A 0.50 $m ^ { 3 }$ gas tank holds 3.0 moles of ideal diatomic nitrogen gas at a temperature of $350 \mathrm {~K} .$ The atomic mass of nitrogen is $14.0 \mathrm {~g} / \mathrm { mol }$ . What is the rms speed of the molecules? (The Boltzmann constant is 1.38 × 10^-23 J/K, N_A = 6.022 × 10²³ molecules/mol.)

Question

Quizplus · Accepted Answer

The rms speed $ v_{rms} $ is given by the formula $ v_{rms} = \sqrt{\frac{3kT}{m}} $, where $ k $ is the Boltzmann constant, $ T $ is the temperature, and $ m $ is the mass of one molecule. For nitrogen, the molar mass is 28 g/mol, so the mass of one molecule is $ \frac{28 \times 10^{-3}}{6.022 \times 10^{23}} $ kg. Substituting the values, we find $ v_{rms} \approx 560 $ m/s.

A 050 m3m ^ { 3 }m3 Gas Tank Holds 3 350 K.350 \mathrm {~K} .350 K.

A 050 $m ^ { 3 }$ Gas Tank Holds 3 $350 \mathrm {~K} .$