At what approximate temperature would the rms speed of $\mathrm{H}_{2}$ molecules equal the Earth's escape speed $(11,200 \mathrm{~m} / \mathrm{s})$ ?
A) $10^{8} \mathrm{~K}$
B) $102 \mathrm{~K}$
C) $106 \mathrm{~K}$
D) $104 \mathrm{~K}$

Question

Quizplus · Accepted Answer

The rms speed of a gas is given by:$$v_{rms}=\sqrt{\frac{3RT}{M}}$$where R is the gas constant, T is the temperature, and M is the molar mass. For $\mathrm{H}_{2}$, M = 2 g/mol.Setting $v_{rms}$ equal to the Earth's escape speed and solving for T, we get:$$T=\frac{Mv_{rms}^2}{3R}=\frac{(2 \mathrm{~g/mol})(11,200 \mathrm{~m/s})^2}{3(8.314 \mathrm{~J/mol~K})}=104 \mathrm{~K}$$

At What Approximate Temperature Would the Rms Speed Of H2\mathrm{H}_{2}H2​ Molecules Equal the Earth's Escape Speed

At What Approximate Temperature Would the Rms Speed Of $\mathrm{H}_{2}$ Molecules Equal the Earth's Escape Speed