How Do You Calculate for the Root-Mean-Square Speed?

Calculating the root-mean-square speed of a gas requires measurements of the gas's temperature and mass. The formula also requires finding the square root, which can be calculated on a graphing calculator and some simple calculators.

1. Find the temperature of the gas

All formulas for determining the root-mean-square speed require a temperature measurement expressed in Kelvin. If necessary, convert to Kelvin from Celsius or Fahrenheit measurements.

2. Find the mass

Depending on the constant used, the formula for root-mean-square speed requires either the molar mass of the gas or the mass of a single molecule of the gas. Express the molar mass with the kilograms per mole unit, converting from grams if necessary. The mass of a single molecule can be determined through energy formulas.

3. Choose the constant

If you are using the molar mass, use the constant R, which is the molar gas constant. If you are using the mass of a single molecule, find the value of the Boltzmann constant, represented by K.

4. Plug the values into the equation

For the equation using the molar gas constant, multiply it by three and multiply that product by the temperature measurement. Divide that product by the molar mass. Find the square root of the result.

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