Vapor pressure

 ( Engineering Thermodynamics ) 

Experimental measurement of vapor pressure is a simple procedure for common pressures between 1 and 200 kPa. The most accurate results are obtained near the boiling point of the substance; measurements smaller than are subject to major errors. Procedures often consist of purifying the test substance, isolating it in a container, evacuating any foreign gas, then measuring the equilibrium pressure of the gaseous phase of the substance in the container at different temperatures. Better accuracy is achieved when care is taken to ensure that the entire substance and its vapor are both at the prescribed temperature. This is often done, as with the use of an isoteniscope, by submerging the containment area in a liquid bath.

Very low vapor pressures of solids can be measured using the Knudsen effusion cell method.

In a medical context, vapor pressure is sometimes expressed in other units, specifically millimeters of mercury (mmHg). Accurate knowledge of the vapor pressure is important for volatile inhalational anesthetics, most of which are liquids at body temperature but have a relatively high vapor pressure.

$$\backslash log\; P\; =\; A-\backslash frac\{B\}\{C+T\}$$

and it can be transformed into this temperature-explicit form:

$$T\; =\; \backslash frac\{B\}\{A-\backslash log\; P\}\; -\; C$$

where:

• $P$ is the absolute vapor pressure of a substance
• $T$ is the temperature of the substance
• $A$, $B$ and $C$ are substance-specific coefficients (i.e., constants or parameters)
• $\backslash log$ is typically either $\backslash log\_\{10\}$ or $\backslash log\_e$

A simpler form of the equation with only two coefficients is sometimes used:

$$\backslash log\; P\; =\; A-\; \backslash frac\{B\}\{T\}$$

which can be transformed to:

$$T\; =\; \backslash frac\{B\}\{A-\backslash log\; P\}$$

Sublimations and vaporizations of the same substance have separate sets of Antoine coefficients, as do components in mixtures. Each parameter set for a specific compound is only applicable over a specified temperature range. Generally, temperature ranges are chosen to maintain the equation's accuracy of a few up to 8–10 percent. For many volatile substances, several different sets of parameters are available and used for different temperature ranges. The Antoine equation has poor accuracy with any single parameter set when used from a compound's melting point to its critical temperature. Accuracy is also usually poor when vapor pressure is under 10 Torr because of the limitations of the apparatus used to establish the Antoine parameter values.

The Wagner equation gives "one of the best"Perry's Chemical Engineers' Handbook, 7th Ed. pp. 4–15 fits to experimental data but is quite complex. It expresses reduced vapor pressure as a function of reduced temperature.

For example, at any given temperature, methyl chloride has the highest vapor pressure of any of the liquids in the chart. It also has the lowest normal boiling point at , which is where the vapor pressure curve of methyl chloride (the blue line) intersects the horizontal pressure line of one atmosphere (atm) of absolute vapor pressure.

Although the relation between vapor pressure and temperature is non-linear, the chart uses a logarithmic vertical axis to produce slightly curved lines, so one chart can graph many liquids. A nearly straight line is obtained when the logarithm of the vapor pressure is plotted against 1/(T + 230) where T is the temperature in degrees Celsius. The vapor pressure of a liquid at its boiling point equals the pressure of its surrounding environment.

$P\_\{\backslash rm\; tot\}\; =\backslash sum\_i\; P\; y\_i\; =\; \backslash sum\_i\; P\_i^\{\backslash rm\; sat\}\; x\_i\; \backslash ,$

where $P\_\{\backslash rm\; tot\}$ is the mixture's vapor pressure, $x\_i$ is the mole fraction of component $i$ in the liquid phase and $y\_i$ is the mole fraction of component $i$ in the vapor phase respectively. $P\_i^\{\backslash rm\; sat\}$ is the vapor pressure of component $i$. Raoult's law is applicable only to non-electrolytes (uncharged species); it is most appropriate for non-polar molecules with only weak intermolecular attractions (such as ).

Systems that have vapor pressures higher than indicated by the above formula are said to have positive deviations. Such a deviation suggests weaker intermolecular attraction than in the pure components, so that the molecules can be thought of as being "held in" the liquid phase less strongly than in the pure liquid. An example is the azeotrope of approximately 95% ethanol and water. Because the azeotrope's vapor pressure is higher than predicted by Raoult's law, it boils at a temperature below that of either pure component.

There are also systems with negative deviations that have vapor pressures that are lower than expected. Such a deviation is evidence for stronger intermolecular attraction between the constituents of the mixture than exists in the pure components. Thus, the molecules are "held in" the liquid more strongly when a second molecule is present. An example is a mixture of trichloromethane (chloroform) and 2-propanone (acetone), which boils above the boiling point of either pure component.

The negative and positive deviations can be used to determine thermodynamic activity coefficients of the components of mixtures.

There are a number of methods for calculating the sublimation pressure (i.e., the vapor pressure) of a solid. One method is to estimate the sublimation pressure from extrapolated liquid vapor pressures (of the supercooled liquid), if the heat of fusion is known, by using this particular form of the Clausius–Clapeyron relation:

$\backslash ln\backslash ,P^\{\backslash rm\; sub\}\_\{\backslash rm\; s\}\; =\; \backslash ln\backslash ,P^\{\backslash rm\; sub\}\_\{\backslash rm\; l\}\; -\; \backslash frac\{\backslash Delta\_\{\backslash rm\; fus\}H\}\{R\}\; \backslash left(\; \backslash frac\{1\}\{T\_\{\backslash rm\; sub\}\}\; -\; \backslash frac\{1\}\{T\_\{\backslash rm\; fus\}\}\; \backslash right)$

where:

• $P^\{\backslash rm\; sub\}\_\{\backslash rm\; s\}$ is the sublimation pressure of the solid component at the temperature .
• $P^\{\backslash rm\; sub\}\_\{\backslash rm\; l\}$ is the extrapolated vapor pressure of the liquid component at the temperature .
• $\backslash Delta\_\{\backslash rm\; fus\}H$ is the heat of fusion.
• $R$ is the gas constant.
• $T\_\{\backslash rm\; sub\}$ is the sublimation temperature.
• $T\_\{\backslash rm\; fus\}$ is the melting point temperature.

This method assumes that the heat of fusion is temperature-independent, ignores additional transition temperatures between different solid phases, and it gives a fair estimation for temperatures not too far from the melting point. It also shows that the sublimation pressure is lower than the extrapolated liquid vapor pressure (Δ_fus H > 0) and the difference grows with increased distance from the melting point.

$\backslash log\_\{10\}\backslash left(\backslash frac\{P\}\{1\backslash text\{\; Torr\}\}\backslash right)\; =\; 8.07131\; -\; \backslash frac\{1730.63\backslash \; \{\}^\backslash circ\backslash text\{C\}\}\{233.426\backslash \; \{\}^\backslash circ\backslash text\{C\}\; +\; T\_b\}$

or transformed into this temperature-explicit form:

$T\_b\; =\; \backslash frac\{1730.63\backslash \; \{\}^\backslash circ\backslash text\{C\}\}\{8.07131\; -\; \backslash log\_\{10\}\backslash left(\backslash frac\{P\}\{1\backslash text\{\; Torr\}\}\backslash right)\}\; -\; 233.426\backslash \; \{\}^\backslash circ\backslash text\{C\}$

where the temperature $T\_b$ is the boiling point in degrees Celsius and the pressure $P$ is in torr.

(Alternate title: "Water Vapor Myths: A Brief Tutorial".)