We are going to use the following corresponding$-$state formulation of residual molar Gibbs free

energy for pure species: $G_{{?}^{?}}(R)=G_{-}{G}_{{?}^{?}}(ig),$ where $T_r=\frac{T}{T_c},P_{\text{I}}=\frac{P}{P_c},$ and $$ are reduced temperature,

reduced pressure, and acentric factor, respectively, and $T_c$ and $P_c$ are critical temperature and critical

pressure. $\frac{G^R}{RT}=\frac{P_r}{T_r}[0\mathrm{.}083-\frac{0\mathrm{.}422}{T_r^{1\mathrm{.}6}}+(0\mathrm{.}139-\frac{0\mathrm{.}172}{T_r^{4\mathrm{.}2}})]$

$($a$)(15$ pts$)$ Considering $T=T_r{T}_c$ and $P=P_r{P}_c,$ convert $d(\frac{G_{{?}^{?}}(R)}{RT})=\frac{V_{{?}^{?}}(R)}{RT}dP-\frac{H_{{?}^{?}}(R)}{R{T}^2}dT$ to

$d(\frac{G_{{?}^{?}}(R)}{RT})=\frac{P_c}{T_c}\frac{V_{{?}^{?}}(R)}{R{T}_r}d{P}_r-\frac{1}{T_c}\frac{H_{{?}^{?}}(R)}{R{T}_r^2}d{T}_r$

$($b$)(15$ pts$)$ Use $($a$)$ to get $V_{{?}^{?}}(R)$ and then $Z-1=\frac{P{V}_{{?}^{?}}(R)}{RT}$ to obtain the corresponding compressibility

factor as $Z=1+\frac{P_r}{T_r}[0\mathrm{.}083-\frac{0\mathrm{.}422}{T_r^{1\mathrm{.}6}}+(0\mathrm{.}139-\frac{0\mathrm{.}172}{T_r^{4\mathrm{.}2}})]$

Evaluate the molar enthalpy change $H_{?}$ of saturated water vapor from $6\mathrm{.}97C$ to $107\mathrm{.}11C$

$($a$)(25$ pts$)$ using the heat capacity correlation in textbook Table D$.1($low vapor $P$ ideal gas state$)$

$($b$)(15$ pts$)$ using the steam table in the textbook and determining the $\%$ difference w$.$r$.$t$.($a$)($note:

unit conversion is needed in order to ensure consistency$)$

Two flow streams represented by $K$ and $M$ on the triangular diagram enter a mixer at $40k\frac{g}{m}in$ and

$80k\frac{g}{m}in,$ respectively.

$($a$)(10$ pts$)$ carry out mass balance to determine the overall composition in the mixer and mark it on

the phase diagram.

$($b$)(25$ pts$)$ Two equilibrium liquid phases will develop in the mixer. Draw a tie line to determine

their compositions and then the flow rate in $k\frac{g}{m}in$ of the water$-$rich liquid phase.