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How to Measure the Velocity Distribution of Gases

The study of the behavior of gas molecules is part of the sciences of chemistry, kinetic molecular theory and thermodynamics. An important part of the study of gas molecules is learning how to predict the actions of the gas molecules through knowledge of the properties of the gas as a whole. Starting with nothing but the temperature of a gas, you can predict not only the average speed of the molecules, but also the speed distribution.

Things You'll Need

Thermometer
Molar mass table

Instructions

- 1
  Take the temperature of the gas. If you measured the temperature in degrees Celsius, then add 273.15 to it. If you measured the temperature in degrees Fahrenheit, then subtract 32 from the temperature, divide by 1.8 and then add 273.15 to the result. Either way, the result will be the temperature on the Kelvin scale, which is necessary for these calculations.
- 2
  Multiply the temperatures by 8.3145, the molar gas constant. Multiply the result by two. Divide it by the molar mass of the gas you are studying. Make sure that the molar mass is expressed in kilograms per mole. Take the square root of the result. The result will be the most probable speed for any molecule of gas.
- 3
  Multiply the temperatures by 8.3145. Multiply the result by three. Divide it by the molar mass. Take the square root of the result. The result will be the root-mean-square (rms) speed of the gas molecules. The rms speed is the conventional way to describe magnitudes of a variable that averages to zero.
- 4
  Multiply the temperatures by 8.3145. Multiply the result by eight. Divide it by pi (approximately 3.1416). Divide it by the molar mass. Take the square root of the result. The result will be the mean speed of the gas molecules. This is the average speed of the gas molecules.
- 5
  Divide the molar mass by the temperature in Kelvins. Divide the result by 8.3145. Divide this result by two times pi. Take the square root of the result. Label this result "A." Pick any speed expressed in meters per second. Square it. Multiply it by the molar mass. Divide it by 8.3145. Divide this result by the temperature in Kelvins. Divide the result of that by two. Multiply it by --1. Label this result "B." Raise 2.7183 to the B power. Multiply the result by A. This result is the probability that any given molecule of gas has the speed that you chose.

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