Q.Derive the relationship between degree of dissociation of an electrolyte and van't Hoff factor.

Showing the 12 most recent of 22 on this concept.

1. CBSE 2026Set V11 mark
   Q.Van't Hoff factor

   (i) for a non-electrolyte in a solution is ________.

   ›Reveal solutionSolution

   For a non-electrolyte solute the van't Hoff factor $i = 1$, since the number of particles in solution is unchanged.

   The van't Hoff factor is

   $i = \dfrac{\text{actual number of particles in solution after dissociation/association}}{\text{number of formula units dissolved}}$

   A non-electrolyte (e.g. glucose, urea) neither dissociates into ions nor associates in solution, so the number of particles equals the number of molecules dissolved. Hence $i = 1$.

   ✓Final answer

   $i = 1$

2. CBSE 2026Set ANNUAL1 markMCQ
   Q.The strong electrolyte having maximum value of Van't Hoff factor

   (i) among the following is

   (a) NaCl

   (b) KCl

   (c) MgSO4

   (d) K2SO4

   ›Reveal solutionSolution

   The van't Hoff factor i equals the number of ions a formula unit produces on complete dissociation, so the electrolyte giving the most ions has the largest i.

   • NaCl -> Na+ + Cl- : i = 2
   • KCl -> K+ + Cl- : i = 2
   • MgSO4 -> Mg2+ + SO4^2- : i = 2
   • K2SO4 -> 2K+ + SO4^2- : i = 3

   Among the four, only K2SO4 furnishes 3 ions per formula unit, so it has the maximum i.

   ✓Final answer

   (d) K2SO4, i ≈ 3 (2 K+ ions + 1 SO4^2- ion).

3. CBSE 2026Set ANNUAL1 markMCQ
   Q.What is the value of Vant Hoff factor for one molal aqueous solution of Urea?

   (a) Two

   (b) Three

   (c) One

   (d) Four

   ›Reveal solutionSolution

   Van't Hoff factor $i$ measures how many particles a solute actually produces in solution. Urea is a non-electrolyte that neither dissociates nor associates, so $i = 1$.

   The Van't Hoff factor is defined as

   $i = \dfrac{\text{observed colligative property}}{\text{calculated (normal) colligative property}} = \dfrac{\text{actual number of particles after dissolution}}{\text{number of formula units dissolved}}$

   Urea, $\text{CO(NH}_2)_2$, is a covalent, non-electrolytic molecule. In water it dissolves as intact molecules — it does not ionize (so it doesn't split into more particles) and it does not associate/dimerize (so it doesn't combine into fewer particles). Each urea unit dissolved gives exactly one particle in solution.

   ✓Final answer

   $i = 1$ (Urea neither dissociates nor associates in aqueous solution).

4. CBSE 2026Set ANNUAL1 markMCQ
   Q.When mercuric iodide is added to the aqueous solution of Potassium iodide:

   (a) Freezing point is raised

   (b) Freezing point does not change

   (c) Freezing point is lowered

   (d) Boiling point does not change

   ›Reveal solutionSolution

   $HgI_2$ combines with excess $I^-$ to form the complex ion $[HgI_4]^{2-}$, which decreases the number of particles in solution, so the depression in freezing point is less than expected and the freezing point is raised.

   When mercuric iodide is added to an aqueous solution of potassium iodide, it reacts with the iodide ions already present:

   $HgI_2 + 2I^- \rightarrow [HgI_4]^{2-}$

   This reaction combines three particles (one $HgI_2$ and two $I^-$ ions) into a single complex ion, decreasing the total number of solute particles in solution. Since colligative properties (like depression of freezing point) depend on the number of particles, this association makes the van't Hoff factor $i < 1$. A smaller effective particle count means a smaller depression in freezing point than would otherwise be expected, so — compared to the case without complex formation — the freezing point of the solution is raised.

   ✓Final answer

   (a) Freezing point is raised, because $HgI_2$ associates with $I^-$ to form $[HgI_4]^{2-}$, reducing the number of particles in solution.

5. CBSE 2026Set ANNUAL1 mark
   Q.Write answer in one word/sentence: Write the numerical value of 'i' for complete dissociation of electrolyte K2SO4.

   ›Reveal solutionSolution

   Complete dissociation of K2SO4 gives 3 ions, so i = 3.

