Solve this multiple-choice question and choose the correct option.

ConceptFrom the Maxwell–Boltzmann distribution for molecular speeds, the characteristic speeds are: Most probable speed: vmp = √(2RT/M) = √(2kT/m) Mean (average) speed: v̄ = √(8RT/(πM)) RMS speed: vrms = √(3RT/M) Verification (units)R (J/mol·K), T (K), M (kg/mol) ⇒ RT/M has units m²/s²; square root gives m/s. Common pitfallsDo not confuse vmp with vrms (factor 3) or with v̄ (factor 8/π). Final Answervmp = √(2RT/M)

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Kinetic theory of gases: formula for the most probable molecular speed Select the correct expression for the most probable speed of gas molecules in terms of absolute temperature T and molar mass M (or Boltzmann constant k and molecular mass m). Choose the correct formula.

Difficulty: Medium

v_mp = √(2RT/M)
v_mp = √(3RT/M)
v_mp = √(8RT/(πM))
v_mp = √(kT/m) × √3

Correct Answer: v_mp = √(2RT/M)

Explanation:

ConceptFrom the Maxwell–Boltzmann distribution for molecular speeds, the characteristic speeds are:

Most probable speed: v_mp = √(2RT/M) = √(2kT/m)
Mean (average) speed: v̄ = √(8RT/(πM))
RMS speed: v_rms = √(3RT/M)

Verification (units)R (J/mol·K), T (K), M (kg/mol) ⇒ RT/M has units m²/s²; square root gives m/s.

Common pitfallsDo not confuse v_mp with v_rms (factor 3) or with v̄ (factor 8/π).

Kinetic theory of gases: formula for the most probable molecular speed Select the correct expression for the most probable speed of gas molecules in terms of absolute temperature T and molar mass M (or Boltzmann constant k and molecular mass m). Choose the correct formula.

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