gas. (i) Since argon and chlorine both have the same temperature in the flask, the ratio of average kinetic energy (per molecule) of the two gases is : . (ii) Now ½ m v rms = average kinetic energy per molecule = ( / ) ) k B T where m is the mass * E denotes the translational part of the internal energy U that may include energies due to other degrees of freedom also. See section .
. of a molecule of the gas. Therefore, Cl Cl Ar Ar Ar Cl rms rms = . .
= . where M denotes the molecular mass of the gas. (For argon, a molecule is just an atom of argon.) Taking square root of both sides, Ar Cl rms rms = . You should note that the composition of the mixture by mass is quite irrelevant to the above calculation.
Any other proportion by mass of argon and chlorine would give the same answers to (i) and (ii), provided the temperature remains unaltered. Example . Uranium has two isotopes of masses and units. If both are present in Uranium hexafluoride gas which would have the larger average speed ?
If atomic mass of fluorine is units, estimate the percentage difference in speeds at any temperature. Answer At a fixed temperature the average energy = ½ m < v > is constant. So smaller the mass of the molecule, faster will be the speed. The ratio of speeds is inversely proportional to the square root of the ratio of the masses.
The masses are and units. So v / v = ( / ) / = . . Hence difference ∆ = .
%. [ U is the isotope needed for nuclear fission. To separate it from the more abundant isotope U, the mixture is surrounded by a porous cylinder. The porous cylinder must be thick and narrow, so that the molecule wanders through individually, colliding with the walls of the long pore.
The faster molecule will leak out more than the slower one and