Vapor pressure
From Wikipedia, the free encyclopedia
The picture shows the particle transition, as a result of their vapor pressure, from the
liquid phase to the gas phase and converse.
Vapor pressure or equilibrium vapor pressure is defined as the pressure exerted
by a vapor in thermodynamic equilibrium with its condensed phases (solid or liquid)
at a given temperature in a closed system. The equilibrium vapor pressure is an
indication of a liquid's evaporation rate. It relates to the tendency of particles to
escape from the liquid (or a solid). A substance with a high vapor pressure at normal
temperatures is often referred to as volatile.
The vapor pressure of any substance increases non-linearly with temperature
according to the Clausius–Clapeyron relation. The atmospheric pressure boiling
point of a liquid (also known as the normal boiling point) is the temperature at which
the vapor pressure equals the ambient atmospheric pressure. With any incremental
increase in that temperature, the vapor pressure becomes sufficient to overcome
atmospheric pressure and lift the liquid to form vapor bubbles inside the bulk of the
substance. Bubble formation deeper in the liquid requires a higher pressure, and
therefore higher temperature, because the fluid pressure increases above the
atmospheric pressure as the depth increases.
The vapor pressure that a single component in a mixture contributes to the total
pressure in the system is called partial pressure. For example, air at sea level, and
saturated with water vapor at 20 °C, has partial pressures of about 23 mbar of water,
780 mbar of nitrogen, 210 mbar of oxygen and 9 mbar of argon.
Measurement and units
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.
Estimating vapor pressures with Antoine equation
The Antoine equation [2][3] is a mathematical expression of the relation between the
vapor pressure and the temperature of pure liquid or solid substances. The basic
form of the equation is:
and it can be transformed into this temperature-explicit form:
where:
is the absolute vapor pressure of a substance
is the temperature of the substance
,
and
are substance-specific coefficients (i.e., constants or
parameters)
[3]
is typically either
or
A simpler form of the equation with only two coefficients is sometimes used:
which can be transformed to:
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 810 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.
Relation to boiling point of liquids
Further information: Boiling point
A typical 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]
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
(−24.2 °C), 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)[7] 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.
Liquid mixtures
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:
where p tot is the mixture's vapor pressure, i is one of the components of the mixture
and Χi is the mole fraction of that component in the liquid mixture. The term piΧi is
the partial pressure of component i in the mixture. 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.
Solids
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 degrees
Celsius, 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:[8]
with:
= Sublimation pressure of the solid component at the temperature
= Extrapolated vapor pressure of the liquid component at the temperature
= Heat of fusion
= Gas constant
= Sublimation temperature
= 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 (ΔHm is
positive) and the difference grows with increased distance from the melting point.
Boiling point of water
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.
Main article: Vapor pressure of water
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:
or transformed into this temperature-explicit form:
where the temperature
is in Torr.
is the boiling point in degrees Celsius and the pressure
Dühring's rule
Main article: Dühring's rule
Dühring's rule states that a linear relationship exists between the temperatures at
which two solutions exert the same vapor pressure.
Examples
The following table is a list of a variety of substances ordered by increasing vapor
pressure.
Substance
Vapor
Pressure
(SI units)
100 Pa
500 Pa
600 Pa
2.3 kPa
2.4 kPa
5.83 kPa
Tungsten
Ethylene glycol
Xenon difluoride
Water (H2O)
Propanol
Ethanol
Methyl
isobutyl
2.66 kPa
ketone
Freon 113
37.9 kPa
Acetaldehyde
98.7 kPa
Butane
220 kPa
Formaldehyde
435.7 kPa
Propane
1.013 MPa
Carbonyl sulfide
1.255 MPa
Carbon dioxide
5.7 MPa
Vapor
Pressure
(Bar);
0.001
0.005
0.006
0.023
0.024
0.0583
Vapor
Pressure
(mmHg);
0.75
3.75
4.50
17.5
18.0
43.7
3203 °C
20 °C
25 °C
20 °C
20 °C
20 °C
0.0266
19.95
25 °C
0.379
0.987
2.2
4.357
10.133
12.55
57
284
740
1650
3268
7600
9412
42753
20 °C
20 °C
20 °C
20 °C
25.6 °C
25 °C
20 °C
Temperature
Estimating vapor pressure from molecular structure
Several empirical methods exist to estimate liquid vapor pressure from molecular
structure for organic molecules. Some examples are SIMPOL,[9] the method of Moller
et al.,[8] and EVAPORATION.[10][11]
Meaning in meteorology
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,[12] 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.[13]
References
1. Růžička, M. Fulem, V. Růžička. "Vapor Pressure of Organic Compounds.
Measurement and Correlation".
2. What is the Antoine Equation? (Chemistry Department, Frostburg State
University, Maryland)
3. R.K.Sinnot (2005). Chemical Engineering Design (4th ed.). ButterworthHeinemann. p. 331. ISBN 0-7506-6538-6.
4. , W. (1973), "New vapour pressure measurements for argon and nitrogen and
a new method for establishing rational vapour pressure equations",
Cryogenics 13 (8): 470–482
5. Perry's Chemical Engineers' Handbook, 7th Ed. pg 4-15
6. Perry, R.H. and Green, D.W. (Editors) (1997). Perry's Chemical Engineers'
Handbook (7th ed.). McGraw-Hill. ISBN 0-07-049841-5.
7. Dreisbach, R. R. and Spencer, R. S. (January 1949). "Infinite Points of Cox
Chart Families and dt/dP Values at any Pressure". Industrial and Engineering
Chemistry, 41 (1). p. 176.
8. Moller B., Rarey J., Ramjugernath D., "Estimation of the vapour pressure of
non-electrolyte organic compounds via group contributions and group
interactions ", J.Mol.Liq., 143(1), 52-63, 2008
9. J. F. Pankow et al. (2008). "SIMPOL.1: a simple group contribution method for
predicting vapor pressures and enthalpies of vaporization of multifunctional
organic compounds". Atmos. Chem. Phys. 8: 2773–2796. doi:10.5194/acp-82773-2008.
10. "Vapour pressure of pure liquid compounds. Estimation by EVAPORATION"
11. S. Compernolle et al. (2011). "EVAPORATION: a new vapour pressure
estimation method for organic molecules including non-additivity and
intramolecular interactions". Atmos. Chem. Phys. 11: 9431–9450.
doi:10.5194/acp-11-9431-2011.
12. Glossary (Developed by the American Meteorological Society)
13. A Brief Tutorial (An article about the definition of equilibrium vapor pressure