A certain cryogenic process is concerned with an equimolar mixture of argon $(1)$ and eth$-$

ane $(2)$ at $110K.$ To design a separation process, a rough estimate is required for the en$-$

thalpy of mixing for this liquid mixture. Make this estimate using van der Waals' equa$-$

tion of state with the customary mixing rules, $b_{\text{m}\text{i}\text{x}\text{t}}={}_i{x}_i{b}_i$ and $a_{\text{m}\text{i}\text{x}\text{t}}={}_i{}_j{x}_i{x}_j{a}_{ij}$

with $a_{ij}=(a_{ij}{)}^{\frac{1}{2}}(1-k_{ij}).$ Assume that $v_{\text{m}\text{i}\text{x}\text{t}}={\displaystyle \underset{i}{\overset{?}{}}}{x}_i{v}_i$ and, because pressure is low, that

${}_{\text{m}\text{i}\text{x}}U={}_{\text{m}\text{i}\text{x}}H,$ where $U$ is the internal energy and $H$ is the enthalpy. Data are:

Second$-$virial$-$coefficient data for this mixture indicate that $k_{ij}(ij)=0\mathrm{.}1.$

"This $b$ is obtained from critical volume. The inadequacy of the van der Waals equation is evident because, as

shown here, $b>v$ at $110K.$ Fortunately this unrealistic result does not affect the solution to Problem $9.$