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At \(0^{\circ} \mathrm{C}\), the density of a certain oxide of a gas at 2 bar is same as that of dinitrogen at 5 bar. What is the molecular mass of the oxide ?
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Verified Answer
Using the expression, \(\mathrm{d}=\frac{\mathrm{MP}}{\mathrm{RT}}\)
\(\therefore \mathrm{d}_1=\mathrm{d}_2\)
\(\begin{aligned}
&\Rightarrow \frac{\mathrm{M}_1 \mathrm{P}_1}{\mathrm{RT}}=\frac{\mathrm{M}_2 \mathrm{P}_2}{\mathrm{RT}} \\
&\Rightarrow \frac{2 \times \mathrm{M}_1}{\mathrm{RT}}=\frac{5 \times 28}{\mathrm{RT}} \\
&\mathrm{M}_1=70 \mathrm{u}
\end{aligned}\)
\(\therefore \mathrm{d}_1=\mathrm{d}_2\)
\(\begin{aligned}
&\Rightarrow \frac{\mathrm{M}_1 \mathrm{P}_1}{\mathrm{RT}}=\frac{\mathrm{M}_2 \mathrm{P}_2}{\mathrm{RT}} \\
&\Rightarrow \frac{2 \times \mathrm{M}_1}{\mathrm{RT}}=\frac{5 \times 28}{\mathrm{RT}} \\
&\mathrm{M}_1=70 \mathrm{u}
\end{aligned}\)
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