Question

8 g each of oxygen and hydrogen at ${27}^{o}C$ will have total kinetic energy in the ratio of x:y.

Find the value $x$.

Answer 1

The kinetic energy of a gas at a given temperature T is given by the expression:

$KE=\frac{3}{2}nRT=\frac{3}{2}\times \frac{w}{M}RT$.

Here, n is the number of moles of a gas, w is the mass of gas and M is the molar mass of a gas. Thus, the kinetic energy of a gas molecule is inversely proportional to the molar mass of the gas molecule.

$\frac{K.E_{O_2}}{K.E_{H_2}}=\frac{x}{y}=\frac{M_{H_2}}{M_{O_2}}=\frac{2}{32}=\frac{1}{16}$

Hence, $x=1$.