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What is the RMS speed of an ideal gas in terms of its temperature and molar mass

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Question: What is the RMS speed of an ideal gas in terms of its temperature and molar mass?

Options:

  1. sqrt((3RT)/M)
  2. sqrt((2RT)/M)
  3. sqrt((RT)/M)
  4. sqrt((3M)/RT)

Correct Answer: sqrt((3RT)/M)

Solution: 

The RMS speed (v_rms) of an ideal gas is given by the formula v_rms = sqrt((3RT)/M), where R is the universal gas constant, T is the absolute temperature, and M is the molar mass.

What is the RMS speed of an ideal gas in terms of its temperature and molar mass

Practice Questions

Q1
What is the RMS speed of an ideal gas in terms of its temperature and molar mass?
  1. sqrt((3RT)/M)
  2. sqrt((2RT)/M)
  3. sqrt((RT)/M)
  4. sqrt((3M)/RT)

Questions & Step-by-Step Solutions

What is the RMS speed of an ideal gas in terms of its temperature and molar mass?
  • Step 1: Understand that RMS speed refers to the root mean square speed of gas molecules.
  • Step 2: Know that the formula for RMS speed is v_rms = sqrt((3RT)/M).
  • Step 3: Identify the variables in the formula: R is the universal gas constant, T is the absolute temperature in Kelvin, and M is the molar mass of the gas in kg/mol.
  • Step 4: Recognize that the formula shows how the speed of gas molecules depends on temperature and molar mass.
  • Step 5: Remember that higher temperatures (T) lead to higher RMS speeds, while larger molar masses (M) lead to lower RMS speeds.
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