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For a gas with molar mass M, what is the relationship between RMS speed and mole

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Question: For a gas with molar mass M, what is the relationship between RMS speed and molecular mass?

Options:

  1. v_rms is directly proportional to M
  2. v_rms is inversely proportional to M
  3. v_rms is independent of M
  4. v_rms is proportional to M^2

Correct Answer: v_rms is inversely proportional to M

Solution: 

The RMS speed is inversely proportional to the square root of the molar mass (v_rms = sqrt((3RT)/M)). Thus, as molar mass increases, RMS speed decreases.

For a gas with molar mass M, what is the relationship between RMS speed and mole

Practice Questions

Q1
For a gas with molar mass M, what is the relationship between RMS speed and molecular mass?
  1. v_rms is directly proportional to M
  2. v_rms is inversely proportional to M
  3. v_rms is independent of M
  4. v_rms is proportional to M^2

Questions & Step-by-Step Solutions

For a gas with molar mass M, what is the relationship between RMS speed and molecular mass?
  • Step 1: Understand what RMS speed is. RMS speed (v_rms) is a measure of the average 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 in Kelvin, and M is the molar mass.
  • Step 3: Identify the relationship between RMS speed and molar mass. The formula shows that v_rms is divided by the square root of M.
  • Step 4: Recognize that if M (molar mass) increases, the value of sqrt(M) also increases.
  • Step 5: Since v_rms is divided by sqrt(M), an increase in M means that v_rms will decrease.
  • Step 6: Conclude that RMS speed is inversely proportional to the square root of molar mass.
  • RMS Speed and Molar Mass Relationship – The relationship between the root mean square (RMS) speed of gas molecules and their molar mass, highlighting that RMS speed decreases as molar mass increases.
  • Gas Laws – Understanding the ideal gas law and how temperature and molar mass affect gas behavior.
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