According to the kinetic molecular theory, which of the following expressions correctly gives the average speed v_{avg} of molecules in an ideal gas?

• A. v_{avg} = rac{3RT}{M}
• B. v_{avg} = rac{2RT}{M}
• C. v_{avg} = rac{8RT}{\pi M}
• D. v_{avg} = rac{RT}{2M}

Answer: (C)

Verified step by step guidance

1. Recall that the kinetic molecular theory relates the average speed of gas molecules to temperature and molar mass through the Maxwell-Boltzmann distribution.
2. Understand that the average speed \(v_{avg}\) is different from the root-mean-square speed \(v_{rms}\) and the most probable speed \(v_{mp}\); each has a distinct formula.
3. The formula for the average speed \(v_{avg}\) of gas molecules is given by \(v_{avg} = \sqrt{\dfrac{8RT}{\pi M}}\), where \(R\) is the gas constant, \(T\) is the absolute temperature, and \(M\) is the molar mass in kilograms per mole.
4. Note that the factor \(\dfrac{8}{\pi}\) arises from integrating the Maxwell-Boltzmann speed distribution to find the mean speed, which differs from the factors in the formulas for \(v_{rms}\) and \(v_{mp}\).
5. Therefore, to identify the correct expression for \(v_{avg}\), look for the formula that includes the square root of \(\dfrac{8RT}{\pi M}\), confirming it matches the kinetic molecular theory's prediction for average molecular speed.