Calculate vapor pressure, temperature, or enthalpy with the Clausius-Clapeyron equation, Antoine equation, or Raoult's law for liquids and solutions.

Constant positive vaporization enthalpy and ideal vapor approximation. Use absolute pressures.

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Clausius Clapeyron Equation Formula

The Clausius-Clapeyron equation is used to calculate the vapor pressure of a substance at different temperatures. The equation is as follows:

ln(P2 / P1) = (ฮ”Hvap / R) ร— (1 / T1 - 1 / T2)

Variables:

  • P1 is the vapor pressure at temperature T1
  • P2 is the vapor pressure at temperature T2
  • ฮ”Hvap is the enthalpy of vaporization
  • R is the ideal gas constant (8.31446261815324 J/(molยทK))
  • T1 is the initial absolute temperature in kelvin
  • T2 is the final absolute temperature in kelvin

To calculate the vapor pressure at a different temperature, take the natural logarithm of the ratio of the vapor pressures at the two temperatures. Multiply the enthalpy of vaporization by the reciprocal of the ideal gas constant, and then multiply that by the difference in the reciprocals of the initial and final temperatures.

What is a Clausius Clapeyron Equation?

The Clausius-Clapeyron equation is a mathematical relationship that describes the phase transition between two states of matter, such as the transition from liquid to gas during evaporation. It was developed by physicists Rudolf Clausius and Benoรฎt Paul ร‰mile Clapeyron in the 19th century. The equation provides a quantitative way of understanding how the pressure at which this phase transition occurs depends on the temperature. It is derived from the principles of thermodynamics and assumes that the transition between phases is an equilibrium process. The equation is ln(P2/P1) = -ฮ”Hvap/R(1/T2 – 1/T1), where P1 and P2 are the pressures at temperatures T1 and T2, ฮ”Hvap is the enthalpy of vaporization, and R is the ideal gas constant. This equation is particularly useful in meteorology and physical chemistry for calculating the saturation vapor pressure of water or other liquids.

How to Calculate Clausius Clapeyron Equation?

The following steps outline how to calculate the Clausius Clapeyron Equation:

  1. First, determine the vapor pressure of the substance at one temperature (P1) and its corresponding temperature (T1).
  2. Next, select the unknown value and enter the other four quantities, including a positive molar vaporization enthalpy when it is known.
  3. Use the reciprocal-temperature difference (1/T2 – 1/T1) and the natural logarithm of the pressure ratio, not ordinary temperature and pressure differences.
  4. Finally, apply ln(P2/P1) = -ฮ”Hvap/R * (1/T2 – 1/T1), using kelvin, consistent absolute pressures, and ฮ”Hvap in J/mol. This approximation assumes constant positive enthalpy, ideal vapor and negligible liquid volume; avoid phase changes and critical conditions.
  5. After inserting the values and calculating the result, check your answer with the calculator above.

Example Problem:

Use the following variables as an example problem to test your knowledge:

Vapor pressure at T1 (P1) = 2.5 atm

Temperature at T1 (T1) = 300 K

Vapor pressure at T2 (P2) = 4.2 atm

Temperature at T2 (T2) = 350 K. Solving for enthalpy gives 9.058332 kJ/mol. Antoine presets instead use NIST WebBook bar/kelvin coefficients within their documented ranges; custom coefficients require an explicit convention and fit limits. Raoultโ€™s law gives total solution vapor pressure only for a nonvolatile solute in an ideal solution; otherwise it gives solvent partial pressure.