Vapor Pressure Calculator

What is Vapor Pressure?

Vapor pressure is the pressure exerted by a vapor in thermodynamic equilibrium with its condensed phases (solid or liquid) at a given temperature in a closed system. At the molecular level, vapor pressure arises when molecules at the surface of a liquid gain enough kinetic energy to escape into the gas phase. Simultaneously, gas-phase molecules collide with and re-enter the liquid surface. When the rate of evaporation equals the rate of condensation, the system reaches a dynamic equilibrium, and the pressure of the vapor at this point is the vapor pressure.

Every substance has a characteristic vapor pressure that depends on temperature. As temperature increases, more molecules have sufficient kinetic energy to escape the liquid phase, so vapor pressure rises exponentially. When the vapor pressure of a liquid equals the external atmospheric pressure, the liquid boils. This is why water boils at 100 °C (373.15 K) at standard atmospheric pressure (1 atm = 101.325 kPa), but at lower temperatures at higher altitudes where atmospheric pressure is reduced.

Vapor pressure is a critical concept in chemistry, meteorology, environmental science, and engineering. It influences phenomena from the drying of paint to the formation of clouds, from the operation of vacuum distillation columns to the cavitation of pump impellers.

Clausius-Clapeyron Equation

The Clausius-Clapeyron equation provides a way to relate the vapor pressure of a substance at one temperature to its vapor pressure at another temperature, given the enthalpy of vaporization. It is derived from the Clapeyron equation, which describes the slope of a phase boundary on a pressure-temperature diagram:

For a liquid-vapor transition, assuming the vapor behaves as an ideal gas and the molar volume of the liquid is negligible compared to the vapor, this simplifies to the Clausius-Clapeyron equation:

Integrating between two states (T₁, P₁) and (T₂, P₂) while assuming ΔH_vap is constant over the temperature range yields the integrated form:

Where R = 8.3145 J/(mol·K) is the ideal gas constant, and all temperatures must be in Kelvin. This equation is remarkably useful because it requires knowing the vapor pressure at only one temperature, along with the enthalpy of vaporization, to estimate vapor pressure at any other temperature. The approximation is best over small temperature ranges where ΔH_vap does not change significantly.

What is Enthalpy of Vaporization?

The enthalpy of vaporization (ΔH_vap), also called the heat of vaporization, is the amount of energy required to convert one mole of a substance from the liquid phase to the gas phase at constant pressure. It reflects the strength of intermolecular forces: substances with strong intermolecular interactions (hydrogen bonding, dipole-dipole forces) require more energy to vaporize and thus have higher ΔH_vap values.

Below is a table of enthalpy of vaporization values for common substances at their normal boiling points:

Note that water has a relatively high ΔH_vap compared to other small molecules due to its extensive hydrogen bonding network. Mercury, a liquid metal, has an even higher value because of its strong metallic bonding.

Antoine Equation

The Antoine equation is a semi-empirical correlation that provides a more accurate relationship between vapor pressure and temperature than the Clausius-Clapeyron equation over wider temperature ranges. It takes the form:

Where P is the vapor pressure (typically in mmHg), T is the temperature (typically in °C), and A, B, and C are substance-specific constants determined by fitting experimental data. The Antoine constants are available in published tables for thousands of compounds and are widely used in chemical engineering process design.

The Antoine equation is essentially a simplification of a more general equation and works well within specified temperature ranges. Outside these ranges, the accuracy decreases. For precision work, the modified Antoine equation or other correlations such as the Wagner equation may be preferred.

Common Antoine constants (temperature in °C, pressure in mmHg):

Raoult's Law

Raoult's Law describes the vapor pressure of an ideal solution. It states that the partial vapor pressure of each component in an ideal liquid mixture is equal to the vapor pressure of the pure component multiplied by its mole fraction in the mixture:

Where χ_solvent is the mole fraction of the solvent and P°_solvent is the vapor pressure of the pure solvent at that temperature. This law is a consequence of the fact that solute molecules at the surface reduce the number of solvent molecules available to escape into the vapor phase.

The key consequence is vapor pressure lowering: adding a non-volatile solute to a solvent always decreases the vapor pressure of the solution compared to the pure solvent. The change in vapor pressure (ΔP) is:

Raoult's Law applies strictly to ideal solutions where intermolecular interactions between solute and solvent are similar to those in the pure components. Real solutions often show positive deviations (higher vapor pressure than predicted) or negative deviations (lower vapor pressure), depending on the relative strengths of intermolecular forces.

