The ratio of root mean square velocity of hyd | vedclass

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Question

(A) The root mean square velocity $(v_{rms})$ of a gas is given by the formula: $v_{rms} = \sqrt{\frac{3RT}{M}}$where $R$ is the gas constant,$T$ is t

Vedclass · Accepted Answer

$1.18$

Vedclass · Answer

(A) The root mean square velocity $(v_{rms})$ of a gas is given by the formula: $v_{rms} = \sqrt{\frac{3RT}{M}}$where $R$ is the gas constant,$T$ is the temperature,and $M$ is the molar mass of the gas.For hydrogen gas $(H_2)$: $M = 2 \, g/mol$,$T = 50 \, K$.$(v_{rms})_{H_2} = \sqrt{\frac{3 	imes R 	imes 50}{2}} = \sqrt{75R}$.For nitrogen gas $(N_2)$: $M = 28 \, g/mol$,$T = 500 \, K$.$(v_{rms})_{N_2} = \sqrt{\frac{3 	imes R 	imes 500}{28}} = \sqrt{\frac{1500R}{28}} = \sqrt{53.57R}$.The ratio is $\frac{(v_{rms})_{H_2}}{(v_{rms})_{N_2}} = \sqrt{\frac{75R}{53.57R}} = \sqrt{1.4} \approx 1.18$.

The ratio of root mean square velocity of hydrogen at $50 \, K$ to that of nitrogen at $500 \, K$ is closest to

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