$******3\mathrm{.}2\mathrm{.}11.$ In preparing $2\mathrm{.}50$ moles of a mixture of three gases, $S{O}_2,H_{2}S,$ and $C{S}_2,$ gases from three

tanks are combined into a fourth tank. The tanks have the following compositions $($mole

fractions$)$:

Combined Tanks Mixture

In the right$-$hand column is listed the supposed composition obtained by analysis of the

mixture. Does the set of three mole balances for the three compounds have a solution for

the number of moles taken from each of the three tanks and used to make up the mixture? If

so$,$ what does the solution mean?

a$)$ Denote the total number of moles, sum of the three components, in each tank as

a$)$ Tank $1$:$n_{t1}$

b$)$ Tank $2$: $n_{t2}$

c$)$ Tank $3$: $n_{t3}$

d$)$ Tank $4$: $n_{t4}=2\mathrm{.}5$ moles

b$)$ Write the mass balance $($MB$)$ equation for each compound $(5$ points$)$

c$)$ Calculate the degree of freedom $(2$ points$)$

d$)$ Solve the problem if the system is determined. If the system is under$-$determined, assume

additional constraint$($s$)$ to have a determined system. You may use MS Excel or MATLAB to solve

the $MB$ equations. $(5$ points$)$

e$)$ Analyze your solution, and answer the questions asked in the stated problem. $(3$ points$)$