Question

. In a mixture of acetone and trichlormethane at 298 K, K_{trichloromethane} = 22.0 kPa, whereas p^*_{trichloromethane} = 36.4 kPa. What is the relation between the standard chemical potential and that of the pure liquid?

Answer 1

If a solute of a solution follows henry's law with the vapour pressure p_a, then p_a=K_ax_a

So, the chemical potential of the solute will be,_a =_a^* + RT(lnp_a/p_a^*) =_a^* + RT(lnK_a/p_a^*) + RTlnx_a

Where, R= gas constant = 8.314 4621 J K^-1 mol^-1

So, the new standard chemical potential, '_a = _a^* + RT(lnK_a/p_a^*)

from the above data, K_{trichloromethane} = 22.0 kPa and p^*_{trichloromethane} = 36.4 kPa

the temperature of the mixture is 298 K

So, the relation between the standard chemical potential and that of the pure liquid,

'_{trichloromethane} = ^*_{trichloromethane} + RT(lnK_{trichloromethane}/p^*_{trichloromethane})

= ^*_{trichloromethane} + 8.3144621J K^-1 mol^-1298 K(ln 22.0 kPa/ 36.4 kpa)

=  ^*_{trichloromethane} -1247.59 Jmol^-1

Here,

'_{trichloromethane} = standard chemical potential of trichloromethane

^*_{trichloromethane} = chemical potential of pure trichloromethane