An equimolar vapor mixture of propane $(1)$ and n$-$pentane $(2)$ at $75C$ and $2$ bar has the

following $2^{nd}$ virial coefficients:

$B_{11}=-276c\frac{m^3}{m}ol$

$B_{22}=-809c\frac{m^3}{m}ol$

$B_{12}=-466c\frac{m^3}{m}ol$

a$)$ Evaluate the fugacities hat$(f{)}_1,$hat$(f{)}_2$ at $75C$ and $2$ bar according to Virial EOS for mixtures

b$)$ Evaluate the fugacities hat$(f{)}_1,$hat$(f{)}_2$ at $75C$ and $2$ bar according to the ideal solution model,

where the fugacity coefficients are approximated by the pure fugacity coefficients ${}_i$