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Van't Hoff Factor, Association, and Dissociation

Van't Hoff factor, i, is the ratio of observed colligative property to the calculated colligative property when the solute is assumed to neither associate nor dissociate.

In one line: Dissociation divides one particle into many, so i increases; association joins particles, so i decreases.

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Understand it

  • The value of i corrects colligative property calculations for the actual number of particles in solution.
  • If a solute dissociates, the number of particles increases and i is greater than 1.
  • If a solute associates, the number of particles decreases and i is less than 1.
  • For a non-electrolyte with no association, i is approximately 1.

Example

NaCl dissociates into Na+ and Cl- in water, so the freezing point depression is greater than that expected for the same molality of a non-electrolyte.

Rule to remember

i = observed colligative property/calculated colligative property.

Corrected formulas include Delta Tb = i Kb m, Delta Tf = i Kf m, π = i C R T, and relative lowering = i xsolute for suitable dilute cases.

See it worked out

Follow the example line by line, then use the same method on new questions.

Worked example

A 0.10 m solution has calculated freezing point depression 0.186 K, but observed depression is 0.372 K.

  1. 1i = 0.372/0.186 = 2.
  2. 2Interpretation: the solute effectively produces twice the expected number of particles, consistent with complete dissociation into two ions.

Method you can reuse

  1. 1First calculate the expected colligative property without association or dissociation.
  2. 2Compare it with the observed value to find i.
  3. 3If i is greater than 1, infer dissociation; if i is less than 1, infer association.
  4. 4Use the corrected formula only after identifying the relevant colligative property.

Visual tip

A particle-count sketch can help distinguish dissociation from association, but a required diagram is not necessary for most exam questions.

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

If a solute associates in solution, is i greater than 1 or less than 1?

Think first, then show answer
It is less than 1 because the number of solute particles decreases.

Common wrong answer

Saying i greater than 1 means association is a common conceptual reversal.

Don't mix this up

Students often write i as calculated value divided by observed value. The required ratio is observed colligative property divided by calculated colligative property.

Exam tip

Before applying i, decide whether the solute dissociates or associates. This predicts whether the observed molar mass will appear lower or higher than the normal molar mass.

Write it in the exam

Each point is worth about one mark. Write point 1 for a 1-mark question and keep adding points as the marks go up.

How CBSE asks it

Questions ask for i from observed and calculated colligative property, abnormal molar mass, degree of dissociation or association in simple cases, and reasoning about electrolytes versus non-electrolytes.
  1. 1

    Enough for 1 mark

    Van't Hoff factor, i, is the ratio of observed colligative property to the calculated colligative property when the solute is assumed to neither associate nor dissociate.

  2. 2

    Add for 2 marks

    Example: NaCl dissociates into Na+ and Cl- in water, so the freezing point depression is greater than that expected for the same molality of a non-electrolyte.

  3. 3

    Add for 3 marks

    The value of i corrects colligative property calculations for the actual number of particles in solution.

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