Question

The kinetic energy of $N$ molecules of $O_2$ is $x$ joule at $-{123}^{\circ }\text{C}$. Another sample of $O_2$ at ${27}^{\circ }\text{C}$ has a kinetic energy of $2x$. The latter sample contains ____ molecules of $O_2$:

• A. $N$
• B. $\frac{N}{2}$
• C. $2N$
• D. $3N$

Answer 1

The correct option is A $N$

As,
K.E. $=\frac{3}{2}nRT$
so,
$x=\frac{3}{2}\times \frac{N}{N_A}\times 150\times R$
and
$2x=\frac{3}{2}\times \frac{N^{{}^{\prime }}}{N_A}\times 300\times R$
$N^{{}^{\prime }}$ is the number of molecules of $O_2$
So, to calculate $N^{{}^{\prime }}$
$\frac{x}{2x}=\frac{\frac{3}{2}\times \frac{N}{N_A}\times 150\times R}{\frac{3}{2}\times \frac{N^{{}^{\prime }}}{N_A}\times 300\times R}$
$\Rightarrow \frac{1}{2}=\frac{N}{N^{{}^{\prime }}\times 2}$
$\Rightarrow N^{{}^{\prime }}=N$
Hence, the correct answer is option (a).