MHT CET · Chemistry · Solutions

What is the expected value of \(\Delta T_f\) for \(1.25 \mathrm{~m} \mathrm{CaCl}_2\) solution if 1.25 m sucrose solution has \(\Delta \mathrm{T}_{\mathrm{f}}\) value \(\mathrm{x} K\) ?

A \(x\) K
B \(\frac{x}{2} \mathrm{~K}\)
C \(2 x \mathrm{K}\)
D \(3 x\) K

Verified Solution

Answer & Solution

Correct Answer

(D) \(3 x\) K

Step-by-step Solution

Detailed explanation

For sucrose solution, \(\left(\Delta T_f\right)_1=K_f m_1 \ldots\). (i)
For \(\mathrm{CaCl}_2\) solution, \(\left(\Delta \mathrm{T}_{\mathrm{f}}\right)_2=\mathrm{iK}_{\mathrm{f}} \mathrm{m}_2 \quad \ldots\) (ii),
From equation (i) and (ii),
\(\frac{\left(\Delta T_f\right)_1}{\left(\Delta T_f\right)_2} =\frac{m_1}{i_2} \)
\( \therefore \left(\Delta T_f\right)_2 =\frac{\left(\Delta T_f\right)_1 \times i \times m_2}{m_1} \)
\( =\frac{x K \times 3 \times 1.25 \mathrm{~m}}{1.25 \mathrm{~m}} \quad\left(\because \text { i for } \mathrm{CaCl}_2=3\right) \)
\( =3 x \mathrm{K}\)

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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