- Amal Augustine
- January 30, 2026
Perfect Your Concepts with Van’t Hoff Factor Numerical Problems with Answers
Understanding abnormal colligative properties is impossible without mastering Van’t Hoff factor numerical problems with answers. In physical chemistry, the Van’t Hoff factor (i) plays a crucial role in explaining deviations observed in boiling point elevation, freezing point depression, osmotic pressure, and vapour pressure lowering. For competitive exams, Van’t Hoff factor numerical problems with answers are frequently asked because they test both conceptual clarity and numerical accuracy.
The Van’t Hoff factor is defined as the ratio of the observed colligative property to the theoretical colligative property assuming no association or dissociation. In simple terms, it tells us how many effective particles a solute produces in solution. This concept forms the backbone of Van’t Hoff factor numerical problems with answers in examinations.
Concept of Van’t Hoff Factor
Mathematically, the Van’t Hoff factor is expressed as:
i=Observed colligative propertyCalculated colligative propertyi = \frac{\text{Observed colligative property}}{\text{Calculated colligative property}}
When solutes dissociate (like NaCl) or associate (like acetic acid in benzene), deviations occur. Practicing Van’t Hoff factor numerical problems with answers helps aspirants understand these deviations clearly.
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If i>1i > 1: dissociation occurs
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If i<1i < 1: association occurs
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If i=1i = 1: normal behavior
Most Van’t Hoff factor numerical problems with answers revolve around this classification.
Numerical Problem 1 (Dissociation)
A 0.1 molal NaCl solution shows a freezing point depression of 0.372 K.
Given Kf=1.86 K kg mol−1K_f = 1.86 \, \text{K kg mol}^{-1}
Solution:
Theoretical depression:
ΔTf=Kf×m=1.86×0.1=0.186 K\Delta T_f = K_f \times m = 1.86 \times 0.1 = 0.186 \, K
Observed depression = 0.372 K
i=0.3720.186=2i = \frac{0.372}{0.186} = 2
This is a classic example included in Van’t Hoff factor numerical problems with answers, confirming complete dissociation of NaCl.
Numerical Problem 2 (Association)
Acetic acid in benzene shows a Van’t Hoff factor of 0.5. Find the degree of association.
Solution:
For dimerization:
i=1−α2i = 1 – \frac{\alpha}{2} 0.5=1−α2⇒α=10.5 = 1 – \frac{\alpha}{2} \Rightarrow \alpha = 1
This type of association-based question is very common in Van’t Hoff factor numerical problems with answers.
Numerical Problem 3 (Electrolyte with Partial Dissociation)
A 0.2 molal KCl solution freezes at −0.68°C.
i=ΔTfKf×m=0.681.86×0.2=1.83i = \frac{\Delta T_f}{K_f \times m} = \frac{0.68}{1.86 \times 0.2} = 1.83
Such calculations form the core of Van’t Hoff factor numerical problems with answers in NEET chemistry.
Exam Importance
Almost every competitive exam includes Van’t Hoff factor numerical problems with answers because they combine:
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Colligative properties
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Electrolyte behavior
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Degree of dissociation or association
Repeated exposure to Van’t Hoff factor numerical problems with answers improves speed and accuracy.
Common Mistakes to Avoid
While solving Van’t Hoff factor numerical problems with answers, aspirants often:
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Forget to multiply molality with ii
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Apply wrong association formulas
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Ignore partial dissociation
Avoiding these mistakes is essential for mastering Van’t Hoff factor numerical problems with answers.
Tips to Solve Faster
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Always calculate theoretical colligative property first
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Compare with observed value
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Identify dissociation or association
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Apply correct formula for ii
Following this approach will make Van’t Hoff factor numerical problems with answers much easier.
Why Practice Matters
Without consistent practice, Van’t Hoff factor numerical problems with answers can feel confusing. However, once patterns are recognized, these problems become scoring opportunities. Repeated revision of Van’t Hoff factor numerical problems with answers strengthens conceptual understanding and boosts confidence.