How to Calculate Vapor Pressure

Here is a step-by-step worked example using the Clausius-Clapeyron equation to find the vapor pressure of water at 90 °C.

Boiling Point at Different Altitudes

One of the most practical applications of vapor pressure calculations is determining the boiling point of water at different altitudes. As altitude increases, atmospheric pressure decreases, meaning that water requires less energy (lower temperature) to reach the point where its vapor pressure equals the surrounding pressure.

By rearranging the Clausius-Clapeyron equation to solve for T₂, we can estimate boiling points at different pressures:

This has significant implications for cooking. At high altitudes, food takes longer to cook in boiling water because the water boils at a lower temperature. Pressure cookers are commonly used at high altitudes to compensate for this effect by raising the internal pressure above atmospheric, thereby increasing the boiling point.

Vapor Pressure and Intermolecular Forces

The vapor pressure of a substance is fundamentally determined by the strength of its intermolecular forces. Molecules held together by weak forces can more easily escape into the gas phase, resulting in higher vapor pressure. Conversely, substances with strong intermolecular attractions have lower vapor pressure.

The hierarchy of intermolecular forces and their effect on vapor pressure is as follows:

• London dispersion forces (weakest): Present in all molecules. Small nonpolar molecules like methane (CH₄) and noble gases have only dispersion forces and therefore high vapor pressures at room temperature — they are gases under standard conditions.
• Dipole-dipole forces: Polar molecules such as chloroform (CHCl₃) experience these attractions, giving them intermediate vapor pressures.
• Hydrogen bonding: Molecules like water, alcohols, and carboxylic acids form hydrogen bonds, which are relatively strong intermolecular forces. Water's extensive hydrogen bonding network explains its unusually low vapor pressure (23.8 mmHg at 25 °C) for such a small molecule.
• Ionic and metallic bonding (strongest): Ionic compounds and metals have extremely low vapor pressures at room temperature due to very strong electrostatic interactions.

Molecular size also plays a role. Within a homologous series (e.g., the alkanes), larger molecules have stronger total dispersion forces and thus lower vapor pressures. For example, pentane (C₅H₁₂) has a higher vapor pressure than octane (C₈H₁₈) at the same temperature.

Vapor Pressure Table

The following table lists vapor pressures (in mmHg) for several common substances at various temperatures:

Notice how different the vapor pressures are across substances at the same temperature. At 25 °C, diethyl ether has a vapor pressure of 534 mmHg (close to boiling), while mercury's is only 0.0017 mmHg. This spans more than five orders of magnitude and reflects the vast differences in intermolecular forces between these substances.

Applications of Vapor Pressure

Vapor pressure is a fundamental property that underpins many important processes and technologies:

• Distillation: The separation of liquid mixtures by distillation exploits differences in vapor pressure. Components with higher vapor pressure (lower boiling points) evaporate first and are collected as distillate. This principle is used in petroleum refining, water purification, production of alcoholic beverages, and chemical manufacturing.
• Weather and Meteorology: Atmospheric water vapor pressure drives weather phenomena such as cloud formation, precipitation, fog, and dew. The relative humidity of air is the ratio of the actual water vapor pressure to the saturation vapor pressure at a given temperature. When this ratio reaches 100%, condensation occurs.
• Pump Cavitation: When pressure in a fluid system drops below the vapor pressure of the liquid, the liquid boils locally and forms vapor bubbles. When these bubbles collapse near pump impellers or piping surfaces, the resulting shock waves cause severe erosion known as cavitation. Engineers must ensure that the Net Positive Suction Head (NPSH) of a pump exceeds the vapor pressure of the fluid being pumped.
• Food Processing: Freeze-drying (lyophilization) takes advantage of low vapor pressures at reduced temperatures and pressures to remove water from food while preserving its structure. Vacuum evaporation concentrates fruit juices and dairy products at lower temperatures to preserve flavor and nutrients.
• Environmental Science: The vapor pressure of volatile organic compounds (VOCs) and pesticides determines their tendency to evaporate into the atmosphere. Henry's law constant, which relates vapor pressure to aqueous solubility, predicts the distribution of pollutants between air and water.
• Refrigeration and Air Conditioning: Refrigerants are chosen partly based on their vapor pressure curves. The refrigerant must have a boiling point low enough to absorb heat from the cooled space and a vapor pressure high enough to reject heat to the environment.
• Fuel Systems: The Reid vapor pressure (RVP) of gasoline determines its volatility and is regulated to prevent excessive evaporative emissions in summer and ensure adequate cold-start performance in winter.

Frequently Asked Questions