Problem $4.(3$ points$)$ Compute the density of the mixture consisting equal

moles of methane and ethane at $1$atm and $20$ degree Celsius, using the Peng$-$

Robinson equation of state $($PR$-$EOS$).$ You may need the critical properties and

normal boiling points $($as provided in the textbook as well as in the class slides$)$ and

the binary interaction coefficients for the PR$-$EOS as provided in Table $1.$ Report

your results using the unit of $\frac{g}{c}{m}^3.$ Please carry out the computation manually

$($instead of designing a MATLAB or R code for the computation$).$ Please list the

details of your solution procedure.