Question

Find the most probable speed $\left(V_{mp}\right)$ of nitrogen gas molecules at $T=560\text{K}$. (Given: Numerical value of $\sqrt{R}$ is $2.88$, where $R$ is gas constant)

• A. $460\text{m/s}$
• B. $500\text{m/s}$
• C. $576\text{m/s}$
• D. $600\text{m/s}$

Answer 1

The correct option is C $576\text{m/s}$

We know that,
$V_{mp}=\sqrt{\frac{2RT}{M}}$
$\Rightarrow V_{mp}=\sqrt{\frac{2\times R\times 560}{28\times {10}^{-3}}}$
($\because$ Molar mass of $N_2=28\times {10}^{-3}\text{kg}$ )
$\Rightarrow V_{mp}=200\sqrt{R}=576\text{m/s}$