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. \(\mathrm{K}_{\mathrm{a}}\) 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

Short answer

(d) I, III

Step-by-step solution

Analyze Statement I

Statement I claims that the rate of transfer of \( \mathrm{D}^{+} \) (deuterium ion) from \( \mathrm{D}_{2} \mathrm{O} \) (heavy water) is slower than that of \( \mathrm{H}^{+} \) (hydronium ion) from regular \( \mathrm{H}_{2} \mathrm{O} \). This is a correct statement due to kinetic isotope effects, as deuterium is heavier than hydrogen, leading to slower reaction rates.

Analyze Statement II

Statement II compares the acid dissociation constant \( \mathrm{K}_{ ext{a}} \) of acetic acid \( \mathrm{CH}_{3} \mathrm{COOH} \) with that of the protonated aniline derivative \( \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{N}^{+} \mathrm{H}_{3} \). In reality, these two have different \( \mathrm{K}_{ ext{a}} \) values due to differences in their structure and acidity levels; hence, this statement is incorrect.

Analyze Statement III

Statement III mentions that \( _{1} \mathrm{H}^{3} \), also known as tritium, is a radioactive isotope of hydrogen. This statement is correct because tritium is indeed a radioactive isotope that undergoes beta decay.

Conclusion Based on Correct Statements

Based on the analysis: Statement I is correct, Statement II is incorrect, and Statement III is correct. Therefore, the correct statements are I and III.

Key concepts

Kinetic Isotope Effect

Kinetic Isotope Effect (KIE) is an intriguing concept in physical chemistry that describes how isotopes of an element can affect the rate of a chemical reaction. This occurs because isotopes, though chemically similar, differ in their atomic mass due to the presence of additional neutrons. These mass differences can influence the reaction rates when atoms are involved in the making or breaking of chemical bonds.

If we consider statement I from the exercise, it can be explained by the KIE. The transfer rate of the deuterium ion (\(\mathrm{D}^{+}\)) from heavy water (\(\mathrm{D}_2\mathrm{O}\)) is slower than that of the hydrogen ion (\(\mathrm{H}^{+}\)) from regular water (\(\mathrm{H}_2\mathrm{O}\)). This is because deuterium is heavier than hydrogen. The heavier mass means that the deuterium bonds in a chemical structure are stronger and require more energy to break compared to hydrogen. As a result:

• The reaction proceeds more slowly when deuterium is involved.
• This effect has practical implications in both chemical kinetics and understanding molecular dynamics.

Recognizing the KIE helps chemistry students appreciate why even small changes in molecular structure can significantly impact reaction speed.

Acid Dissociation Constant

The Acid Dissociation Constant, denoted as \(\mathrm{K}_a\), is a crucial parameter in chemistry that measures the extent to which an acid dissociates in solution. It gives insight into the acid's strength by indicating how many of its molecules donate protons to the solution.

In statement II from the exercise, the comparison of the \(\mathrm{K}_a\) values of acetic acid (\(\mathrm{CH}_3\mathrm{COOH}\)) and protonated aniline (\(\mathrm{C}_6\mathrm{H}_5\mathrm{NH}_3^+\)) can be examined. These acids feature significantly different structures, contributing to their varying acid dissociation constants. Here are some key points to understand:

• Acetic acid is a carboxylic acid, and its \(\mathrm{K}_a\) value reflects its comparative ability to donate a proton.
• Protonated aniline differs in structure as it contains an additional amine group, affecting its dissociation properties.
• The differences in molecular structures lead to a variation in electron densities around the acid groups, which in turn impacts the \(\mathrm{K}_a\) values.

This distinction helps explain why the \(\mathrm{K}_a\) values of these two acids are not nearly similar, thereby making statement II incorrect. Understanding \(\mathrm{K}_a\) allows chemists to predict the behavior of different acids in chemical reactions.

Radioactive Isotopes

Radioactive Isotopes are atoms with unstable nuclei that decay over time, emitting radiation. This is a fundamental concept in nuclear chemistry and affects various applications, from medical imaging to radiometric dating.

Statement III in the exercise highlights that \(_1\mathrm{H}^3\), known as tritium, is a radioactive isotope. Tritium is an isotope of hydrogen with two neutrons and one proton. Here's what makes radioactive isotopes notable:

• Instability and Decay: Such isotopes undergo decay as their nuclei attempt to reach a stable state. During decay, radiation is released, which can be in forms such as alpha, beta, and gamma rays.
• Applications: The unique properties of radioactive isotopes allow them to be harnessed in a variety of ways, such as carbon dating in archaeology, or tritium in fusion reactions and luminescent watches.
• Safety Concerns: Proper handling and use are critical because exposure to radiation can be harmful to living organisms.

Tritium’s radioactivity confirms the validity of statement III, highlighting its importance in scientific and practical applications.