Q$1.(25$ marks$)$

For methyl chloride vapor at $100C,$ second and third virial coefficients are:

$B=-242\mathrm{.}5c\frac{m^3}{m}ol$ and $C=25,200c\frac{m^6}{m}o{l}^2$

Calculate work of mechanically reversible, isothermal compression of $1$mol of methyl

chloride from $1$ bar to $55$ bar at $100C$ using:

a$.Z=1+\frac{B}{V}+\frac{C}{V^2}=P\frac{V}{R}T(10$ marks$)$

b$.Z=1+B^{\text{'}}P+C^{\text{'}}{P}^2(10$ marks$)$

$B^{\text{'}}=\frac{B}{RT}$ and $C^{\text{'}}=\frac{C-B^2}{(RT{)}^2}$

Also find $Z_1$ and $Z_2(5$ marks$)$PLEASE ACCOUNT FOR ALL CONVERSIONS PLEASE IT CONFUSES ME EXAIVIPLE PRUBLEIVI $2-$ For methyl chloride at $100$ oC the second and third virial coefficient are:

B$=-242\mathrm{.}5$cm$^3$mol$^-1$ C$=25,200$cm$^6$mol$^-2$

Calculate the work of mechanically reversible, isothermal compression of $1$ mol of methyl chloride from $1$ bar to $55$ bar at $100$ oC$.$ Base calculations on the following forms of the virial equation: $($a$)$ Z$=1+$B$/$V$+$C$/$V$^2($b$)$ Z$=1+$B P$+$ P$^2$ where B$=$B$/$R T and C$=^\text{'}$ C$-$B$^2/($R T$)^2$ Why don't both equations give the same result?