Question

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.

• A. Both (A) and (R) are true and (R) is the correct explanation of (A).
• B. Both (A) and (R) are true but (R) is not the correct explanation of (A).
• C. (A) is true but (R) is false.
• D. (A) is false but (R) is true.

Answer 1

The Correct Option is A

\(Density\) = \(‘x’\) \(gm\) \(ml^{–1}\)

\(∴\; molality\),

\(m=\frac{5×1000}{[x(1000)−372.5]}=7.96\)

\(≃ 8 m (Assuming \;x = 1)\)

\(∴ ΔT_f = iK_fm\)

Assuming complete dissociation of salt \((100\%)\); \((i = 2)\)

\(ΔT_f = 2 × 1.86 × 8 ≃ 29.76\)

Therefore, the solution does not freeze at \(–21°C\). 

This means that molality of the solution won’t change as \(x ≥ 1\).

Statement (II) is also correct as molality is mass dependent and hence, does not change with temperature.

However, as solvents are not mentioned, statement (I) can also be incorrect.

Therefore, the correct option is (A): Both (A) and (R) are true and (R) is the correct explanation of (A).