Out of the three states of matter, only the gases have most of the physical properties common. They neither have definite shapes nor volumes. Upon mixing they form homogeneous mixture irrespective of their nature and can also be compressed on applying pressure. In addition to these, the gases obey different gas laws such as Boyle's Law, Charles's Law, Dalton's Law of partial pressures, Graham's Law of diffusion etc. Based upon these laws, ideal gas equation `PV = nRT` has been derived.
For an ideal gas, number of moles per litre in terms of its pressure P, gas constant R and temperature T is :

Options

A. `PT//R`
B. `PRT`
C. `P//RT`
D. `RT//P`

Explanation

To solve the problem, we need to derive the expression for the number of moles per liter of an ideal gas in terms of its pressure (P), gas constant (R), and temperature (T) using the ideal gas equation \( PV = nRT \).

### Step-by-Step Solution:

1. **Start with the Ideal Gas Equation**:
The ideal gas equation is given by:
\[ PV = nRT \]
where:
- \( P \) = pressure of the gas
- \( V \) = volume of the gas
- \( n \) = number of moles of the gas
- \( R \) = universal gas constant
- \( T \) = temperature in Kelvin

2. **Rearranging the Equation**:
We need to find the number of moles per liter. To do this, we can rearrange the ideal gas equation to solve for \( n \):
\[ n = \frac{PV}{RT} \]

3. **Finding Moles per Liter**:
To find the number of moles per liter, we need to express \( n \) in terms of volume in liters. If we consider \( V \) as 1 liter (since we want moles per liter), we can substitute \( V = 1 \) into the equation:
\[ n = \frac{P \cdot 1}{RT} = \frac{P}{RT} \]

4. **Final Expression**:
Thus, the number of moles per liter of an ideal gas can be expressed as:
\[ \text{Number of moles per liter} = \frac{P}{RT} \]

### Conclusion:
The final answer for the number of moles per liter in terms of pressure, gas constant, and temperature is:
\[ \frac{P}{RT} \]

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