   The van't Hoff factor i is the number of particles actually present in solution per formula unit of the dissolved solute. On complete dissociation:

   K2SO4 -> 2K+ + SO4^2-

   One formula unit gives 2 potassium ions and 1 sulphate ion = 3 ions in total. Hence for complete dissociation, i = 3.

   ✓Final answer

   i = 3.

6. CBSE 2025Set ANNUAL1 markMCQ
   Q.Which one of the following has maximum value of Van't Hoff Factor -

   (a) K2SO4

   (b) NaCl

   (c) MgSO4

   (d) KCl

   ›Reveal solutionSolution

   Van't Hoff factor increases with the number of ions produced on complete dissociation.

   For a strong electrolyte dissociating completely into $n$ ions, the Van't Hoff factor $i \approx n$.

   • $K_2SO_4 \to 2K^+ + SO_4^{2-}$ : $n = 3$
   • $NaCl \to Na^+ + Cl^-$ : $n = 2$
   • $MgSO_4 \to Mg^{2+} + SO_4^{2-}$ : $n = 2$
   • $KCl \to K^+ + Cl^-$ : $n = 2$

   $K_2SO_4$ gives the largest number of ions (3), so it has the maximum Van't Hoff factor.

   ✓Final answer

   (a) K2SO4

7. CBSE 2025Set ANNUAL1 markMCQ
   Q.The value of Van't Hoff factor

   (i) for complete dissociation of MgSO4 is -

   (a) 1

   (b) 2

   (c) 3

   (d) 4

   ›Reveal solutionSolution

   MgSO4 is a strong electrolyte that on complete dissociation gives 2 ions per formula unit, so i = 2.

   The Van't Hoff factor is defined as:

   i = (observed colligative property)/(calculated colligative property assuming no dissociation) = (actual number of particles in solution)/(number of formula units dissolved)

   MgSO4 dissociates in water as:

   MgSO4 -> Mg2+ + SO4^2-

   One formula unit gives 2 ions (1 Mg2+ + 1 SO4^2-) on complete dissociation. So for complete dissociation:

   i = 2

   (Note: in practice MgSO4, being a 2-2 electrolyte, shows some ion-pairing so the experimental i is a little less than 2, but for 'complete dissociation' the theoretical value is exactly 2.)

   ✓Final answer

   (b) 2.

8. CBSE 2025Set ANNUAL1 markMCQ
   Q.For solutes which do not undergo any association or dissociation in solution, the Van't Hoff factor

   (i) will be –

   (i) less than 1

   (ii) more than 1

   (iii) equal to 1

   (iv) zero

   ›Reveal solutionSolution

   The van't Hoff factor $i$ measures the ratio of actual to normal number of particles; if a solute neither associates nor dissociates, that ratio is exactly 1.

   The van't Hoff factor is defined as:

   $i = \dfrac{\text{normal molar mass}}{\text{observed molar mass}} = \dfrac{\text{observed number of particles after dissolution}}{\text{number of particles as per formula}}$

   • If the solute dissociates (e.g. NaCl → Na⁺ + Cl⁻), the number of particles increases, so $i > 1$.

   • If the solute associates (e.g. acetic acid dimerising in benzene), the number of particles decreases, so $i < 1$.

   • If the solute neither associates nor dissociates (e.g. glucose, urea in water), the number of particles in solution equals the number of formula units dissolved, so $i = 1$.

   ✓Final answer

   $i$ = equal to 1 (option iii).

9. CBSE 2024Set ANNUAL1 markMCQ
   Q.In comparison to a 0.01 M solution of glucose, the depression in the freezing point of 0.01 M MgCl2 solution is :

   (a) remains same

   (b) about twice

   (c) about three times

   (d) about four times

   ›Reveal solutionSolution

   $MgCl_2$ dissociates into 3 ions (van't Hoff factor $i \approx 3$), so its colligative effect — including freezing-point depression — is about 3 times that of a non-electrolyte like glucose at the same molar concentration.

   Depression in freezing point is a colligative property proportional to the number of solute particles in solution:

   $\Delta T_f = i \cdot K_f \cdot m$

   Glucose is a non-electrolyte, so $i = 1$ (it does not dissociate).

   $MgCl_2$ dissociates fully: $MgCl_2 \rightarrow Mg^{2+} + 2Cl^-$, giving 3 particles per formula unit, so its theoretical $i \approx 3$.

