Question

At what temperature (in ${}^{\circ }C$) is the root mean square velocity of $O_2$ gas at $300\text{K}$ equal to the most probable velocity of $Ne$ (Given 273 K = 0${}^{\circ }C$)?

Answer 1

According to question
$u_{\text{rms}}=u_{\text{mp}}$
$\sqrt{\frac{3R{T}_1}{M_1}}=\sqrt{\frac{2R{T}_2}{M_2}}$
$T_1=300K$
$M_1=32g/mol$ , $M_2=20g/mol$
$\frac{3\times 300}{32}=\frac{2T_2}{20}$
$T_2=281.25\text{K}$
Thus, $T_2=281.25-273={8.25}^{\circ }C$