If the rms speed of oxygen molecules at 0^{ci | vedclass

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(A) The $rms$ speed of gas molecules is given by the formula: $V_{rms} = \sqrt{\frac{3RT}{M}}$,where $R$ is the universal gas constant,$T$ is the temp

Vedclass · Accepted Answer

$640$

Vedclass · Answer

(A) The $rms$ speed of gas molecules is given by the formula: $V_{rms} = \sqrt{\frac{3RT}{M}}$,where $R$ is the universal gas constant,$T$ is the temperature in Kelvin,and $M$ is the molar mass of the gas.Since the temperature $T$ is the same for both gases,we have $V_{rms} \propto \frac{1}{\sqrt{M}}$.Therefore,the ratio of the $rms$ speeds is: $\frac{(V_{rms})_{O_2}}{(V_{rms})_{H_2}} = \sqrt{\frac{M_{H_2}}{M_{O_2}}}$.The molar mass of oxygen $(O_2)$ is $32 \; {g/mol}$ and the molar mass of hydrogen $(H_2)$ is $2 \; {g/mol}$.Substituting the values: $\frac{160}{(V_{rms})_{H_2}} = \sqrt{\frac{2}{32}} = \sqrt{\frac{1}{16}} = \frac{1}{4}$.Thus,$(V_{rms})_{H_2} = 160 	imes 4 = 640 \; {m/s}$.

If the $rms$ speed of oxygen molecules at $0^{\circ} {C}$ is $160 \; {m/s}$,find the $rms$ speed of hydrogen molecules at $0^{\circ} {C}$ (in ${m/s}$).

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