Question

The molar gas constant is the same for all gases because at the same temperature and pressure, equal volumes of gases have the same

A) Number of molecules
B) Average potential energy
C) Ratio of specific heats
D) Density

Answer 1

Hint: We can use the ideal gas equation to find which quantity varies with the variation in volume. We can check how that quantity is dependent on volume, whether directly or inversely proportional. If it’s directly proportional then the variation in both the quantities will be alike and in case of inverse proportionality, the changes in both the quantities are opposite to each other.

Complete step by step answer:
According to the ideal gas equation, we have:
\[PV = nRT\;\] where, n is the number of moles, R is the universal gas constant and T is the temperature.
Number of moles (n) is the number of molecules (N) divided by the Avogadro’s number $\left( {{N_A}} \right)$.

$ \to n = \dfrac{N}{{{N_A}}}$
$ \Rightarrow PV = \dfrac{N}{{{N_A}}}RT$
So, for the value of volume, this can be written as:
$V = \dfrac{N}{{{N_A}}} \times \dfrac{{RT}}{P}$
It is given that the Pressure and temperature are the same for the gas that means they are constant. Every quantity except the number of molecules (N) on the R.H.S of the equation.
$ \Rightarrow V \propto N$
Volume is directly proportional to the number of molecules, with the increase in volume, it will increase and vice – versa.
Thus, for equal volume of gases, the number of molecules will also be equal.

So, the correct answer is “Option A”.

Note:
The question can also be directly answered by the Avogadro’s law:
It is given that the pressure and temperature of the gases are the same. So according to the Avogadro’s law, under same conditions of temperature and pressure the number of molecules are equal for equal volume of gases