volume. With this interpretation of temperature, kinetic theory of an ideal gas is completely consistent with the ideal gas equation and the various gas laws based on it. For a mixture of non-reactive ideal gases, the total pressure gets contribution from each gas in the mixture. Equation ( .
) becomes P = ( / ) [ n m + n m +… ] ( . ) In equilibrium, the average kinetic energy of the molecules of different gases will be equal. That is, ½ m = ½ m = ( / ) k B T so that P = ( n + n +… ) k B T ( . ) which is Dalton’s law of partial pressures.
From Eq. ( . ), we can get an idea of the typical speed of molecules in a gas. At a temperature T = K, the mean square speed of a molecule in nitrogen gas is : – .
. kg. = k B T / m = ( ) m s - The square root of is known as root mean square (rms) speed and is denoted by v rms , ( We can also write as < v >.) v rms = m s - The speed is of the order of the speed of sound in air. It follows from Eq.
( . ) that at the same temperature, lighter molecules have greater rms speed. Example . A flask contains argon and chlorine in the ratio of : by mass.
The temperature of the mixture is °C. Obtain the ratio of (i) average kinetic energy per molecule, and (ii) root mean square speed v rms of the molecules of the two gases. Atomic mass of argon = . u; Molecular mass of chlorine = .
u. Answer The important point to remember is that the average kinetic energy (per molecule) of any (ideal) gas (be it monatomic like argon, diatomic like chlorine or polyatomic) is always equal to ( / ) k B T . It depends only on temperature, and is independent of the nature of the