What is the kinetic energy (in $\mathrm{J} \mathrm{mol}^{-1}$ ) of one mole of an ideal gas (molar mass $=0.1 \mathrm{~kg} \mathrm{~mol}^{-1}$ ) if its rms velocity is $4 \times 10^2 \mathrm{~ms}^{-1}$ at $T(\mathrm{~K})$ ?

Two statement are given below.

Statement I : The ratio of the molar volume of a gas to that of an ideal gas at constant temperature and pressure is called the compressibility factor.

Statement II : The rms velocity of a gas is directly proportional to square root of $T(\mathrm{~K})$.

The correct answer is

At 133.33 K . the rms velocity of an ideal gas is $$ \left(M=0.083 \mathrm{~kg} \mathrm{~mol}^{-1} ; R=8.3 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}\right) $$

Identify the correct statements from the following I. For an ideal gas, the compressibility factor is 1.0 II. The kinetic energy of $\mathrm{NO}(g)$ (molar mass $=30 \mathrm{~g} \mathrm{~mol}^{-1}$ ) at $T(\mathrm{~K})$ is $x \mathrm{~J} \mathrm{~mol}^{-1}$. The kinetic energy of $\mathrm{N}_2 \mathrm{O}_4(g)\left(\right.$ molar mass $\left.=92 \mathrm{~g} \mathrm{~mol}^{-1}\right)$ at $T(\mathrm{~K})$ is $2 x \mathrm{~J} \mathrm{~mol}^{-1}$ III. The rate of diffusion of a gas is inversely proportional to square root of its density.