Vapor pressure (VP) is the pressure exerted by a vapor in thermodynamic equilibrium with its condensed phase (liquid or solid) at a specific temperature in a closed system. This pressure originates from molecules gaining enough energy to escape the liquid surface and enter the gaseous phase, counterbalanced by gas molecules re-entering the liquid. VP measurement provides a direct indication of a substance’s volatility, which is its tendency to evaporate. Calculating vapor pressure is paramount in many industrial and scientific applications, such as designing distillation columns, creating phase diagrams, and determining a liquid’s boiling point, which occurs when VP equals the surrounding atmospheric pressure.
Using the Clausius-Clapeyron Equation
The Clausius-Clapeyron equation provides a theoretical method for calculating vapor pressure based on thermodynamic properties. This relationship describes how the vapor pressure of a pure substance changes with temperature, assuming a constant enthalpy of vaporization over the temperature range considered. The integrated form is useful for predicting a new vapor pressure (\(P_2\)) at a second temperature (\(T_2\)) if one vapor pressure (\(P_1\)) at a corresponding temperature (\(T_1\)) is known. The mathematical form is typically expressed as \(\ln(P_2/P_1) = (\Delta H_{vap}/R) \cdot (1/T_1 – 1/T_2)\).
To use this equation, the molar enthalpy of vaporization (\(\Delta H_{vap}\)) must be known, which is the energy required to convert one mole of the liquid into a gas. The variable \(R\) represents the universal gas constant, a constant value of \(8.314\) Joules per mole-Kelvin. Since this is a thermodynamic relationship, all temperature values (\(T_1\) and \(T_2\)) must be expressed on the absolute Kelvin scale to ensure the calculation is physically accurate.
The calculation requires inserting the known values into the equation and solving the resulting logarithmic expression for the unknown pressure, \(P_2\). Because the enthalpy of vaporization is always a positive value, the equation demonstrates that vapor pressure increases exponentially as the temperature rises. This powerful thermodynamic tool allows scientists and engineers to extrapolate vapor pressure values from a single known data point.
Applying the Antoine Equation
While the Clausius-Clapeyron equation relies on fundamental thermodynamic properties, the Antoine equation offers an alternative, more practical method for calculating vapor pressure over a defined temperature range. This equation is an empirical correlation, derived from experimental data rather than theoretical principles, and is widely used in chemical engineering due to its simplicity and accuracy for common applications. The standard form is \(\log_{10} P = A – B/(C+T)\), where \(P\) is the vapor pressure and \(T\) is the temperature.
The utility of this method stems from the use of three substance-specific constants, \(A\), \(B\), and \(C\), which are determined by fitting the equation to extensive experimental vapor pressure data. These unique constants for thousands of pure substances are conveniently cataloged in chemical handbooks and databases. Once the specific constants are known, calculating the vapor pressure at any temperature within the constants’ validity range becomes a straightforward algebraic process.
An important consideration is that the Antoine constants are only accurate over the specific temperature range for which they were derived, typically near the normal boiling point of the substance. Using the equation outside this specified range can introduce significant errors. Unlike the Clausius-Clapeyron equation, the Antoine equation often requires the temperature (\(T\)) to be in Celsius, depending on the units used when the specific constants were published, so consistency is paramount.
Determining Vapor Pressure in Solutions
Calculating the vapor pressure of a mixture, such as a liquid solution, introduces the complexity of multiple components interacting, which is addressed primarily through Raoult’s Law. This law states that the partial vapor pressure of any single component in an ideal solution is equal to the vapor pressure of the pure component multiplied by its mole fraction in the solution. For an ideal solution consisting of a solvent and a non-volatile solute, the total vapor pressure of the solution is \(P_{solution} = X_{solvent} P_{pure\ solvent}\).
The mole fraction (\(X\)) is a measure of the concentration of a component, calculated by dividing the moles of that component by the total moles of all components in the solution. For example, if a solvent has a mole fraction of \(0.8\), this is the factor by which the pure solvent’s vapor pressure is reduced. By multiplying the pure solvent’s vapor pressure by this mole fraction, the new, lower vapor pressure of the solution is determined.
Raoult’s Law explains the colligative property of vapor pressure lowering, where the addition of a solute effectively reduces the number of solvent molecules available to escape into the vapor phase, resulting in a lower pressure. While this law holds accurately for ideal solutions where intermolecular forces are similar between all components, real solutions can exhibit deviations. These non-ideal solutions may show a greater or lesser vapor pressure than predicted, depending on whether the component molecules attract or repel each other more strongly than in their pure states.