Question

The quantity $pV/{K_B}T$ represents the:
A. Number of molecules in a gas
B. Mass of a gas
C. Number of moles of a gas
D. Molar mass of a gas

Answer 1

To solve this type of question, you need to know the ideal gas equation and the Boltzmann constant. The ideal gas equation is given by $pv = nRT$. The Boltzmann constant ${K_B}$ is given by $\dfrac{R}{{{N_A}}}$.

Complete step by step answer:
- We know that the ideal gas equation is $pv = nRT$ where p is the pressure of the gas, v is the volume of the gas, n is the number of moles of gas, R is the universal gas constant and T is the temperature at which the gas exists. While we rearrange the ideal gas equation as:
$pv = nRT$
$n = \dfrac{{pv}}{{RT}}$, this will give the total number of moles of gas.
- We know that the Boltzmann constant${K_B}$, ${K_B} = \dfrac{R}{{{N_A}}}$
- While we rearrange this equation as:
${N_A} \times {K_B} = R$
Then substitute the value of R as ${K_B} \times {N_A}$, we get:
$n = \dfrac{{pv}}{{{N_A} \times K{}_B \times T}}$
$n \times {N_A} = \dfrac{{pv}}{{{K_B} \times T}}$
- The RHS of the equation is the same as given in the question. In the LHS, we know that it is the Avogadro number of times the number of moles. Which means it is the total number of molecules present in the gas.
So, $pV/{K_B}T$ represents the number of molecules of gas
So the correct answer is “A”:

Note: You may have doubt that what is the Boltzmann constant is. Boltzmann constant is a physical constant in thermodynamics relating the average kinetic energy of the gas particles and temperature of the gas.