Explanation:
\begin{aligned}
&\eta N _{2}=0.25 mol , \eta O _{2}=0.15 mol , \\
&\eta He =0.4 mol \\
&\eta_{\text {Toul }}=0.25+0.15+0.4=0.8 mol \\
&\text { required equations (formulae) } \\
&\text { Mole fraction } X_{A}=\frac{\eta_{A}}{\eta_{T}} \ldots \ldots \ldots . . .(1)
\end{aligned}
also \(X_{A}=\frac{P_{A}}{P_{T}}\).
\(X_{A}=\) mole fraction of gas \(A\)
\(\eta_{1}=\) no of mole of gas \(A\)
\(\eta_{T}\) - Total no of mole of the gases
\(P_{A}=\) Partial pressure of \(A\)
\(P_{T}=\) Total partial pressure of the gases
\(P_{O_{2}}=2.5 atm\)
\(X_{o_{1}}=\frac{\eta_{o_{7}}}{\eta_{T}}=\frac{0.15}{0.8}=0.1275\)rom eqn (2)
\begin{aligned}
P_{T} &=\frac{P_{O_{2}}}{X_{A}}=\frac{2.5}{0.1875}=13.33 atm \\
X_{H e} &=\frac{0.4}{0.8}=0.5 \\
P_{H e} &=X_{H e} \times P_{T}=0.5 \times 13.33 \\
&=6.67 atm
\end{aligned}