Question

The vapor pressure of a liquid in a certain temperature range is given by the formula ln(p)=a-b/T, where a and b are constant. Find the enthalpy of vaporization of the liquid. (Hints: Clausius-Clapeyron equation; p is the numerical value of the pressure, i.e. it is dimensionless.)

Answer 1

Recall that in equilibrium; especially in vapor-liquid equilibriums, we can use Clasius Clapyeron combination equation in order to relate two points in the same equilibrium line.

The equation is given as:

ln(P2/P1) = -dHvap/R*(1/T2-1/T1)

Where

P2,P1 = vapor pressure at point 1 and 2

dH = Enthalpy of vaporization, typically reported in kJ/mol, but we need to use J/mol

R = 8.314 J/mol K

T1,T2 = Saturation temperature at point 1 and 2

Therefore, we need at least 4 variables in order to solve this.

Substitute all known data:

ln(P2/P1) = -dHvap/R*(1/T2-1/T1)

Change negative signs

ln(P2/P1) = dHvap/R*(1/T1-1/T2)

if numerical data is given then

dHvap = R * ( lnP2/P1 ) / (1/T1-1/T2)