The rms speed of hydrogen is sqrt{7} times th | vedclass

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(C) The formula for $rms$ speed is $v_{rms} = \sqrt{\frac{3RT}{M}}$.Given $\frac{v_{rms}(H_2)}{v_{rms}(N_2)} = \sqrt{7}$.So,$\sqrt{\frac{T(H_2)}{M(H_2

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$T(H_2) < T(N_2)$

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(C) The formula for $rms$ speed is $v_{rms} = \sqrt{\frac{3RT}{M}}$.Given $\frac{v_{rms}(H_2)}{v_{rms}(N_2)} = \sqrt{7}$.So,$\sqrt{\frac{T(H_2)}{M(H_2)}} 	imes \sqrt{\frac{M(N_2)}{T(N_2)}} = \sqrt{7}$.Substituting molar masses $M(H_2) = 2 \ g/mol$ and $M(N_2) = 28 \ g/mol$:$\sqrt{\frac{T(H_2)}{2} 	imes \frac{28}{T(N_2)}} = \sqrt{7}$.$\sqrt{14 	imes \frac{T(H_2)}{T(N_2)}} = \sqrt{7}$.Squaring both sides: $14 	imes \frac{T(H_2)}{T(N_2)} = 7$.$\frac{T(H_2)}{T(N_2)} = \frac{7}{14} = \frac{1}{2}$.Therefore,$T(N_2) = 2T(H_2)$,which implies $T(H_2) < T(N_2)$.

The $rms$ speed of hydrogen is $\sqrt{7}$ times the $rms$ speed of nitrogen. If the temperature of the gases is $T$,then:

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