MCQ Detailed View

The average speed of gas molecules is explained by the kinetic molecular theory of gases. According to this theory, the speed of a gas molecule depends on two important factors: the temperature (in Kelvin) and the molar mass of the gas. The mathematical expression used is the root mean square speed (uₘₛ):

urms=3RTMu_{rms} = \sqrt{\dfrac{3RT}{M}}urms=M3RT

Here, R is the gas constant, T is the absolute temperature in Kelvin, and M is the molar mass of the gas in kilograms per mole. From this formula, it is clear that the speed of gas molecules increases with temperature but decreases with molar mass. Lighter gases always move faster than heavier ones at the same temperature.

Let us analyze the options:

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  Hydrogen (H₂) at –73 °C (200 K): Hydrogen is the lightest molecule with a molar mass of 2 g/mol. Even at a low temperature, its molecules move very fast because of the extremely small mass.

  
  


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  Methane (CH₄) at 300 K: Methane has a molar mass of 16 g/mol. Although the temperature is moderate, its heavier mass reduces molecular speed compared to hydrogen.

  
  


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  Nitrogen (N₂) at 1,027 °C (1300 K): Nitrogen has a molar mass of 28 g/mol. High temperature increases its speed, but its heavier mass keeps it slower than hydrogen.

  
  


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  Oxygen (O₂) at 0 °C (273 K): Oxygen has a molar mass of 32 g/mol. Its higher mass and lower temperature result in slower movement.

  
  

Even though nitrogen is at a very high temperature, hydrogen remains faster because molecular speed depends more strongly on molar mass than temperature differences in this case.

Therefore, among the given gases, hydrogen (H₂) at –73 °C has the highest average molecular speed due to its extremely low molar mass.