determined Magnus formula from the real value can increase sharply, which is why one should limit oneself to the specified temperature ranges. ${\ displaystyle E_ {0} (t)}$

The Magnus formulas only apply to flat surfaces and here only to pure water. However, their error is comparatively large, so that these two effects are usually negligible if they are low. The standard deviation of the results is up to half a percent on both sides. With curved surfaces, for example with spherical droplets, the saturation vapor pressure is higher (curvature effect see below), on the other hand it is lower with saline solutions (solution effect see below). These two modifying influences play an essential role in the formation of precipitation particles.

In laboratory experiments, condensation over a flat surface with distilled water and very pure air can only be achieved after over-saturation of several hundred percent. In the real atmosphere, however, aerosols play an essential role as condensation nuclei . As a result, in reality oversaturation of more than one percent is rarely observed.

To compare the Magnus formula with another form of representation, we recommend the article water vapor . The Magnus formula was first drawn up in 1844 by Heinrich Gustav Magnus and has only been supplemented with more precise values since then, with the values used here coming from D. Sonntag (1990). A more precise calculation and many example values can be found in the next section.

Effects

In contrast to the ideal case of a pure substance and a flat surface described by the above equations, in reality there are other influencing factors that help determine the ultimate saturation vapor pressure.

Curvature and dissolving effect

When liquid particles form on condensation nuclei, the curvature effect occurs. It can be seen here that a higher saturation vapor pressure occurs over the curved surfaces of the liquid droplets produced than in comparison to a planar water surface. If the liquid is not in the form of a pure substance when there is a change in its physical state, the dissolving effect must also be taken into account. The particles dissolved in the liquid make it difficult to leave the liquid compound, which is why the saturation vapor pressure is lower than would be the case with a pure liquid.

Under atmospheric conditions, both effects usually occur together, and a stand-alone consideration is not very effective.

Charge effect

The electric charge of the surface also has an effect on the saturation vapor pressure, which is minimal compared to the other effects and therefore does not play a practical role.

Correction factors for humid air

The correction factors ( English : enhancement factor ) are necessary because the water vapor is not present in pure form, but within the humid air. They only apply at an air pressure of 1013.25 hPa (normal pressure). They are larger at higher pressures and correspondingly smaller at lower pressures.

above water in the temperature range from −50 ° C to 90 ° C: ${\ displaystyle f_ {w} = 1 {,} 00519 \ pm 0 {,} 00108}$
over ice in the temperature range from −90 ° C to 0 ° C: ${\ displaystyle f_ {i} = 1 {,} 00686 \ pm 0 {,} 00235}$

Since the correction factors are temperature-dependent and include rather large temperature intervals in the above values, they only represent very rough approximations to the actual deviation. The negative temperatures above water refer to supercooled water. To obtain the resulting values for the saturation vapor pressure, the following applies:

${\ displaystyle E_ {w} '\; = \; f_ {w} \; \ cdot \; E_ {w} \ qquad}$ ( - table value) ${\ displaystyle E_ {w}}$
${\ displaystyle E_ {i} '\; \; = \; f_ {i} \; \; \ cdot \; E_ {i} \; \ qquad}$ ( - table value) ${\ displaystyle E_ {i}}$

Relationship with the amount of saturation

According to the general gas equation , the saturation vapor pressure is (approximately) also the product of the saturation amount with the individual gas constant and the temperature (in Kelvin ). Represented as a formula like this:

{\ displaystyle E _ {\ gamma, \ varphi} (T) = \ rho _ {\ gamma, \ varphi; \ mathrm {max}} (T) \ cdot R _ {\ gamma} \ cdot T \ ;,}

see. Vapor pressure or saturation .

Here γ still stands for the respective gas (e.g. water vapor ) - with gas constant R _γ ,

φ for the alternative physical state (" phase ", solid or liquid ); where γ = water vapor, E _{γ, φ is} the water vapor pressure and ρ _{γ, φ is} the amount of saturation “above ice” or “above water”.

In addition to the term saturation quantity , one also finds saturation concentration and saturation (vapor) density (title from Sonntag 1982), the SI unit is mostly g / m ³ . In the case of water vapor , one speaks of the maximum humidity .

literature

Dietrich Sonntag: Important new Values of the Physical Constants of 1986, Vapor Pressure Formulations based on ITS-90, and Psychrometer Formulas. In: Journal of Meteorology. Vol. 40, No. 5, 1990, ISSN 0084-5361 , pp. 340-344.
Leslie A. Guildner, Daniel P. Johnson, Frank E. Jones: Vapor pressure of Water at Its Triple Point. In: Journal of Research of the National Bureau of Standards. Section A: Physics and Chemistry. Vol. 80A, No. 3, 1976, ISSN 0022-4332 , pp. 505-521, doi : 10.6028 / jres.080A.054
Daniel M. Murphy, Thomas Koop: Review of the vapor pressures of ice and supercooled water for atmospheric applications. In: Quarterly Journal of the Royal Meteorological Society. Vol. 131, No. 608, 2005, ISSN 0035-9009 , pp. 1539-1565, doi : 10.1256 / qj.04.94 .

The vapor pressure of iodine

Web links

Footnotes

↑ ^a ^b Helmut Hager: [Munich Calibration Day 2018 - Fundamentals of humidity calibration] (pdf), p. 7f. In: ESZ-AG.de. G. Lufft Mess- und Regeltechnik GmbH, Fellbach

[hager-1] Helmut Hager: [Munich Calibration Day 2018 - Fundamentals of humidity calibration] (pdf), p. 7f. In: ESZ-AG.de. G. Lufft Mess- und Regeltechnik GmbH, Fellbach