Which of the following statement is false?

Active mass of 56 g of \(N_2\) contained in a 2-litre flask is \(0.1\, \ molL^{–1}\).

The correct answer is option 2. Active mass of 56 g of \(N_2\) contained in a 2-litre flask is \(0.1\, \ molL^{–1}\).

Let us examine each statement in detail to understand why statement (2) is false.

1. The number of gram molecules of a substance present in unit volume is known as active mass.

Active Mass: This term is used to refer to the concentration of a substance in a solution or gas phase. It is expressed in moles per unit volume (molarity, \( \text{mol/L} \)).

Gram Molecules: This term refers to the number of moles of a substance.

Unit Volume: Typically refers to one liter (L) when discussing molarity.

In summary, active mass is indeed the number of moles (gram molecules) of a substance per unit volume. This definition aligns with the concept of molarity (moles per liter).

Thus, this statement is correct.

2. Active mass of 56 g of \(N_2\) contained in a 2-litre flask is \(0.1 \, \text{mol/L}\).

To verify this, we need to calculate the active mass (concentration) of \(N_2\):

Molecular Weight of \(N_2\): The molecular weight of nitrogen (\(N_2\)) is \(28 \, \text{g/mol}\).

Moles of \(N_2\): Moles (\( \text{n} \)) are calculated as:

\(\text{n} = \frac{\text{Mass}}{\text{Molecular Weight}} = \frac{56 \, \text{g}}{28 \, \text{g/mol}} = 2 \, \text{mol}\)

Volume of the Flask: The volume (\( \text{V} \)) is \(2 \, \text{L}\).

Concentration (Active Mass): Concentration (\( \text{C} \)) is calculated as:

\(\text{C} = \frac{\text{Moles}}{\text{Volume}} = \frac{2 \, \text{mol}}{2 \, \text{L}} = 1 \, \text{mol/L}\)

The active mass (concentration) is \(1 \, \text{mol/L}\), not \(0.1 \, \text{mol/L}\). Therefore, this statement is false.

3. The attainment of equilibrium state in a gaseous reaction is known by constancy of pressure.

Equilibrium in Gaseous Reactions: When a gaseous reaction reaches equilibrium, the macroscopic properties, including pressure, remain constant provided the system is closed and the temperature and volume are constant. This is because the rates of the forward and reverse reactions become equal.

Thus, this statement correctly describes one of the indicators of equilibrium in a gaseous system and is true.

4. There is no effect of pressure on the equilibrium in which all the reactants and products are in liquid state.

Effect of Pressure on Liquid-Phase Equilibria: In systems where all reactants and products are liquids, pressure changes generally have a negligible effect on the equilibrium position because liquids are nearly incompressible. Therefore, changes in external pressure do not significantly alter the concentrations of reactants and products in the liquid phase.

Thus, this statement is true.

Hence, the false statement is: (2) Active mass of 56 g of \(N_2\) contained in a 2-litre flask is \(0.1 \, \text{mol/L}\).

The correct active mass (concentration) is \(1 \, \text{mol/L}\), not \(0.1 \, \text{mol/L}\). This error makes statement (2) false.