Animated Solution for Chemistry - States of Matter: For an ideal gas, number of moles per litre in terms of its pressure $p$, temperature $T$ and gas constant $R$ is

Imagine you are looking at a closed container filled with an ideal gas. The gas molecules are zipping around, colliding with the walls and creating a certain pressure, $p$. The container has a specific volume, $V$, and the gas is at a uniform temperature, $T$. Inside this volume, there are $n$ moles of the gas.

Our goal is to find the "number of moles per litre". Mathematically, this phrase translates to the ratio of the number of moles to the volume, which is $\frac{n}{V}$.

To find this ratio, we need a relationship that connects all these state variables together. For an ideal gas, this relationship is given by the famous Ideal Gas Equation:

Here, $R$ is the universal gas constant. This single equation is the master key to unlocking almost any basic gas law problem. It perfectly balances the macroscopic properties of the gas.

We need to isolate the term $\frac{n}{V}$. Let's perform a simple algebraic rearrangement. We can divide both sides of the equation by $V$ to move the volume to the right side:

Next, we divide both sides by $RT$ to isolate the $\frac{n}{V}$ ratio completely:

And there we have it! The number of moles per unit volume (or per litre, if $V$ is in litres) is exactly equal to $\frac{p}{RT}$.

Final Answer: The correct expression is $\frac{p}{RT}$, which corresponds to option (c).

This simple ratio is incredibly powerful. If you were to multiply this result by the molar mass of the gas, you would instantly find the density of the gas!