If the most probable speed of gas molecules is v p = √(2RT/M), and the rms speed is v rms = √(3RT/M), the ratio v rms /v p is:

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If the most probable speed of gas molecules is vp = √(2RT/M), and the rms speed is vrms = √(3RT/M), the ratio vrms/vp is:

Answer: √(3/2).

A √(3/2)
B √(2/3)
C 3/2
D 1

Correct answer: A. √(3/2)

Explanation: vrms/vp = √(3RT/M)/√(2RT/M) = √(3/2) ≈ 1.22, showing vrms is always greater than vp.

Not all gas molecules move at the same speed - the Maxwell-Boltzmann distribution shows the spread, with the most probable speed v_p slightly less than the average v_avg, which is slightly less than the root-mean-square speed v_rms used in the pressure formula.

Concept context

Kinetic theory of gases connects molecular motion to pressure and temperature, explaining gas laws, specific heats, and molecular speeds.

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If the most probable speed of gas molecules is v<sub>p</sub> = √(2RT/M), and the rms speed is v<sub>rms</sub> = √(3RT/M), the ratio v<sub>rms</sub>/v<sub>p</sub> is:

Concept context

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