Problem 107 - A Complete Resource Book in Chemistry for JEE Main

Question

Consider the following statements: I. Rate of transfer of \(\mathrm{D}^{+}\)from \(\mathrm{D}_{2} \mathrm{O}\) is slower than that of \(\mathrm{H}^{+}\)from \(\mathrm{H}_{2} \mathrm{O} .\) II. \(\mathrm{K}_{\text {a for }} \mathrm{CH}_{3} \mathrm{COOH} \rightleftharpoons \mathrm{CH}_{3} \mathrm{COO}^{-}+\mathrm{H}^{+}\)is nearly similar to that of \(\mathrm{K}_{\mathrm{a}}\) for \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{~N}^{+} \mathrm{H}_{3}\) III. \({ }_{1} \mathrm{H}^{3}\) is a radioactive isotope. Here, correct statements are: (a) I, II, III (b) II, III (c) I, II (d) I, III

Step-by-Step Solution

Answer

The correct statements are I and III, so the answer is (d) I, III.

Step 1: Understanding Statement I

Statement I claims that the rate of transfer of \(\mathrm{D}^{+}\) from \(\mathrm{D}_{2} \mathrm{O}\) is slower than that of \(\mathrm{H}^{+}\) from \(\mathrm{H}_{2} \mathrm{O}\). This is correct because the deuterium ion \(\mathrm{D}^{+}\) is heavier than the hydrogen ion \(\mathrm{H}^{+}\), leading to slower movement in solution. Therefore, Statement I is true.

Step 2: Analyzing Statement II

Statement II states that the acid dissociation constant \(\mathrm{K}_a\) for both acetic acid \(\mathrm{CH}_3 \mathrm{COOH}\) and the anilinium ion \(\mathrm{C}_6 \mathrm{H}_5 \mathrm{N}^{+} \mathrm{H}_3\) are nearly similar. This is incorrect because acetic acid is a weak acid and its \(\mathrm{K}_a\) value greatly differs from that of the anilinium ion, which is far weaker.

Step 3: Examining Statement III

Statement III suggests that \(\,{ }_{1} \mathrm{H}^{3}\) (known as tritium) is a radioactive isotope. Tritium is indeed radioactive and undergoes beta decay. Thus, Statement III is correct.

Step 4: Determining the Correct Answer

Based on the analysis, Statements I and III are correct. We ignore Statement II because it contradicts the known \(\mathrm{K}_a\) values of acetic acid and the anilinium ion. Therefore, the correct answer is option (d) I, III.

Key Concepts

Deuterium vs Hydrogen

Deuterium and hydrogen are both isotopes of the element hydrogen, but they differ in their atomic structures. Hydrogen, often referred to as protium, has just one proton in its nucleus, while deuterium adds one neutron to this proton, making it twice as heavy. This extra neutron causes deuterium to have a greater mass than protium.
When it comes to the rate of transfer in solutions, the mass plays a significant role. In aqueous solutions, \(\mathrm{D}^{+}\), a deuterium ion, moves more slowly than \(\mathrm{H}^{+}\), a hydrogen ion, due to its heavier mass. Therefore, any chemical or physical activity involving deuterium is generally slower, owing to this larger mass, resulting in what is known as an "isotope effect." This effect makes chemical reactions involving deuterium more sluggish compared to their hydrogen counterparts.
Deuterium's distinct characteristics lead to unique research applications, particularly in studies of reaction mechanisms and kinetics in chemistry.

Acid Dissociation Constant (K_a)

The acid dissociation constant, marked as \(K_a\), is a key concept in understanding how acids behave in solutions. It provides a quantitative measure of an acid's strength, specifically its ability to donate \(\mathrm{H}^{+}\) ions to the solution. The larger the \(K_a\) value, the stronger the acid, meaning it dissociates more in solution.
Strong acids, which have high \(K_a\) values, dissociate nearly completely in water, while weak acids only partially dissociate, indicated by smaller \(K_a\) values. This dissociation constant is crucial for predicting the pH of solutions and the behavior of acids in chemical reactions.
For instance, acetic acid \(\mathrm{CH}_3 \mathrm{COOH}\) is a weak acid with a certain \(K_a\) value that is much larger compared to even weaker acids, such as the anilinium ion \(\mathrm{C}_6 \mathrm{H}_5 \mathrm{N}^{+} \mathrm{H}_3\). Understanding these differences is essential when working with acid-base equilibrium and titration calculations.

Radioactive Isotopes

Isotopes are atoms of the same element that differ in the number of neutrons in their nuclei. Radioactive isotopes, also known as radioisotopes, are isotopes that are unstable and undergo radioactive decay – a process by which they release particles or electromagnetic radiation to achieve stability.
Tritium \(\,_{1} \mathrm{H}^{3}\), with one proton and two neutrons in its nucleus, is a well-known radioactive isotope of hydrogen. It undergoes beta decay, where a neutron in its nucleus transforms into a proton, an electron, and an anti-neutrino. This decay process releases energy, which can be hazardous but also useful in various scientific applications, such as tracing and dating studies.
Radioactive isotopes have broad applications. They are employed in medical diagnostic techniques, radioactive tracers in research, and even in nuclear power generation. However, due to their radioactivity, handling such isotopes necessitates care and strict safety protocols to prevent exposure and contamination.