Question

Oxygen and hydrogen are kept under the same temperature and pressure. Oxygen molecule is 16 times more massive than hydrogen one. The average speed of molecule of oxygen is:______.

Answer 1

Answer:

The average speed of molecule of oxygen is one-fourth of the speed of the hydrogen molecule.

Explanation:

The kinetic energy of gas molecule is given by following equation:

$K.E = \frac{3}{2} KT$

Since the temperature (T) is constant for both molecules. Therefore, there kinetic energies will also be the same. Therefore,

$K.E_{O_2} = K.E_{H_2}\\\frac{1}{2}m_{O_2}v_{O_2}^2 = \frac{1}{2}m_{H_2}v_{H_2}^2 \\\\but,\\\\m_{O_2} = 16m_{H_2}\\\\therefore,\\16 m_{H_2}v_{O_2}^2 = m_{H_2}v_{H_2}^2\\\\\\taking square root on both sides, we get:\\4v_{O_2} = v_{H_2}\\\\v_{O_2} = \frac{v_{H_2}}{4}$

The average speed of molecule of oxygen is one-fourth of the speed of the hydrogen molecule.