The van't Hoff factor for an infinitely dilute solution of ${\mathrm{NaHSO}}_4$ is :

The van't Hoff factor is a measure of the number of particles into which a compound dissociates in solution. For an infinitely dilute solution of sodium bisulfate (NaHSO₄), complete dissociation occurs, allowing us to calculate the van't Hoff factor accurately.

Dissociation of NaHSO₄

When NaHSO₄ is dissolved in an infinitely dilute solution, it dissociates completely as follows:

NaHSO₄ → Na⁺ + HSO₄⁻

In this reaction, the compound dissociates into one sodium ion (Na⁺) and one hydrogen sulfate ion (HSO₄⁻), contributing two particles to the solution.

Further Dissociation of HSO₄⁻

The hydrogen sulfate ion (HSO₄⁻) undergoes further dissociation as:

HSO₄⁻ → H⁺ + SO₄²⁻

This step adds two more particles to the solution: a hydrogen ion (H⁺) and a sulfate ion (SO₄²⁻).

Calculation of the Van't Hoff Factor

The van't Hoff factor (i) is defined as the total number of particles formed in solution per formula unit of solute. For NaHSO₄, the dissociation can be summarized as:

• NaHSO₄ → 1 Na⁺ + 1 HSO₄⁻
• HSO₄⁻ → 1 H⁺ + 1 SO₄²⁻

Adding these particles together, we get a total of three ions: Na⁺, H⁺, and SO₄²⁻.

Therefore, the van't Hoff factor for NaHSO₄ in an infinitely dilute solution is: i = 3

This result shows that the van't Hoff factor plays a crucial role in understanding the behavior of electrolytes in solution and helps predict colligative properties like boiling point elevation, freezing point depression, and osmotic pressure.