Kinetic Molecular Theory - Part 2

Molecular Speed

Remember that temperature is the average kinetic energy of a gas's molecules. So not all of the molecules are moving at the same speed. Some molecules are moving faster or slower.

Below is the distribution of speeds for oxygen at different temperatures. Notice that as the temperature increases the curve shifts to the right (temperature increasing), but there are still some molecules moving slowly so the curve is also flattening out.

Root Mean Square

One way to estimate the average speed of the molecules in a gas is to find the root-mean-square speed from the distribution.

R is the gas constant. M is the molar mass of the gas. Therefore the heavier the gas the slower it moves.

Graham's Law of Diffusion

From personal experience you may know that a gas does not instantly fill a room. If perfume is sprayed on one side of a room it may take a while before someone on the other side notices.

This process happens because of diffusion. A highly concentrated substance will spread out over time to areas of lower concentration. This will continue until the substance is evenly distributed.

Heavier gases will take a longer time to diffuse and lighter gases shorter.

The rate at which two gases diffuse is proportional to the square root of the inverse of their molar masses:

Gas Effusion

Gas effusion happens when gases diffuse through a small opening. However the rate of effusion has the same formula as the rate of diffusion.

Non-Ideal Gas Behavior

The KMT assumes that gases have no attraction or repulsion. While this is largely true in most cases, this is not always true in some extreme cases.

When the pressure is very high, gas molecules are forced into close proximity with each other. In this case attractive forces between molecules can occur. Additionally, at low temperatures gases will not have enough kinetic energy to break free of attractive forces. These two factors are how gases condense into liquids.

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