Multiple Choice
According to the kinetic molecular theory, why do gases compress more easily than liquids and solids?
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7. Gases
Kinetic Molecular Theory
Multiple Choice
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}
Verified step by step guidance1
Recall that the kinetic molecular theory relates the average speed of gas molecules to temperature and molar mass through the Maxwell-Boltzmann distribution.
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.
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.
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 \(v_{mp}\).
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.
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