At what temperature will hydrogen molecules have the same kinetic energy as nitrogen molecules have at 35 degree Celsius?

The average kinetic energy of oxygen molecules and hydrogen molecules will be the same at any particular temperature. If we keep in mind that the formula for kinetic energy is 0.5mv2 it stands to reason that the lighter molecules(hydrogen) will have a greater speed than the oxygen molecules.
Since the average kinetic energy of oxygen and hydrogen are equal we can write the expression below.

However the molecular mass of oxygen is 32 and that of hydrogen is 2. So we can rewrite the above expression

Transforming the formula we obtain the expression below which gives the ratio of the average velocities of oxygen and hydrogen molecules

The average velocity of hydrogen molecules is 4 times greater than that of oxygen molecules.

It is important to note that although the average kinetic energy of all gases is the same at a particular temperature, the average velocity of the molecules is not. The heavier molecules tend to travel slower relative to the lighter ones.

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b) Draw a curve to show the distribution of energies for 2 mole of gas at 300 K

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