JEE Main 2022 · 27 June · morning · Single correct · +4 / −1

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : At 10°C, the density of a 5 M solution of KCl [atomic masses of K Cl are 39 35.5 g mol⁻¹ respectively], is 'x' g ml⁻¹. The solution is cooled to -21°C. The molality of the solution will remain unchanged.
Reason (R) : The molality of a solution does not change with temperature as mass remains unaffected with temperature.
In the light of the above statements, choose the correct answer from the options given below :

  1. (a) Both (A) and (R) are true and (R) is the correct explanation of (A).
  2. (b) Both (A) and (R) are true but (R) is not the correct explanation of (A).
  3. (c) (A) is true but (R) is false.
  4. (d) (A) is false but (R) is true.
Answer and solution

Answer (a) Both (A) and (R) are true and (R) is the correct explanation of (A).

Solution

Chemistry ma’am · 4 steps

Cooling changes the volume, not the masses. Molality uses only masses, so it stays exactly the same.

  1. Two different units. Molarity divides moles of solute by the volume of solution. Molality divides moles of solute by the mass of solvent.

    m = nₛₒₗᵤₜₑ/(wₛₒₗᵥₑₙₜ (kg))

  2. What cooling does. Going from 10°C to -21°C, the solution contracts, so its volume and density change. That changes the molarity of 5 M. No solute or solvent is added or removed, so the moles of KCl and the mass of water stay fixed.
  3. Extra data. The density x and the molar mass of KCl (74.5 g mol⁻¹) only give the actual value, m = 5000/(1000x - 372.5). You do not need them to decide whether it changes.
  4. So. (A) is true, because the molality stays the same on cooling. (R) is true and gives exactly that reason: molality is built from masses, and mass does not depend on temperature. The answer is (a).

The idea to keep. Any concentration built only from masses or moles (molality, mole fraction, mass percent) ignores temperature. Anything with volume in it (molarity, normality) changes when the solution is heated or cooled.

Answer from the NTA final answer key. Solution by PrepWiser.

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Asked about 150 times in JEE Main since 2020. This question is from 2022.