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The root mean square speed of molecules of ideal gases at the same temperature are:
  • a)
    The same
  • b)
    Inversely proportional to the square root of the molecular weight
  • c)
    Directly proportional to molecular weight
  • d)
    None of the above
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
The root mean square speed of molecules of ideal gases at the same tem...
The formula to derive the root mean square speed is given as:

where:
  • Vrms is the root mean square speed,
  • k is Boltzmann's constant (1.38 x 10-23 J/K),
  • T is the temperature in Kelvin (K),
  • m is the molecular mass of the gas in kilograms (kg).
  • Here the root mean square speed is dependent on the mass of the molecules: for a given temperature, lighter molecules will move faster than heavier ones.
  • However, you asked for the root mean square speeds of molecules of ideal gases at the same temperature. If we consider this condition but we don't specify which gases we are considering, we cannot provide specific numerical values since the rms speed would still vary depending on the molecular mass of each specific gas.
  • If you're referring to the comparison between different gases at the same temperature, the lighter gas molecules will have higher root-mean-square speeds than heavier ones, given that they are at the same temperature.
  • This means,
  • The root mean square speed of molecules of ideal gases at the same temperature is Inversely proportional to the square root of the molecular weight
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The root mean square speed of molecules of ideal gases at the same temperature are:a)The sameb)Inversely proportional to the square root of the molecular weightc)Directly proportional to molecular weightd)None of the aboveCorrect answer is option 'B'. Can you explain this answer?
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