# Problem: What is the ratio of the average kinetic energy of a SO2 molecule to that of an O2 molecule in a mixture of two gases? What is the ratio of the root mean square speeds, urms, of the two gases?

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###### FREE Expert Solution

According to the kinetic molecular theory of gases, the average kinetic energy of a gas is directly proportional to the temperature of the gas: a higher temperature results in a higher average kinetic energy.

Assuming that the gas samples are all at the same temperature. This means they will have the same kinetic energy.

The ratio of the average kinetic energy of a SO2 molecule to that of an O2 molecule is equal to 1.

$\overline{){\mathbf{\mu }}_{\mathbf{rms}}\mathbf{=}\sqrt{\frac{\mathbf{3}\mathbf{RT}}{\mathbf{M}}}}$

3RT is constant

Recall that Graham's Law of Effusion allows us to compare the rate of effusion of two gases. Graham's Law states that the rate of effusion of a gas is inversely proportional to its molar mass.

$\mathbf{rate}\mathbf{=}\frac{\mathbf{1}}{\sqrt{{\mathbf{MM}}_{\mathbf{gas}}}}$

This means that when comparing two gases:

Let's designate SO2 as gas 1 and O2 as gas 2.

###### Problem Details

What is the ratio of the average kinetic energy of a SO2 molecule to that of an O2 molecule in a mixture of two gases? What is the ratio of the root mean square speeds, urms, of the two gases?