MCQs on Van’t Hoff Factor Numerical Problems with Answers
1. Solution “X” dimerises in water to the extent of 80%.
2.5 g of X in 100 g of water increases the boiling point by 0.3°C.
The molar mass of X is (Kb=0.52 K kg mol−1)(K_b = 0.52\ \text{K kg mol}^{-1})
A. 65
B. 55
C. 86
D. 26
Answer: D
2. In comparison to 0.01 M glucose solution, the depression in freezing point of a 0.01 M MgCl₂ solution is
A. About twice
B. About three times
C. About six times
D. The same
Answer: B
3. Which relation is true for partial pressure and mole fraction?
A. pi=xi×Tp_i = x_i \times T
B. pi=xi×ptotalp_i = x_i \times p_{\text{total}}
C. pixi=V\frac{p_i}{x_i} = V
D. pixi=ptotalp_i x_i = p_{\text{total}}
Answer: B
4. Which does not show positive deviation from Raoult’s law?
A. Benzene–Chloroform
B. Benzene–Acetone
C. Benzene–Ethanol
D. Benzene–Carbon tetrachloride
Answer: A
5. Which change decreases vapour pressure of water in a sealed vessel?
A. Adding salt to water
B. Decreasing quantity of water
C. Decreasing volume of vessel
D. Keeping temperature constant
Answer: A
6. Henry’s constant for O₂ in water is 4.34×1044.34 \times 10^4 atm.
If PO2=0.434P_{O_2} = 0.434 atm, the mole fraction of O₂ is
A. 1.0×10−61.0 \times 10^{-6}
B. 7.93×10−47.93 \times 10^{-4}
C. 1.0×10−51.0 \times 10^{-5}
D. 4.0×10−64.0 \times 10^{-6}
Answer: C
7. Unit of Henry’s constant KhK_h is
A. atm mol⁻¹ dm³
B. mol⁻¹ dm³ atm⁻¹
C. atm mol dm⁻³
D. mol dm⁻³ atm⁻¹
Answer: D
8. Elevation in boiling point of 0.25 m solution
(Kb=0.52)(K_b = 0.52) is
A. 0.15 K
B. 0.13 K
C. 2.08 K
D. 0.52 K
Answer: B
9. Vapour pressure of solution when 9 g oxalic acid is dissolved in 9.9 mol water is
A. 0.99P100.99 P_1^0
B. 0.1P100.1 P_1^0
C. 0.9P100.9 P_1^0
D. 1.1P101.1 P_1^0
Answer: A
10. Relative lowering of vapour pressure is 0.002. Molality is
A. 0.02
B. 0.018
C. 0.111
D. 0.021
Answer: C
11. Deviations from Raoult’s law for acetone in
(A) chloroform and (B) carbon disulphide are
A. Positive, positive
B. Positive, negative
C. Negative, positive
D. Negative, negative
Answer: D
12. Vapour pressure of solution formed from CHCl₃ and CH₂Cl₂ is
A. 80.5
B. 79.5
C. 94.3
D. 105.5
Answer: C
13. Lowering of vapour pressure when 0.6 g urea is dissolved in 360 g water is
A. 0.027 mmHg
B. 0.031 mmHg
C. 0.017 mmHg
D. 0.018 mmHg
Answer: C
14. Acetic acid dimerisation in benzene: weight % and dissociation %
A. 1.62%, 98.3%
B. 0.81%, 98.3%
C. 0.5%, 8.6%
D. 1.4%, 98.3%
Answer: A
15. Van’t Hoff factor for KCl solution freezing at −0.68°C is
A. 3.72
B. 2
C. 1.83
D. 1.86
Answer: C
16. Solution boiling above both components shows
A. Negative deviation
B. Positive deviation
C. No deviation
D. Composition dependent
Answer: A
17. Change in internal energy for vaporisation of 3 moles is
A. 33 kcal
B. 39 kcal
C. 36 kcal
D. 15 kcal
Answer: A
18. Expression for molar depression constant is
A. RM1Tb21000ΔHvap\frac{R M_1 T_b^2}{1000 \Delta H_{vap}}
B. RM2Tf21000ΔHf\frac{R M_2 T_f^2}{1000 \Delta H_f}
C. RM2Tb21000ΔHvap\frac{R M_2 T_b^2}{1000 \Delta H_{vap}}
