JEE Mains · Chemistry · STD 12 -1. Solution and colligative properties

Elevation in boiling point for \(1.5\) molal solution of glucose in water is \(4 \,K\). The depression in freezing point for \(4.5\) molal solution of glucose in water is \(4\, K\) The ratio of molal elevation constant to molal depression constant \(\left( K _{ b } / K _{ f }\right)\) is \(....\)

A \(4\)
B \(1\)
C \(2\)
D \(3\)

Verified Solution

Answer & Solution

Correct Answer

(D) \(3\)

Step-by-step Solution

Detailed explanation

\(\Delta T _{ b }= i\,K _{ b } \,m\) \(\Delta T _{ f }= i\,K _{ i } \,m\) \(\frac{4}{4}=\frac{ K _{ b } 1.5}{ K _{ f } 4.5}\) \(\frac{ K _{ b }}{ K _{ f }}=3\)

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.

Same subject

Which of the following oxidation reactions are carried out by both \(\mathrm{K}_2 \mathrm{Cr}_2 \mathrm{O}_7\) and \(\mathrm{KMnO}_4\) in acidic medium?
A. \(\Gamma^{-} \rightarrow \mathrm{I}_2\)
B. \(S^{2-} \rightarrow S\)
C. \(\mathrm{Fe}^{2+} \rightarrow \mathrm{Fe}^{3+}\)
D. \(\Gamma^{-} \rightarrow \mathrm{IO}_3{ }^{-}\)
E. \(\mathrm{S}_2 \mathrm{O}_3{ }^{2-} \rightarrow \mathrm{SO}_4{ }^{2-}\)
Choose the correct answer from the options given below:

JEE Mains 2025 Medium

The results given in the below table were obtained during kinetic studies of the following reaction: \(2 A + B \longrightarrow C + D\)

Experiment	\([ A ] / molL ^{-1}\)	\([ B ] / molL ^{-1}\)	Initial \(rate/molL\) \(^{-1}\) \(\min ^{-1}\)
\(I\)	\(0.1\)	\(0.1\)	\(6.00 \times 10^{-3}\)
\(II\)	\(0.1\)	\(0.2\)	\(2.40 \times 10^{-2}\)
\(III\)	\(0.2\)	\(0.1\)	\(1.20 \times 10^{-2}\)
\(IV\)	\(X\)	\(0.2\)	\(7.20 \times 10^{-2}\)
\(V\)	\(0.3\)	\(Y\)	\(2.88 \times 10^{-1}\)

\(X\) and \(Y\) in the given table are respectively :

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