Question

Each mole of two ideal gases have pressures P and 2P respectively at the same temperature. If V is the volume of the second gas at that temperature, then 
1. the volume of the first gas will be 3V
2. the volume of the first gas will be 2V
3. the volume of the first gas will be 4V
4. the volume of the first gas will be V

Answer 1

Correct Answer - Option 2 : the volume of the first gas will be 2V

The correct answer is option 2) i.e. the volume of the first gas will be 2V

CONCEPT:

• Ideal gas law: The ideal gas law states that the product of the pressure and the volume of one gram molecule of an ideal gas is equal to the product of the absolute temperature of the gas and the universal gas constant.

The ideal gas equation is given by:

PV = nRT

Where P is the pressure of the gas, V is the volume of the gas, n is the number of moles, T is the temperature and R is the universal gas constant.

EXPLANATION:

• Let P₁ and P₂ be the pressure of two gases and V₁ and V₂ be their volumes at temperature T.
• The universal gas constant R will be the same and given that one mole of both the gas is considered. 

⇒ n₁ = n₂ = n = 1 mol

Given that, P1 = P and P2 = 2P

The ideal gas equation for both the gases will be:  

P₁V₁ = nRT and P2V2​ = nRT

Dividing the two equations, 

P₁V₁ =  P₂V₂

⇒ PV1 =  2PV2

⇒ V1 =  2V2

If V is the volume of the second gas, V1 =  2V, and V₂ = V

Therefore, the volume of the first gas will be 2V.