Question

The quantity $\left(PV/K_{B}T\right)$ represents :

• A. Number of molecules in the gas
• B. Mass of the gas
• C. Number of moles of the gas.
• D. Translational energy of the gas

Answer 1

The correct option is A Number of molecules in the gas

$PV=nRT$

$n=\frac{PV}{RT}$

$PV=\frac{N}{N_A}RT$

where N= no of molecules

$N_A=$ Avogadro's number

$PV=NT\frac{R}{N_A}$

But $\frac{R}{N_A}=K_B$ is Boltzman constant

$\therefore PV=N{K}_{B}T$

$\therefore N=\frac{PV}{K_{B}T}$

Hence, $\frac{PV}{K_{B}T}$ represents the number of molecules

Hence, the correct option is $\text{A}$