# If N molecules of $O_2$ at $- 73^{\circ}$ possess the same kinetic energy as another sample of $H_2$ at $27^{\circ}$ then the number of molecules of $H_2$ is ?

(A) N (B) 1.1N (C) 0.9N (D) 2N

Kinetic Energy of an ideal gas $= \large\frac{3}{2}$
$\large\frac{3}{2}$$n_{O_2} \times R \times (273-73)=\large\frac{3}{2}$$ n_{H_2} \times R \times (273 +27)$
$\Rightarrow 500 n_{O_2} = 450 n_{H_2} \rightarrow n_{H_2} = 1.1 n_{O_2}$
edited Aug 9, 2014