Question

If the solvent follows the Henry rule of P2=k'x2, prove that the solvent meets the Raoullt rule. (Use Gibbs-Dubheem expression)

Answer 1

Gibbs duhem equation in terms of fugacity

x1 * (ln f1)/x1 = x2* (ln f2)/x2

f1 = partial fugacity

dx2= -dx1

Therefore x1 * ln f1 = - x2 * ln f2

Component 2 obey Henry's rule ,therefore f2 = k2 * x2

d ln f1 = - (x2 / x1)* d ln ( k2 * x2)= - ( x2 / x1 ) * ( k2 * dx2)/( k2 * x2)

= - (dx2)/ x1= (dx1)/ x1 = d ln x1

Integrating

ln f1 = ln x1 + C

At x1 = 1 , f1 = f1pure = full fugacity ,therefore C = ln f1pure

ln (f1 / f1pure )= lnx1

f1 = x1 * f1pure

Therefore it is raoult's law.

That is if component two obey Henry's law , component one obey the raoults law.