$1.$ A semi$-$permeable membrane which allows only N$2$ to pass divides two containers which are kept at $350$ K$.$ Initially, container A holds $2$ kg of CO$2$ at $10$ bar, and container B holds $3$ kg of Xe at $20$ bar. Now an unknown amount of nitrogen is added to the system, such that the pressures of A and B do not change. After thermodynamic equilibrium is established, it is observed that the volume of container A has increased by $25\%.$ a$)$ Determine the amount of N$2$ added to container A$.$ b$)$ Determine the amount of N$2$ added to container B$.$ c$)$ Determine the minimum work to separate the nitrogen out of container A$.1.$ A semi$-$permeable membrane which allows only $\backslash (\backslash$mathrm$\{$N$\}\_\{2\}\backslash )$ to pass divides two containers which are kept at $350$ K $.$ Initially, container A holds $2$ kg of $\backslash (\backslash$mathrm$\{$CO$\}\_\{2\}\backslash )$ at $10$ bar, and container B holds $3$ kg of Xe at $20$ bar. Now an unknown amount of nitrogen is added to the system, such that the pressures of A and B do not change. After thermodynamic equilibrium is established, it is observed that the volume of container A has increased by $\backslash (25\backslash \%\backslash ).$

a$)$ Determine the amount of $\backslash (\backslash$mathrm$\{$N$\}\_\{2\}\backslash )$ added to container A $.$

b$)$ Determine the amount of $\backslash (\backslash$mathrm$\{$N$\}\_\{2\}\backslash )$ added to container B$.$

c$)$ Determine the minimum work to separate the nitrogen out of container A $.$