How do you determine highest van’t Hoff factors?

The van ‘t Hoff factor ##i## is the number of particles obtained when a dissolves.

For most non-electrolytes dissolved in water, the van’ t Hoff factor is 1.

For most dissolved in water, the maximum van ‘t Hoff factor is equal to the number of discrete ions in a formula unit of the substance.

For NaCl: NaCl(s) → Na⁺(aq) + Cl⁻(aq), so ##i## = 2.
For CaCl₂: CaCl₂(s) → Ca²⁺(aq) + 2Cl⁻(aq), so ##i## = 3
For K₃Fe(CN)₆: K₃Fe(CN)₆(s) → 3K⁺(aq) + Fe(CN)₆³⁻(aq), so ##i## = 4.

These are the maximum values of ##i##. They are found only in ideal — solutions that are infinitely dilute.

In real solutions, some of the ions are paired within the same solvation shell and count as a single particle.

This causes deviations from the maximum van ‘t Hoff factor. The deviation is greatest when the ions have multiple charges.

Here are some observed values of the van’t Hoff factor for 0.1 mol/kg aqueous solutions.

NH₄Cl: ##i## = 1.85 (not 2).
CuSO₄: ##i## = 1.45 (not 2).
K₂SO₄: ##i## = 2.32 (not 3).
K₃Fe(CN)₆: ##i## = 2.85 (not 4).

Here are some more values.

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