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If the molar mass of a gas is halved, what happens to its RMS speed?

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Question: If the molar mass of a gas is halved, what happens to its RMS speed?

Options:

  1. Increases by a factor of sqrt(2)
  2. Increases by a factor of 2
  3. Decreases by a factor of sqrt(2)
  4. Remains the same

Correct Answer: Increases by a factor of sqrt(2)

Solution: 

If the molar mass is halved, the RMS speed increases by a factor of sqrt(2) because RMS speed is inversely proportional to the square root of molar mass.

If the molar mass of a gas is halved, what happens to its RMS speed?

Practice Questions

Q1
If the molar mass of a gas is halved, what happens to its RMS speed?
  1. Increases by a factor of sqrt(2)
  2. Increases by a factor of 2
  3. Decreases by a factor of sqrt(2)
  4. Remains the same

Questions & Step-by-Step Solutions

If the molar mass of a gas is halved, what happens to its RMS speed?
Correct Answer: RMS speed increases by a factor of sqrt(2)
  • Step 1: Understand that RMS speed (Root Mean Square speed) is a measure of the speed of gas molecules.
  • Step 2: Know the formula for RMS speed: v_rms = sqrt(3RT/M), where R is the gas constant, T is the temperature, and M is the molar mass.
  • Step 3: Recognize that in this formula, the RMS speed is inversely related to the square root of the molar mass (M).
  • Step 4: If the molar mass (M) is halved, it means M becomes M/2.
  • Step 5: Substitute M/2 into the RMS speed formula: v_rms = sqrt(3RT/(M/2)).
  • Step 6: Simplify the equation: v_rms = sqrt(3RT * (2/M)) = sqrt(2) * sqrt(3RT/M).
  • Step 7: Notice that the new RMS speed is sqrt(2) times the original RMS speed.
  • Step 8: Conclude that if the molar mass is halved, the RMS speed increases by a factor of sqrt(2).
  • RMS Speed and Molar Mass Relationship – The root mean square (RMS) speed of a gas is inversely proportional to the square root of its molar mass, meaning that as the molar mass decreases, the RMS speed increases.
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