Vapor pressure

Vapor pressure is measured in the standard units of pressure. The International System of Units (SI) recognizes pressure as a derived unit with the dimension of force per area and designates the pascal (Pa) as its standard unit. One pascal is one newton per square meter (N·m⁻² or kg·m⁻¹·s⁻²).

Experimental measurement of vapor pressure is a simple procedure for common pressures between 1 and 200 kPa.[1] Most accurate results are obtained near the boiling point of substances and large errors result for measurements smaller than 1kPa. 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 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). This is important for volatile anesthetics, most of which are liquids at body temperature, but with a relatively high vapor pressure.

The Antoine equation[2][3] is a pragmatic mathematical expression of the relation between the vapor pressure and the temperature of pure liquid or solid substances. It is obtained by curve-fitting and is adapted to the fact that vapor pressure is usually increasing and concave as a function of temperature. The basic form of the equation is:

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

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

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

where:

• ${\displaystyle P}$ is the absolute vapor pressure of a substance
• ${\displaystyle T}$ is the temperature of the substance
• ${\displaystyle A}$, ${\displaystyle B}$ and ${\displaystyle C}$ are substance-specific coefficients (i.e., constants or parameters)
• ${\displaystyle \log }$ is typically either ${\displaystyle \log _{10}}$ or ${\displaystyle \log _{e}}$[3]

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

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

which can be transformed to:

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

Sublimations and vaporizations of the same substance have separate sets of Antoine coefficients, as do components in mixtures.[2] 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[4] gives "one of the best"[5] fits to experimental data but is quite complex. It expresses reduced vapor pressure as a function of reduced temperature.

A log-lin vapor pressure chart for various liquids

As a general trend, vapor pressures of liquids at ambient temperatures increase with decreasing boiling points. This is illustrated in the vapor pressure chart (see right) that shows graphs of the vapor pressures versus temperatures for a variety of liquids.[6] At the normal boiling point of a liquid, the vapor pressure is equal to the standard atmospheric pressure defined as 1 atmosphere,[7] 760 Torr, 101.325 kPa, or 14.69595 psi.

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 −24.2 °C (−11.6 °F), 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)[8] 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.

Raoult's law gives an approximation to the vapor pressure of mixtures of liquids. It states that the activity (pressure or fugacity) of a single-phase mixture is equal to the mole-fraction-weighted sum of the components' vapor pressures:

${\displaystyle P_{\rm {tot}}=\sum _{i}Py_{i}=\sum _{i}P_{i}^{\rm {sat}}x_{i}\,}$

where ${\displaystyle P_{\rm {tot}}}$ is the mixture's vapor pressure, ${\displaystyle x_{i}}$ is the mole fraction of component ${\displaystyle i}$ in the liquid phase and ${\displaystyle y_{i}}$ is the mole fraction of component ${\displaystyle i}$ in the vapor phase respectively. ${\displaystyle P_{i}^{\rm {sat}}}$ is the vapor pressure of component ${\displaystyle i}$. 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 London forces).

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.

Vapor pressure of liquid and solid benzene

Equilibrium vapor pressure can be defined as the pressure reached when a condensed phase is in equilibrium with its own vapor. In the case of an equilibrium solid, such as a crystal, this can be defined as the pressure when the rate of sublimation of a solid matches the rate of deposition of its vapor phase. For most solids this pressure is very low, but some notable exceptions are naphthalene, dry ice (the vapor pressure of dry ice is 5.73 MPa (831 psi, 56.5 atm) at 20 °C, which causes most sealed containers to rupture), and ice. All solid materials have a vapor pressure. However, due to their often extremely low values, measurement can be rather difficult. Typical techniques include the use of thermogravimetry and gas transpiration.

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:[9]

${\displaystyle \ln \,P_{\rm {s}}^{\rm {sub}}=\ln \,P_{\rm {l}}^{\rm {sub}}-{\frac {\Delta _{\rm {fus}}H}{R}}\left({\frac {1}{T_{\rm {sub}}}}-{\frac {1}{T_{\rm {fus}}}}\right)}$

where:

• ${\displaystyle P_{\rm {s}}^{\rm {sub}}}$ is the sublimation pressure of the solid component at the temperature ${\displaystyle T_{\rm {sub}}<T_{\rm {fus}}}$.
• ${\displaystyle P_{\rm {l}}^{\rm {sub}}}$ is the extrapolated vapor pressure of the liquid component at the temperature ${\displaystyle T_{\rm {sub}}<T_{\rm {fus}}}$.
• ${\displaystyle \Delta _{\rm {fus}}H}$ is the heat of fusion.
• ${\displaystyle R}$ is the gas constant.
• ${\displaystyle T_{\rm {sub}}}$ is the sublimation temperature.
• ${\displaystyle T_{\rm {fus}}}$ 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_fusH > 0) and the difference grows with increased distance from the melting point.

Graph of water vapor pressure versus temperature. At the normal boiling point of 100 °C, it equals the standard atmospheric pressure of 760 Torr or 101.325 kPa.

Like all liquids, water boils when its vapor pressure reaches its surrounding pressure. In nature, the atmospheric pressure is lower at higher elevations and water boils at a lower temperature. The boiling temperature of water for atmospheric pressures can be approximated by the Antoine equation:

${\displaystyle \log _{10}\left({\frac {P}{1{\text{ Torr}}}}\right)=8.07131-{\frac {1730.63\ {}^{\circ }{\text{C}}}{233.426\ {}^{\circ }{\text{C}}+T_{b}}}}$

or transformed into this temperature-explicit form:

${\displaystyle T_{b}={\frac {1730.63\ {}^{\circ }{\text{C}}}{8.07131-\log _{10}\left({\frac {P}{1{\text{ Torr}}}}\right)}}-233.426\ {}^{\circ }{\text{C}}}$

where the temperature ${\displaystyle T_{b}}$ is the boiling point in degrees Celsius and the pressure ${\displaystyle P}$ is in Torr.

Dühring's rule states that a linear relationship exists between the temperatures at which two solutions exert the same vapor pressure.

The following table is a list of a variety of substances ordered by increasing vapor pressure (in absolute units).

Several empirical methods exist to estimate the vapor pressure from molecular structure for organic molecules. Some examples are SIMPOL.1 method,[13] the method of Moller et al.,[9] and EVAPORATION (Estimation of VApour Pressure of ORganics, Accounting for Temperature, Intramolecular, and Non-additivity effects).[14][15]

In meteorology, the term vapor pressure is used to mean the partial pressure of water vapor in the atmosphere, even if it is not in equilibrium,[16] and the equilibrium vapor pressure is specified otherwise. Meteorologists also use the term saturation vapor pressure to refer to the equilibrium vapor pressure of water or brine above a flat surface, to distinguish it from equilibrium vapor pressure, which takes into account the shape and size of water droplets and particulates in the atmosphere.[17]

• Absolute humidity
• Antoine equation
• Lee–Kesler method
• Osmotic coefficient
• Raoult's law: vapor pressure lowering in solution
• Reid vapor pressure
• Relative humidity
• Relative volatility
• Saturation vapor density
• Triple point
• True vapor pressure
• Vapor–liquid equilibrium
• Vapor pressures of the elements (data page)
• Vapour pressure of water

• Fluid Characteristics Chart
• Hyperphysics
• MSDS Vapor Pressure
• Online vapor pressure calculation tool (Requires Registration)
• Prediction of Vapor Pressures of Pure Liquid Organic Compounds