Physics - Heat & Thermo Question with Solution | TestHub

A number of moles of,$O_2=\frac{m_1}{32}$, the number of moles of,$H_2=\frac{m_2}{2}$. Using the ideal gas equation,$PV=\left[\frac{m_1}{32}+\frac{m_2}{2}\right]\frac{25}{3}\times 300$,
$$\begin{gathered} 400\times {10}^3\times 500\times {10}^{-6}=\left[\frac{m_1}{32}+\frac{m_2}{2}\right]25\times 100 \\ \Rightarrow 2\times {10}^2=\left[\frac{m_1}{m_2}\times \frac{1}{32}+\frac{1}{2}\right]m_2\times 25\times 100 \end{gathered}$$
$\Rightarrow \frac{2}{25}=\left[\frac{m_1}{m_2}\times \frac{1}{32}+\frac{1}{2}\right]m_{2 }...\left(1\right)$
$\Rightarrow m_1+m_2=0.76$
$\Rightarrow m_2\left[1+\frac{m_1}{m_2}\right]=\frac{76}{100} ...\left(2\right)$
$\left(1\right)$divided by$\left(2\right)$;$\frac{\left[\frac{m_1}{m_2}\times \frac{1}{32}+\frac{1}{2}\right]}{\left[\frac{m_1}{m_2}+1\right]}=\frac{2}{25}\times \frac{100}{76}$
Let assume,
$$\begin{gathered} \Rightarrow \frac{m_1}{m_2}=x\Rightarrow \frac{x+16}{32\left[x+1\right]}=\frac{8}{76} \\ \Rightarrow 76x+76\times 16=8\times 32x+8\times 32 \\ \Rightarrow 76x+1216=256x+256 \end{gathered}$$
$960=180x\Rightarrow x=\frac{96}{18}=\frac{16}{3}$