The rate of diffusion of methane at 1.0 atm | vedclass

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(A) According to Graham's law of diffusion, the rate of diffusion $(r)$ is inversely proportional to the square root of the density $(\rho)$ of the ga

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$44$

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(A) According to Graham's law of diffusion, the rate of diffusion $(r)$ is inversely proportional to the square root of the density $(ho)$ of the gas: $r \propto \frac{1}{\sqrt{ho}}$.From the ideal gas equation, $PV = nRT = \frac{m}{MW} RT$, where $m$ is the mass and $MW$ is the molecular weight.Rearranging gives $\frac{m}{V} = ho = \frac{P 	imes MW}{RT}$.Since $T$ is constant, $ho \propto P 	imes MW$.Therefore, the rate of diffusion is given by $r \propto \frac{1}{\sqrt{P 	imes MW}}$.For two gases, $\frac{r_{CH_4}}{r_X} = \sqrt{\frac{P_X 	imes (MW)_X}{P_{CH_4} 	imes (MW)_{CH_4}}}$.Given $r_{CH_4} = 2r_X$, $P_{CH_4} = 1.0 \ atm$, $P_X = 1.45 \ atm$, and $(MW)_{CH_4} = 16 \ g/mol$:$2 = \sqrt{\frac{1.45 	imes (MW)_X}{1.0 	imes 16}}$.Squaring both sides: $4 = \frac{1.45 	imes (MW)_X}{16}$.$(MW)_X = \frac{4 	imes 16}{1.45} = \frac{64}{1.45} \approx 44.13 \approx 44$.

Column-$I$	Column-$II$
$A$. Hydrogen gas $(P=200 \ atm, T=273 \ K)$	$p$. Compressibility factor $Z \neq 1$
$B$. Hydrogen gas $(P \approx 0, T=273 \ K)$	$q$. Attractive forces are dominant
$C$. $CO_2$ $(P=1 \ atm, T=273 \ K)$	$r$. $PV=nRT$
$D$. Real gas with very large molar volume	$s$. $P(V_m-b)=RT$

The rate of diffusion of methane at $1.0 \ atm$ pressure is twice that of another gas '$X$' kept at $1.45 \ atm$. The molecular weight of the gas '$X$' is
[$T$ kept constant]

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The rate of diffusion of methane at $1.0 \ atm$ pressure is twice that of another gas '$X$' kept at $1.45 \ atm$. The molecular weight of the gas '$X$' is[$T$ kept constant]