In a closed vessel at $25 \, ^oC$ temperature,$4 \, mole$ $O_2$,$3 \, mole$ $Cl_2$,and $3 \, mole$ $N_2$ are mixed,and the total pressure is found to be $50 \, bar$. Find the partial pressure of each gas.

(A) The total number of moles $n_{total} = n_{O_2} + n_{Cl_2} + n_{N_2} = 4 + 3 + 3 = 10 \, mole$.
According to Dalton's Law of Partial Pressure,the partial pressure of a gas is given by $p_i = x_i \times P_{total}$,where $x_i$ is the mole fraction of the gas.
Mole fraction of $O_2$ $(x_{O_2})$ = $4 / 10 = 0.4$.
Mole fraction of $Cl_2$ $(x_{Cl_2})$ = $3 / 10 = 0.3$.
Mole fraction of $N_2$ $(x_{N_2})$ = $3 / 10 = 0.3$.
Partial pressure of $O_2$ $(p_{O_2})$ = $0.4 \times 50 \, bar = 20 \, bar$.
Partial pressure of $Cl_2$ $(p_{Cl_2})$ = $0.3 \times 50 \, bar = 15 \, bar$.
Partial pressure of $N_2$ $(p_{N_2})$ = $0.3 \times 50 \, bar = 15 \, bar$.