Enthalpy of mixing of a non-ideal solution
There are two ways (at least) to solve this:
(1) Evaluate $\Delta S = -\left( \frac{\partial \Delta G}{\partial T} \right)_{p,n} $
and add $T\Delta S$ to $\Delta G$.
or
(1) Evaluate directly $\Delta H = -T^2 \left( \frac{\partial (\Delta G/T)}{\partial T} \right)_{p,n} $
Either way I obtained the result
$\Delta H = \chi n_1 \phi_2 - n_1\phi_2 T \left( \frac{\partial \chi }{\partial T} \right)_{p,n} $