Q$2[1$pts: FS$23$Exam$3]$ Write a MATLAB code $($HW$08$Q$1$LasF.m$)$ to plot the compressibility factor $($z$)$ of $,)=405\mathrm{.}7(K),p_c=111\mathrm{.}3(atm),=(0\mathrm{.}253$ for both liquid and vapor between $p=5$ and $90$atm at $T=250K$ using Redlich$-$Kwong $($RK$)$ EOS model $($The formula was given in HW$07$Q$1$ and HW$08$Q$1).$

Use R$=0\mathrm{.}08206$ atm L$/$gmol K

For HW$08,$ you can define the EOS model either using an anonymous function $($as in HW$07$Q$1)$ or an external function $($as in HW$07$Q$2$: will be asked in the test$).$

Use for$-$loop to change $p$ between $p=5$ atm and $90$atm.

At each $p,$ solve the RK EOS for both liquid molar volume $(v_L)$ and vapor molar volumes $(v_v)($see HW$07$Q$1$ and HW$07$Q$2).$

Then calculate the compressibility factor at each phase: $z_L=p\frac{v_L}{R}T$ and $z_v=p\frac{v_v}{R}T$

The answer should look like the following $($indication of "phase change" is option