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Calculate the ratio of the effusion of \(\mathrm{CO}\) and \(\mathrm{N}_2\), when temperature and pressure gradients are held constant?
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The correct answer is:
\(1: 1\)
The rate of effusion of a gas is inversely proportional to the square root of the mass of its particles.
Rate of effusion \(\propto \frac{1}{\sqrt{\text { Molecular mass }}}\)
If two gases \(\mathrm{CO}\) and \(\mathrm{N}_2\) are at the same temperature and pressure, the ratio of their effusion rates is inversely proportional to the ratio of the square roots of their molar masses.
\(\frac{\text { Rate effusion of } \mathrm{CO}}{\text { Rate of effusion of } \mathrm{N}_2} \propto \frac{\sqrt{M_{\mathrm{N}_2}}}{\sqrt{M_{\mathrm{CO}}}}\)
\(\Rightarrow \quad \sqrt{\frac{28}{28}} \Rightarrow 1: 1\)
Hence, the correct option is (b).
Rate of effusion \(\propto \frac{1}{\sqrt{\text { Molecular mass }}}\)
If two gases \(\mathrm{CO}\) and \(\mathrm{N}_2\) are at the same temperature and pressure, the ratio of their effusion rates is inversely proportional to the ratio of the square roots of their molar masses.
\(\frac{\text { Rate effusion of } \mathrm{CO}}{\text { Rate of effusion of } \mathrm{N}_2} \propto \frac{\sqrt{M_{\mathrm{N}_2}}}{\sqrt{M_{\mathrm{CO}}}}\)
\(\Rightarrow \quad \sqrt{\frac{28}{28}} \Rightarrow 1: 1\)
Hence, the correct option is (b).
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