According to the ** kinetic molecular theory of gases**, the average kinetic energy of a gas is

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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 SO_{2} molecule to that of an O_{2} 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:

$\overline{)\frac{{\mathbf{rate}}_{\mathbf{gas}\mathbf{}\mathbf{1}}}{{\mathbf{rate}}_{\mathbf{gas}\mathbf{}\mathbf{2}}}{\mathbf{=}}\sqrt{\frac{{\mathbf{MM}}_{\mathbf{gas}\mathbf{}\mathbf{2}}}{{\mathbf{MM}}_{\mathbf{gas}\mathbf{}\mathbf{1}}}}}$

Let's designate SO_{2} as gas 1 and O_{2} as gas 2.

What is the ratio of the average kinetic energy of a SO_{2} molecule to that of an O_{2} molecule in a mixture of two gases? What is the ratio of the root mean square speeds, u_{rms}, of the two gases?

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