At what temperature will the root mean square | vedclass

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Question

(B) The root mean square speed $(u_{rms})$ is given by the formula $u_{rms} = \sqrt{\frac{3RT}{M}}$.For the speeds to be equal,$\sqrt{\frac{3RT_1}{M_1

Vedclass · Accepted Answer

$177$

Vedclass · Answer

(B) The root mean square speed $(u_{rms})$ is given by the formula $u_{rms} = \sqrt{\frac{3RT}{M}}$.For the speeds to be equal,$\sqrt{\frac{3RT_1}{M_1}} = \sqrt{\frac{3RT_2}{M_2}}$,which simplifies to $\frac{T_1}{M_1} = \frac{T_2}{M_2}$.Here,$M_1$ (molar mass of $O_3$) = $48 \, g/mol$,$M_2$ (molar mass of $O_2$) = $32 \, g/mol$,and $T_2 = 27 + 273 = 300 \, K$.Substituting the values: $\frac{T_1}{48} = \frac{300}{32}$.$T_1 = \frac{300 	imes 48}{32} = 300 	imes 1.5 = 450 \, K$.Converting back to Celsius: $450 - 273 = 177 \, ^oC$.

At what temperature will the root mean square speed of ozone $(O_3)$ be equal to the root mean square speed of oxygen $(O_2)$ at $27\,^oC$?

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