(a) In a binary liquid system, the enthalpy of species 1 and 2 at constant temperature and pressure is represented by the following equation:

\[ H=400 x_{1}+600 x_{2}+x_{1} x_{2}\left(40 x_{1}+20 x_{2}\right) \quad \text { where } H \text { is in } \mathrm{J} / \mathrm{mol} \]

Determine the expressions for \(\bar{H}_{1}\) and \(\bar{H}_{2}\) as functions of \(x_{1}\) and the numerical values for the pure-species enthalpies \(H_{1}\) and \(H_{2}\).

(b) The activity coefficient of component 1 in a binary solution is represented by

\[ \ln \gamma_{1}=a x_{2}^{2}+b x_{2}^{3}+c x_{2}^{4} \]

where \

(a, b\) and \(c\) are constants independent of concentrations. Obtain an expression for \(\gamma_{2}\) in terms of \(x_{1}\).