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.)

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Quizplus · Accepted Answer

The rms speed of the molecules 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.Plugging in the given values, we get:$$v_{rms}=\sqrt{\frac{3(8.31 J/molK)(350 K)}{28 g/mol}}$$$$v_{rms}=560 m/s$$Therefore, the rms speed of the molecules is 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 $350 \mathrm {~K} .$