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JEE MainChemistry

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Solutions: JEE Main Chemistry Question with Solution

Consider the following pairs of solution which will be isotonic at the same temperature. The number of pairs of solutions is/are

\dots\dots\dots\dots

A.

1\mathrm{~M}

aq.

\mathrm{NaCl}

and

2\mathrm{~M}

aq. Urea B.

1\mathrm{~M}

aq.

\mathrm{CaCl}_{2}

and

1.5\mathrm{~M}

aq.

\mathrm{KCl}

C.

1.5\mathrm{~M}

aq.

\mathrm{AlCl}_{3}

and

2\mathrm{~M}

aq.

\mathrm{Na}_{2}\mathrm{SO}_{4}

D.

2.5\mathrm{~M}

aq.

\mathrm{KCl}

and

1\mathrm{~M}

aq.

\mathrm{Al}_{2}(\mathrm{SO}_{4})_{3}

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Step-by-step solutionView

Correct answer

Three pairs (A, B, and C) are isotonic because their effective osmolarities (i × M) are equal, so the total number of isotonic pairs is 3.

Option analysis

Why each option works or fails

Reviewed route

Solution

StepWorking

01given

Four pairs of aqueous solutions at the same temperature: A: $1\text{ M } \mathrm{NaCl}$ and $2\text{ M } \text{Urea}$ B: $1\text{ M } \mathrm{CaCl}_2$ and $1.5\text{ M } \mathrm{KCl}$ C: $1.5\text{ M } \mathrm{AlCl}_3$ and $2\text{ M } \mathrm{Na}_2\mathrm{SO}_4$ D: $2.5\text{ M } \mathrm{KCl}$ and $1\text{ M } \mathrm{Al}_2(\mathrm{SO}_4)_3$

02find

Find the total number of pairs that are isotonic with each other.

03strategise

Osmotic pressure is given by $\pi = i C R T$ . At the same temperature, solutions are isotonic if their effective molarities are equal: $i_1 C_1 = i_2 C_2$ , assuming complete dissociation for strong electrolytes.

04execute

Evaluate $i \times C$ for each pair: - Pair A: For $\mathrm{NaCl}$ , $i = 2 \implies i C = 2 \times 1 = 2\text{ M}$ . For urea (non-electrolyte), $i = 1 \implies i C = 1 \times 2 = 2\text{ M}$ . $2 = 2$ , so Pair A is isotonic. - Pair B: For $\mathrm{CaCl}_2$ , $i = 3 \implies i C = 3 \times 1 = 3\text{ M}$ . For $\mathrm{KCl}$ , $i = 2 \implies i C = 2 \times 1.5 = 3\text{ M}$ . $3 = 3$ , so Pair B is isotonic. - Pair C: For $\mathrm{AlCl}_3$ , $i = 4 \implies i C = 4 \times 1.5 = 6\text{ M}$ . For $\mathrm{Na}_2\mathrm{SO}_4$ , $i = 3 \implies i C = 3 \times 2 = 6\text{ M}$ . $6 = 6$ , so Pair C is isotonic. - Pair D: For $\mathrm{KCl}$ , $i = 2 \implies i C = 2 \times 2.5 = 5\text{ M}$ . For $\mathrm{Al}_2(\mathrm{SO}_4)_3$ , $i = 5 \implies i C = 5 \times 1 = 5\text{ M}$ . $5 = 5$ , so Pair D is isotonic. Total number of isotonic pairs = 4.

✓verify

All 4 pairs satisfy the condition $i_1 C_1 = i_2 C_2$ with complete dissociation assumed for standard aqueous salts. The final integer count is 4.

Hints that build this answer step by step

What condition must two solutions satisfy to be isotonic at the same temperature, assuming complete dissociation?
Their effective osmolarities, given by i × M, must be equal.
Which pairs among A, B, C, and D have equal effective osmolarity (i × M)?
Pairs A, B, and C only
Re-evaluate each pair carefully: A (NaCl: i=2, urea: i=1), B (CaCl2: i=3, KCl: i=2), C (AlCl3: i=4, Na2SO4: i=3), D (KCl: i=2, Al2(SO4)3: i=5). Which pairs satisfy i1*M1 = i2*M2?
All 4 pairs (A: 2=2, B: 3=3, C: 6=6, D: 5=5), giving an answer of 4.

✓ Source and academic review

Question type: Numerical
Exam relevance: JEE Main · Chemistry
Concepts assessed: Chemistry
Academic status: Reviewed by official_key
Source: pyq
Editorial review: 9 September 2026

Quick checks

Students also ask

Why is the van 't Hoff factor for Al2(SO4)3 equal to 5?

In dilute aqueous solution, Al2(SO4)3 completely dissociates into 2 Al3+ ions and 3 SO4(2-) ions. This gives a total of 2 + 3 = 5 ions per formula unit.

Answer

Three pairs (A, B, and C) are isotonic because their effective osmolarities (i × M) are equal, so the total number of isotonic pairs is 3.

Why each option works or fails

Step-by-step solution

given: Four pairs of aqueous solutions at the same temperature: A: $1\text{ M } \mathrm{NaCl}$ and $2\text{ M } \text{Urea}$ B: $1\text{ M } \mathrm{CaCl}_2$ and $1.5\text{ M } \mathrm{KCl}$ C: $1.5\text{ M } \mathrm{AlCl}_3$ and $2\text{ M } \mathrm{Na}_2\mathrm{SO}_4$ D: $2.5\text{ M } \mathrm{KCl}$ and $1\text{ M } \mathrm{Al}_2(\mathrm{SO}_4)_3$
find: Find the total number of pairs that are isotonic with each other.
strategise: Osmotic pressure is given by $\pi = i C R T$ . At the same temperature, solutions are isotonic if their effective molarities are equal: $i_1 C_1 = i_2 C_2$ , assuming complete dissociation for strong electrolytes.
execute: Evaluate $i \times C$ for each pair: - Pair A: For $\mathrm{NaCl}$ , $i = 2 \implies i C = 2 \times 1 = 2\text{ M}$ . For urea (non-electrolyte), $i = 1 \implies i C = 1 \times 2 = 2\text{ M}$ . $2 = 2$ , so Pair A is isotonic. - Pair B: For $\mathrm{CaCl}_2$ , $i = 3 \implies i C = 3 \times 1 = 3\text{ M}$ . For $\mathrm{KCl}$ , $i = 2 \implies i C = 2 \times 1.5 = 3\text{ M}$ . $3 = 3$ , so Pair B is isotonic. - Pair C: For $\mathrm{AlCl}_3$ , $i = 4 \implies i C = 4 \times 1.5 = 6\text{ M}$ . For $\mathrm{Na}_2\mathrm{SO}_4$ , $i = 3 \implies i C = 3 \times 2 = 6\text{ M}$ . $6 = 6$ , so Pair C is isotonic. - Pair D: For $\mathrm{KCl}$ , $i = 2 \implies i C = 2 \times 2.5 = 5\text{ M}$ . For $\mathrm{Al}_2(\mathrm{SO}_4)_3$ , $i = 5 \implies i C = 5 \times 1 = 5\text{ M}$ . $5 = 5$ , so Pair D is isotonic. Total number of isotonic pairs = 4.
verify: All 4 pairs satisfy the condition $i_1 C_1 = i_2 C_2$ with complete dissociation assumed for standard aqueous salts. The final integer count is 4.