Question

The root mean square speed of $\text{C}{\text{H}}_{\text{4}}$ molecules at ${\text{25}}^{\circ }\text{C}$ is about 0.56 km/s. What is the root mean square speed of ${\text{H}}_{\text{2}}$ molecule at ${\text{25}}^{\circ }\text{C}$?

• A. $0.070km/s$
• B. $0.20km/s$
• C. $1.1km/s$
• D. $16km/s$

Answer 1

Answer: (D)

$16km/s$

$\frac{RM{s}_1}{RM{s}_2}=\frac{0.56}{x}$

$\sqrt{\frac{3R{T}_1}{M_1}}\times \sqrt{\frac{M_2}{3R{T}_2}}=\frac{6-56}{x}$

$\sqrt{\frac{2}{16}}=\frac{0.56}{x}$

$x=2\sqrt{2}\times 0.56$

$=1.6Km/s$.