The enthalpy of a binary liquid system of species $1$ and $2$ at

fixed $T$ and $P$ is represented by the equation

$H=400x_1+600x_2+x_1{x}_2(40x_1+20x_2)$

where $H$ is in $J*mo{l}^{-1}.$ The partial enthalpies are

$\frac{?}{\text{b}\text{a}\text{r}}(H{)}_1=420-60x_1^2+40x_1^3\frac{?}{b}$

$ar(H{)}_2=600+40x_1^3$

Apply the equation $\frac{?}{\text{b}\text{a}\text{r}}(M{)}_i=(\frac{\text{d}\text{e}\text{l}(nM)}{del{n}_i}{)}_{P,T,n_j}$ to equation $(A)$ to verify equations $(B)$ and $(C)$