D. RM1Tf21000ΔHf\frac{R M_1 T_f^2}{1000 \Delta H_f}
Answer: D
19. Increasing pressure at constant temperature causes
A. Decrease in Haber rate
B. Increase in gas solubility
C. Increase in solid solubility
D. CO formation
Answer: B
20. Total vapour pressure of solution is
A. pA0x1x2\frac{p_A^0 x_1}{x_2}
B. pA0x2x1\frac{p_A^0 x_2}{x_1}
C. pB0x1x2\frac{p_B^0 x_1}{x_2}
D. pB0x2x1\frac{p_B^0 x_2}{x_1}
Answer: B
21. Ionic compound producing how many particles?
A. 3
B. 4
C. 2
D. 6
Answer: C
22. Higher elevation in boiling point is shown by
A. NaCl
B. Glucose
C. Both same
D. Neither
Answer: A
23. Highest freezing point is shown by
A. Al₂(SO₄)₃
B. BaCl₂
C. AlCl₃
D. NH₄Cl
Answer: D
24. Boiling point of benzene + benzoic acid solution is
A. 90.52°C
B. 104.35°C
C. 76.12°C
D. 80.42°C
Answer: D
25. Correct vapour pressure relation is
A. P0=Pn1n1+n2P^0 = P \frac{n_1}{n_1+n_2}
B. P0=Pn2n1+n2P^0 = P \frac{n_2}{n_1+n_2}
C. P=P0n2n1+n2P = P^0 \frac{n_2}{n_1+n_2}
D. P=P0n1n1+n2P = P^0 \frac{n_1}{n_1+n_2}
Answer: C
26. Freezing point of ethylene glycol solution is
A. 272 K
B. 271 K
C. 274 K
D. 275 K
Answer: B
27. Boiling point when vapour pressure is 732 mm is
A. 102°C
B. 101°C
C. 103°C
D. 100°C
Answer: B
28. Vapour over benzene–toluene mixture contains
A. Equal amounts
B. No prediction
C. More benzene
D. More toluene
Answer: C
29. For non-volatile solute
A. Vapour pressure increases
B. Vapour pressure is zero
C. Vapour pressure of solute is zero
D. All correct
Answer: C
30. Freezing point of 10% CH₃OH solution is
A. −9.6°C
B. 10°C
C. −6.45°C
D. None
Answer: C
Conclusion
In summary, Van’t Hoff factor numerical problems with answers are essential for mastering colligative properties. They bridge theory and application, making them a high-yield topic in exams. With regular practice and correct strategy, Van’t Hoff factor numerical problems with answers can be solved quickly and accurately, helping aspirants secure top scores in competitive chemistry examinations.
Amal Augustine is the founder of ExQuizMe, a dynamic learning and quiz platform built to make education engaging, competitive, and fun. A passionate learner and an academic achiever, Amal completed his schooling at Government HSS Manjapra, graduating with 92.5% in Computer Science. He later earned his degree from St. Stephen’s College, University of Delhi, one of India’s most prestigious arts and science institutions.
Currently, Amal is pursuing his Master’s degree at National Sun Yat-sen University, Taiwan, where he continues to deepen his interest in research and technology. Throughout his school and college years, he won 50+ national-level interschool and collegiate quiz competitions, was
Beyond academics, Amal Augustine is an avid reader of science journals, a dedicated research student, and a technology enthusiast who loves programming and exploring the world of Computer Science. Through ExQuizMe, he aims to make learning accessible, enjoyable, and empowering for students across the globe.