Question

$RMS$ speed of $O_2$ molecule and that $H_2$ molecule at a given temperature are in the ratio of:

• A. $\frac{u_{O_1}}{u_{H_2}}=\frac{1}{1}$
• B. $\frac{u_{O_1}}{u_{N_3}}=\frac{4}{1}$
• C. $\frac{u_{O_2}}{u_{H_3}}=\frac{1}{4}$
• D. $\frac{u_{O_2}}{u_{N_3}}=\frac{1}{16}$

Answer 1

Answer: (C)

$\frac{u_{O_2}}{u_{H_3}}=\frac{1}{4}$

The RMS values can be calculated using the below formula:

$V_R=\sqrt{\frac{3RT}{M}}{V}_{R{O}_2}=\sqrt{\frac{3RT}{M_{O_2}}}\frac{V_{R_{O2}}}{V_{R_{H_2}}}=\frac{M{H}_2}{M{O}_2}{V}_{R_{O_2}}:V_{R_{H_2}}=1:4$