At what temperature will the oxygen molecules | vedclass

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(D) The root mean square speed $(v_{rms})$ of gas molecules is given by the formula: $v_{rms} = \sqrt{\frac{3RT}{M}}$.Since $v_{rms}$ is the same for

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(D) The root mean square speed $(v_{rms})$ of gas molecules is given by the formula: $v_{rms} = \sqrt{\frac{3RT}{M}}$.Since $v_{rms}$ is the same for both gases and $R$ is a constant,we have $v_{rms} \propto \sqrt{\frac{T}{M}}$.Therefore,$\frac{T_{O_2}}{M_{O_2}} = \frac{T_{H_2}}{M_{H_2}}$.Given $T_{H_2} = 200 \, K$,$M_{H_2} = 2 \, g/mol$,and $M_{O_2} = 32 \, g/mol$.Substituting the values: $\frac{T_{O_2}}{32} = \frac{200}{2}$.$T_{O_2} = 100 	imes 32 = 3200 \, K$.

At what temperature will the oxygen molecules have the same root mean square speed as hydrogen molecules at $200 \, K$ (in $, K$)?

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