Question

A jar has a mixture of hydrogen and oxygen gasses. The ratio of the mean kinetic energies of the hydrogen and oxygen molecules is

Answer 1

In the above question it is given that a jar contains a mixture of hydrogen and oxygen in the same vessel. Hence the mixture will have a common temperature. First we need to obtain the mean kinetic energy of both the gasses and further we can accordingly determine the ratio of their energies.
Formula used:
$E=\dfrac{1}{2}{{k}_{B}}T$

Complete step-by-step solution:
Let us say we have one mole of gas in a container. The mean kinetic energy (E) of the gas is given by,
$E=\dfrac{1}{2}{{k}_{B}}T$
Where ${{k}_{B}}$ is the Boltzmann constant.
In the above question the mixture of gasses is kept in the same jar. Hence they will be in thermal equilibrium with each other and hence have a constant temperature. From the above expression, we can imply that the mean kinetic energy of a gas depends on the temperature of the gas and not the nature of the gas. Hence in a single vessel even if n mixtures of gas is kept, the mean kinetic energy of the individual gasses will be the same.
Therefore the ratio of the mean kinetic energy of hydrogen and oxygen molecules is 1:1.

Note: It is to be noted that the mean kinetic energy of two different gases will be the same even if the amount of different gasses is different. This is because the amount of the gas gets compensated with the root mean square velocity of the individual gases. It is also to be noted that the energy of any gas becomes zero only at absolute zero that is 0 degree Kelvin.