vapor pressure

vapor pressure

vapor pressure, pressure exerted by a vapor that is in equilibrium with its liquid. A liquid standing in a sealed beaker is actually a dynamic system: some molecules of the liquid are evaporating to form vapor and some molecules of vapor are condensing to form liquid. At equilibrium the rates of the two processes are equal and the system appears to be stationary (see chemical equilibrium). The vapor, like any gas, exerts a pressure, and this pressure at equilibrium is called the vapor pressure. Vapor pressure depends on various factors, the most important of which is the nature of the liquid. If the molecules of liquid bind to each other very strongly, there will be less tendency for the molecules to escape as gas and a consequent lower vapor pressure; for example, polar molecules that can form hydrogen bonds between themselves, e.g., water molecules and the alcohols, have relatively low vapor pressures. If there is only weak interaction between the liquid molecules, there will be a greater tendency for the molecules to evaporate and a higher vapor pressure. Temperature also affects the vapor pressure. If the system in equilibrium is perturbed by raising the temperature, then according to Le Châtelier's principle the system should react to relieve this stress; as the temperature is increased, the evaporation process, which absorbs heat, is speeded up to a greater degree than the condensation process, which gives off heat, so that the vapor pressure is higher when equilibrium is restored at the new temperature. If the temperature is increased enough to raise the vapor pressure until it equals atmospheric pressure, the liquid will boil. If the external pressure is reduced, as in a vacuum system, then the liquid will boil much more readily than under atmospheric pressure. This fact is used in the vacuum distillation process to obtain relatively pure samples of liquids with high boiling points. Some solids, e.g., iodine and carbon dioxide, are capable of subliming (going directly from a solid to a gas) at atmospheric pressure and room temperature; thus, such solids also have significant vapor pressures under these conditions. Another factor affecting vapor pressure is the presence of dissolved substances in the liquid or solid; according to Raoult's law, the vapor pressure of a pure liquid or solid is lowered by the addition of a solute.
Vapor pressure (also known as equilibrium vapor pressure or saturation vapor pressure), is the pressure of a vapor in equilibrium with its non-vapor phases. All liquids and solids have a tendency to evaporate to a gaseous form, and all gases have a tendency to condense back into their original form (either liquid or solid). At any given temperature, for a particular substance, there is a pressure at which the gas of that substance is in dynamic equilibrium with its liquid or solid forms. This is the vapor pressure of that substance at that temperature. The equilibrium vapor pressure is an indication of a liquid's evaporation rate. It relates to the tendency of molecules and atoms to escape from a liquid or a solid. A substance with a high vapor pressure at normal temperatures is often referred to as volatile. The Kelvin equation shows how equilibrium vapor pressure depends on droplet size.

An example is water vapor when air is saturated with water vapor. It is the vapor pressure usually found over a flat surface of liquid water, and is a dynamic equilibrium where the rate of condensation of water equals the rate of evaporation of water. In general, the higher the temperature, the higher the vapor pressure. When air is at the saturation vapor pressure, it is said to be at the dew point. Thus, at saturation vapor pressure, air has a relative humidity of 100% and condensation occurs with any increase of water vapor content or a reduction in temperature.

The international standard for saturation vapor pressure over water is given by the Goff-Gratch equation. Another more recent equation for water is the Arden Buck Equation.

Assuming absolutely clean air, if water droplets have a high curvature, which is the case when they are smaller, they require relative humidities in excess of 100% (known as supersaturation) to be at an equilibrium vapor pressure. As droplets approach approximately 20 micrometers, they can survive at 100% relative humidity. As the droplet grows larger by collision and coalescence, it can survive longer because its curvature becomes smoother as the droplet grows. Of course, in actual practice in the Earth's atmosphere, the ability of water to condense into droplets is generally affected by the presence of hygroscopic dust particles (Cloud Condensation nuclei). The relative humidity required for droplets to actually form can be significantly below the real saturation vapor pressure due to the solute effect. Finally, if the temperature becomes low enough in a cloud, as it does in nimbostratus and cumulonimbus clouds, microscopic ice crystals may also serve as condensation nuclei for the cloud in a process known as the Bergeron process.

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 where 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 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.

Relation between vapor pressures and normal boiling points of liquids

The higher the vapor pressure of a liquid at a given temperature, the lower the normal boiling point (i.e., the boiling point at atmospheric pressure) of the liquid.

The vapor pressure chart to the right has graphs of the vapor pressures versus temperatures for a variety of liquids. As can be seen in the chart, the liquids with the highest vapor pressures have the lowest normal boiling points.

For example, at any given temperature, propane has the highest vapor pressure of any of the liquids in the chart. It also has the lowest normal boiling point(-42.1 °C), which is where the vapor pressure curve of propane (the purple 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 in order to obtain slightly curved lines so that one chart can graph many liquids.

Units of vapor pressure

The international SI unit for pressure is the pascal (Pa), equal to one newton per square meter (N·m-2 or kg·m-1·s-2). The conversions to other pressure units are:

Vapor pressure of solids

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, meaning it will cause most sealed containers to explode), 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.

Water vapor pressure

Water, like all liquids, starts to boil when its vapor pressure reaches its surrounding pressure. At higher elevations the atmospheric pressure is lower and water will boil at a lower temperature. The boiling temperature of water for pressures around 100 kPa can be approximated by

T_b = 100 + 0.0002772 cdot (p - 101000) - 1.24 cdot 10^{-9} cdot (p - 101000)^2

where the temperature T_b is the boiling point temperature in degrees Celsius and the pressure p is in pascals. One gets the vapor pressure by solving this equation for p.

In meteorology, the international standard for the vapour pressure of water over a flat surface is given by the Goff-Gratch equation.

Vapor pressure of 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:

p_text{tot} = sum_i p_ichi_i

where p is vapor pressure, i is a component index, and χ is a mole fraction. The term p_ichi_i is the vapor 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.

Examples of vapor pressures

Gas Vapor Pressure
(SI units)
Vapor Pressure
(bar)
Vapor Pressure
(mmHg)
Temperature
Helium 100 kPa 1 750 -269.15 °C
Propane 2.2 MPa 22 16500 55 °C
Butane 220 kPa 2.2 1650 20 °C
Carbonyl sulfide 1.255 MPa 12.55 9412 25 °C
Acetaldehyde 98.7 kPa 0.987 740 20 °C
Freon 113 37.9 kPa 0.379 284 20 °C
Methyl isobutyl ketone 26.48 kPa 0.02648 19.86 25 °C
Tungsten 100 Pa 0.001 0.75 3203 °C
Dioxygen 54.2 MPa 542 407936 20 °C
Dinitrogen 63.2 MPa 632 475106 20 °C

Usage of the term vapor pressure 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 equilibrium, and the equilibrium vapor pressure is specified as such. 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.

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