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  • 57. At what temperature will the rms speed of a hydrogen molecule be equal to that of an oxygen molecule at <img alt="47^{\circ} \mathrm{C}" src="https://entrancecorner.oncodecogs.com/gif.late

57. At what temperature will the rms speed of a hydrogen molecule be equal to that of an oxygen molecule at 47^{\circ} \mathrm{C} 

Option: 1

253


Option: 2

-254^{\circ} \mathrm{C}


Option: 3

+253^{\circ} \mathrm{C}


Option: 4

-253^{\circ} \mathrm{C}


Answers (1)

Molecular weight of Oxygen and hydrogen, respectively are

M_{1}=32 and M_{2}=2 and rms speed, c=\sqrt{\frac{3 R T}{M}}

\therefore \frac{C_{1}}{C_{2}}=\sqrt{\frac{T_{1}}{T_{2}} \cdot \frac{M_{2}}{M_{1}}}

Here, c_{1}=c_{2} and T_{1}=47^{\circ} \mathrm{c}=320 \mathrm{~K}

\begin{aligned} & \therefore \frac{T_{1}}{T_{2}} \cdot \frac{M_{2}}{M_{1}}=1 \\ & \text { or, } {T_{2}}=T_{1} \cdot \frac{M_{2}}{M_{1}}=320 \times \frac{2}{32} \\ & =20 \mathrm{~K}=(20-273)^{\circ} \mathrm{C}=-253^{\circ} \mathrm{C} . \end{aligned}

Posted by

Ramraj Saini

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