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QUESTION

# How do you calculate the vapor pressure of ethanol?

You use the Clausius-Clapeyron equation.

Experiments show that the vapour pressure ##P##, of vaporization, ##ΔH_"vap"##, and temperature ##T## are related by the equation

##lnP = "constant" – (ΔH_"vap")/"RT"##

where ##R## is the ideal gas constant. This equation is the Clausius- Clapeyron equation.

If ##P_1## and ##P_2## are the vapour pressures at two temperatures ##T_1## and ##T_2##, the equation takes the form:

##ln(P_2/(P_1)) = (ΔH_"vap")/R(1/T_1 – 1/T_2)##

The Clausius-Clapeyron equation allows us to estimate the vapour pressure at another temperature, if we know the enthalpy of vaporization and the vapor pressure at some temperature.

Example

Ethanol has a heat of vaporization of 38.56 kJ/mol and a normal boiling point of 78.4 °C. What is the vapor pressure of ethanol at 50.0 °C?

Solution

##T_1 = "(50.0+ 273.15) K = 323.15 K"##; ##P_1 = "?"## ##T_2 = "(78.4 + 273.15) K = 351.15 K"##; ##P_2 = "760 Torr"##

##ln(P_2/P_1) = (ΔH_"vap")/R (1/T_1 – 1/T_2)##

##ln(("760 Torr")/P_1) = ((38 560 color(red)(cancel(color(black)("J·mol"^(-1)))))/(8.314 color(red)(cancel(color(black)("J·K"^(-1)"mol"^-1))))) (1/(323.15color(red)(cancel(color(black)("K")))) – 1/(351.55 color(red)(cancel(color(black)("K")))))##

##ln(("760 Torr")/P_1) = 4638 × 2.500 × 10^(-4) = 1.159##

##("760 Torr")/P_1 = e^1.159 = 3.188##

##P_1## = ##("760 Torr")/3.188 = "238.3 Torr"##