Question $1(30$p$)$: The fugacities of pure components $(1)$ and $(2)$ at $25C$ temperature are given as $646mmHg$ and $283mmHg$ respectively. The partial fugacities of components $(1)$ and $(2)$ were measured as $332mmHg$ and $190mmHg$ in a mixture of them at the same temperature. If the mole fraction of component $(2)$ in the mixture is $0\mathrm{.}6,$ calculate,

a$)$ The activity coefficients, and the excess chemical potentials of components $(1)$ and $(2)$

b$)$ The excess Gibbs free energy of $1$ mol mixture at the same temperature.