Question

A gas at $300$K has pressure $4\times {10}^{-10}$N $m^{-2}$. If $k_B=1.38\times {10}^{-23}$J $K^{-1}$, the number of molecules per $c{m}^3$ is of the order of.

• A. ${10}^3$
• B. ${10}^5$
• C. ${10}^6$
• D. ${10}^9$

Answer 1

Answer: (B)

${10}^5$

Given parameters are

$P=4\times {10}^{-10}N{m}^{-2}$

$T=300K$

$V=1c{m}^3={10}^{-6}{m}^3$

N = No. of molecules

Boltzmann’s constant $=k_B=1.38\times {10}^{-23}J{K}^{-1}$

From the ideal gas law, we have

$PV=N{k}_{B}T$

$N=\frac{PV}{k_{B}T}$

Substituting the values, we get

$N=\frac{4\times {10}^{-10}\times {10}^{-6}}{1.38\times {10}^{-23}\times 300}$

$N=0.967\times {10}^5$

$N\simeq {10}^5$

Thus option B is correct.