The formula to calculate the mean square speed of particles in an ideal gas is given by the root mean square (RMS) formula:
u = sqrt((3RT) / M)
Where:
- u is the mean square speed (RMS speed) of the gas particles.
- R is the ideal gas constant, which is approximately 8.314 J/(mol·K) or 0.0821 L·atm/(mol·K), depending on the units used.
- T is the temperature of the gas in Kelvin.
- M is the molar mass (molecular weight) of the gas in kilograms per mole.
It's important to ensure that the units of temperature and molar mass are consistent with the units of the ideal gas constant to obtain accurate results.
The mean square speed provides an average measure of the kinetic energy of gas particles in an ideal gas at a given temperature.