## Tuesday, November 26, 2019

### Clausius-Clapeyron Equation Example Problem

Clausius Problem The Clausius-Clapeyron equation may be used to estimate vapor pressure as a function of temperature or to find the heat of the phase transition from the vapor pressures at two temperatures. The Clausius-Clapeyron equation is a related named for Rudolf Clausius and Benoit Emile Clapeyron. The equation describes the phase transition between two phases of matter that have the same composition. When graphed, the relationship between temperature and pressure of a liquid is a curve rather than a straight line. In the case of water, for example, vapor pressure increases much faster than temperature. The Clausius-Clapeyron equation gives the slope of the tangents to the curve. Clausius This example problem demonstrates how to use the Clausius-Clapeyron equation to predict the vapor pressure of a solution. Problem: The vapor pressure of 1-propanol is 10.0 torr at 14.7 Ã‚ °C. Calculate the vapor pressure at 52.8 Ã‚ °C.Given:Heat of vaporization of 1-propanol 47.2 kJ/mol Solution The Clausius-Clapeyron equation relates a solutions vapor pressures at different temperatures to the heat of vaporization. The Clausius-Clapeyron equation is expressed byln[PT1,vap/PT2,vap] (ÃŽâ€Hvap/R)[1/T2 - 1/T1]whereÃŽâ€Hvap is the enthalpy of vaporization of the solutionR is the ideal gas constant 0.008314 kJ/KÃ‚ ·molT1 and T2 are the absolute temperatures of the solution in KelvinPT1,vap and PT2,vap is the vapor pressure of the solution at temperature T1 and T2Step 1 - Convert Ã‚ °C to KTK Ã‚ °C 273.15T1 14.7 Ã‚ °C 273.15T1 287.85 KT2 52.8 Ã‚ °C 273.15T2 325.95 KStep 2 - Find PT2,vapln[10 torr/PT2,vap] (47.2 kJ/mol/0.008314 kJ/KÃ‚ ·mol)[1/325.95 K - 1/287.85 K]ln[10 torr/PT2,vap] 5677(-4.06 x 10-4)ln[10 torr/PT2,vap] -2.305take the antilog of both sides 10 torr/PT2,vap 0.997PT2,vap/10 torr 10.02PT2,vap 100.2 torr Answer: The vapor pressure of 1-propanol at 52.8 Ã‚ °C is 100.2 torr.