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Q.

A gas of unknown identity effuses at the rate of $83.3 m l s^{- 1}$ in an effusion apparatus in which carbon dioxide effuses at the rate of $102 m l s^{- 1}$ calculate the molar mass of unknown gas

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answer is 66.

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Detailed Solution

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$r_{x} = 83.3 m l s^{- 1}$ $r_{C O_{2}} = 102 m l s^{- 1}$

From Graham’s law $\frac{r_{x}}{r_{C O_{2}}} = \sqrt{\frac{M_{C O_{2}}}{M_{x}}}$ $\Rightarrow \frac{83.3}{102} = \sqrt{\frac{44}{M_{x}}}$

$M_{x} = 44 \times {(\frac{102}{83.3})}^{2} = 65.97 g m o l^{- 1}$

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A gas of unknown identity effuses at the rate of 83.3 ml s−1 in an effusion apparatus in which carbon dioxide effuses at the rate of 102 ml s−1 calculate the molar mass of unknown gas