mol - K - Calculate (a) rms speed of oxygen and hydrogen molecule (b) Average kinetic energy per oxygen molecule and per hydrogen molecule (c) Ratio of average kinetic energy of oxygen molecules and hydrogen molecules Solution (a) Absolute Temperature T= ° C = + = K. Gas constant R= . J mol - k - For Oxygen molecule: Molar mass M= g = x - kg mol - rms speed v rms = RT M m s m s ≈ For Hydrogen molecule: Molar mass M = × - kg mol - rms speed v rms = RT M m s k m s Note that the rms speed is inversely proportional to M and the molar mass of oxygen is times higher than molar mass of hydrogen. It implies that the rms speed of hydrogen is times greater than rms speed of oxygen at the same temperature.
≈ . Example: Lighter molecules like hydrogen and helium have high ‘ v rms ’ than heavier molecules such as oxygen and nitrogen at the same temperature. (ii) Increasing the temperature will increase the r.m.s speed of molecules We can also write the v rms in terms of gas constant R. Equation ( .
) can be rewritten as follows v rms = N kT N m Where N A is Avogadro number. Since N A k = R and N A m = M (molar mass) The root mean square speed or r.m.s speed v rms = RT M ( . ) The equation ( . ) can also be written in terms of rms speed P nmv rms = since v rms Root mean square speed is not the same as average speed.
Average speed is . times of r.m.s speed. Note Impact of v rms in nature: . Moon has no atmosphere.
The escape speed of gases on the surface of Moon is much less than the root mean square speeds of gases due to low gravity.