A) \[15\times {{10}^{-3}}\]
B) \[64\times {{10}^{-3}}\]
C) \[~5\times {{10}^{-3}}\]
D) \[~46\times {{10}^{-3}}\]
Correct Answer: A
Solution :
Key Idea According to Grahams law of diffusion At constant pressure and temperature, the rate of diffusion of a gas is inversely proportional to the square root of its vapour density. Rate of diffusion \[(r)\propto \frac{1}{\sqrt{d}}\] Molecular weight \[(M)=2\times \]vapour density \[\frac{{{r}_{1}}}{{{r}_{2}}}=\sqrt{\frac{{{M}_{2}}}{{{M}_{1}}}}\] \[{{m}_{A}}=\left( \frac{100}{2} \right)\text{kg/molecule}\] \[{{m}_{B}}=\left( \frac{64}{2} \right)\text{kg/molecule}\] \[{{r}_{A}}=12\times {{10}^{-3}}\]and \[{{r}_{B}}=?\] \[\frac{{{r}_{A}}}{{{r}_{B}}}=\sqrt{\frac{{{d}_{B}}}{{{d}_{A}}}}=\sqrt{\frac{{{M}_{B}}}{{{M}_{A}}}}\] \[\frac{12\times {{10}^{-3}}}{{{r}_{B}}}=\sqrt{\frac{64/2}{100/2}}=\sqrt{\frac{64}{100}}=\frac{8}{10}\] \[{{r}_{B}}=\frac{12\times {{10}^{-3}}\times 10}{8}\] \[=15\times {{10}^{-3}}\]
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