   At the same molar concentration (0.01 M), the depression for $MgCl_2$ is therefore approximately 3 times that of glucose.

   ✓Final answer

   (c) about three times.

10. CBSE 2024Set ANNUAL1 mark
    Q.What is Van't Hoff factor? OR Define Activation Energy.

    ›Reveal solutionSolution

    Van't Hoff factor i measures how many particles a solute actually produces in solution compared to the 'ideal' assumption of one particle per formula unit.

    Raoult's law and the colligative-property formulas (boiling-point elevation, freezing-point depression, osmotic pressure, etc.) assume the solute stays as single, non-interacting particles. But some solutes DISSOCIATE into more particles (e.g. NaCl → Na⁺ + Cl⁻, doubling the particle count) while others ASSOCIATE into fewer, larger particles (e.g. some carboxylic acids dimerise in non-polar solvents). This causes the OBSERVED colligative property to differ from the value calculated for a simple, non-dissociating solute.

    The Van't Hoff factor is defined as:

    i = (observed colligative property) / (calculated colligative property for no dissociation)

    Equivalently, i = actual number of particles in solution after dissociation/association ÷ number of formula units initially dissolved.

    • i > 1 → the solute dissociates (more particles than expected)
    • i < 1 → the solute associates (fewer particles than expected)
    • i = 1 → the solute neither dissociates nor associates

    The colligative-property formulas are then modified to include i, e.g. ΔTb = i·Kb·m, giving accurate predictions for electrolytes and associating solutes.

    ✓Final answer

    The Van't Hoff factor i = (observed colligative property)/(calculated colligative property), correcting for a solute that dissociates (i > 1) or associates (i < 1) in solution.

11. CBSE 2024Set ANNUAL1 markMCQ
    Q.When benzoic acid is dissolved in benzene, the van't Hoff factor will be

    (a) 1

    (b) 0.5

    (c) 2

    (d) 1.5

    ›Reveal solutionSolution

    Benzoic acid dimerises in benzene through intermolecular H-bonding, so the number of effective particles halves and $i = 1/n = 0.5$.

    The van't Hoff factor $i$ measures how the effective number of particles in solution deviates from the number of formula units dissolved:

    $i = \dfrac{\text{normal molar mass}}{\text{observed (abnormal) molar mass}} = \dfrac{\text{observed colligative property}}{\text{calculated colligative property (no association/dissociation)}}$

    In a polar, protic solvent (e.g. water), benzoic acid partially ionises, $i>1$. But benzene is non-polar, so ionisation cannot occur. Instead, two molecules of benzoic acid associate through two intermolecular hydrogen bonds between the $-COOH$ groups of each molecule, forming a stable cyclic dimer:

    $2\,C_6H_5COOH \rightleftharpoons (C_6H_5COOH)_2$

    If association is complete, every $n=2$ monomer units behave as a single kinetic particle, so

    $i = \dfrac{1}{n} = \dfrac{1}{2} = 0.5$

    Why the other options are wrong: (a) $i=1$ would mean the solute neither associates nor dissociates — true for an ideal non-electrolyte, not for benzoic acid in benzene. (c) $i=2$ would mean the molecule dissociates into 2 particles (electrolyte-like behaviour), which cannot happen in a non-polar solvent. (d) $i=1.5$ does not correspond to complete dimerisation of a single solute species.

    ✓Final answer

    $i = 0.5$ (option b) — benzoic acid dimerises in benzene.

12. CBSE 2024Set ANNUAL1 markMCQ
    Q.The values of Van't Hoff factors for KCl, NaCl, K2SO4 respectively are

    (a) 2, 2 and 2

    (b) 2, 2 and 3

    (c) 1, 1 and 2

    (d) 1, 1 and 1

    ›Reveal solutionSolution

    Van't Hoff factor for a fully-dissociating strong electrolyte equals the number of ions it produces per formula unit.

    KCl → K⁺ + Cl⁻ gives 2 ions ⟹ i = 2. NaCl → Na⁺ + Cl⁻ gives 2 ions ⟹ i = 2. K₂SO₄ → 2K⁺ + SO₄²⁻ gives 3 ions ⟹ i = 3. (These are the theoretical/limiting values assuming complete dissociation; measured i is often slightly lower due to inter-ionic attraction, but for the MCQ's purpose the ideal values 2, 2, 3 are used.)

    ✓Final answer

    (b) 2, 2 and 3.