Question

1. Using Antoine’s equation, derive an expression to calculate heats of vaporization as a function of the A, B and C constants in Antoine’s equation and temperature. Use the derived expression to calculate heats of vaporization of water and benzene at their boiling points and 1 atm pressure. Compare the results with tabulated values of water and benzene.

Answer 1

The Antoinne equation is given by: (Be careful of the natural log being used)

Differentiating the above expression with respect to T:

which on rearranging gives:

Also:

Substituting this in the expression:

From the Clausius Clayperon Equation:

Comparing the two equations:

which on rearranging gives:

which is an expression to calculate heats of vaporization as a function of the A, B and C constants in Antoine’s equation and temperature.

Vg is the molar volume of vapor at boiling temperature and atmospheric pressure.

For water:

T = 373 K

A = 11.6972

B = 3826.85

C = - 45.622

Vg = 0.031 m3 / mol

Substituting these values in the above expression:

We get:

ΔHvap = 41.3 kJ / mol

For benzene:

T = 353 K

A = 9.5982

B = 3821.2707

C = - 1.461

Vg = 0.029 m3 / mol

Substituting these values in the above expression:

We get:

ΔHvap = 31.6 kJ / mol

The table given below compares the values:

Component	Calculated Value	Actual Value
Water	41.3 kJ / mol	40.7 kJ / mol
Benzene	31.6 kJ / mol	30.77 kJ / mol