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(C) The total kinetic energy $(E)$ of an ideal gas is given by the formula $E = \frac{3}{2} nRT$,where $n$ is the number of moles,$R$ is the gas const

Vedclass · Accepted Answer

$(E)_{H_2} = 4 	imes (E)_{CH_4}$

Vedclass · Answer

(C) The total kinetic energy $(E)$ of an ideal gas is given by the formula $E = \frac{3}{2} nRT$,where $n$ is the number of moles,$R$ is the gas constant,and $T$ is the temperature.Since $n = \frac{	ext{mass}(m)}{	ext{molar mass}(M)}$,the expression becomes $E = \frac{3}{2} 	imes \frac{m}{M} 	imes R 	imes T$.Let the mass of both gases be $m$. The molar mass of $H_2$ is $M_{H_2} = 2 \ g/mol$ and for $CH_4$ is $M_{CH_4} = 16 \ g/mol$.For $H_2$: $(E)_{H_2} = \frac{3}{2} 	imes \frac{m}{2} 	imes R 	imes 100 = 75 	imes m 	imes R$.For $CH_4$: $(E)_{CH_4} = \frac{3}{2} 	imes \frac{m}{16} 	imes R 	imes 200 = 18.75 	imes m 	imes R$.Comparing the two: $\frac{(E)_{H_2}}{(E)_{CH_4}} = \frac{75}{18.75} = 4$.Therefore,$(E)_{H_2} = 4 	imes (E)_{CH_4}$.

Two flasks $A$ and $B$ of equal volume contain equal masses of $H_2$ and $CH_4$ gases at $100 \ K$ and $200 \ K$ temperature respectively. Which of the following relations is correct about the total kinetic energy $(E)$?

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