Problem 193 - A Complete Resource Book in Chemistry for JEE Main

Question

Mark the correct statements (a) \(\mathrm{pK}_{\mathrm{a}}+\mathrm{pK}_{\mathrm{b}}=\mathrm{pK}_{\mathrm{w}}\), at all temperatures. (b) Acetic acid behaves like a strong acid in \(\mathrm{NH}_{3}\). (c) \(\mathrm{H}_{3} \mathrm{O}^{+}\)is a strong nucleophile (d) \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{O}^{-}\)is a weaker base than \(\mathrm{OH}^{-}\).

Step-by-Step Solution

Answer

Only statement (d) is correct.

Step 1: Analyze Statement (a)

We are given that \( \mathrm{pK}_{\mathrm{a}} + \mathrm{pK}_{\mathrm{b}} = \mathrm{pK}_{\mathrm{w}} \) at all temperatures. Typically, the relationship \( \mathrm{pK}_{\mathrm{a}} + \mathrm{pK}_{\mathrm{b}} = \mathrm{pK}_{\mathrm{w}} \) holds at 25°C, where \( \mathrm{pK}_{\mathrm{w}} \) is 14. However, this relationship depends on temperature, as \( \mathrm{pK}_{\mathrm{w}} \) changes with temperature. Hence, (a) is false.

Step 2: Analyze Statement (b)

Acetic acid is a weak acid with a \( \mathrm{K}_{\mathrm{a}} \) value of about \(1.8 \times 10^{-5}\). In liquid ammonia, which is a more basic environment compared to water, acetic acid may ionize more completely compared to in water, but it does not mean it behaves like a strong acid as it does not completely dissociate. Therefore, (b) is false.

Step 3: Analyze Statement (c)

Hydronium ion \( \mathrm{H}_{3} \mathrm{O}^{+} \) is known as a proton donor, and in general chemical reactivity, it is not typically considered a strong nucleophile. Nucleophiles are species that donate electron pairs, and \( \mathrm{H}_{3} \mathrm{O}^{+} \) is proton-rich, hence not electron-rich. Therefore, (c) is false.

Step 4: Analyze Statement (d)

The ethoxide ion \( \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{O}^{-} \) is an alkoxide ion, which generally is a strong base due to the electron donation capability of the ethyl group. On the other hand, \( \mathrm{OH}^{-} \) is the hydroxide ion, known to be a very strong base. In comparison, \( \mathrm{OH}^{-} \) is stronger due to less steric hindrance and greater electronegativity impact of oxygen. Hence, (d) is true.

Key Concepts

pKa and pKb relationship

The relationship between the dissociation constants of an acid (\(\mathrm{pK}_a\)) and its conjugate base (\(\mathrm{pK}_b\)) is a fundamental concept in acid-base chemistry. It is commonly expressed as \(\mathrm{pK}_a + \mathrm{pK}_b = \mathrm{pK}_w\), where \(\mathrm{pK}_w\) is the ionic product of water. This equation holds true under standard conditions, which are typically at 25°C, where \(\mathrm{pK}_w\) equals 14.
This relation is crucial because it helps us understand the balance between acidity and basicity. However, it is important to note that \(\mathrm{pK}_w\) is temperature-dependent. As the temperature changes, so does \(\mathrm{pK}_w\). Therefore, the equation may not be valid at all temperatures. Understanding this temperature dependency is important in predicting behavior in different chemical environments.

Acid behavior in different solvents

Acids can behave differently depending on the solvent they are in. Solvent polarity, proticity (ability to donate protons), and dielectric constant can influence how acids dissociate.
For instance, acetic acid is considered a weak acid in water because it only partially dissociates. However, when in a more basic solvent like liquid ammonia, it appears to ionize more completely. This is because ammonia is more accepting of protons than water.
Yet, this does not mean acetic acid becomes a strong acid in ammonia. To be categorized as a strong acid, full ionization must occur, irrespective of the solvent. By understanding these principles, one can better anticipate how acid behavior changes in various environments.

Nucleophilicity

Nucleophilicity refers to the ability of a species to donate an electron pair. Strong nucleophiles are generally electron-rich and are typically anionic. Examples include \(\mathrm{OH}^{-}\), \(\mathrm{NH}_3\), and alkoxide ions.
The hydronium ion, \(\mathrm{H}_3\mathrm{O}^+\), is not a strong nucleophile because it is protonated and not electron-rich. Instead, \(\mathrm{H}_3\mathrm{O}^+\) acts as an electrophile—it donates protons rather than electrons.
Understanding nucleophilicity is important in predicting reaction mechanisms, as nucleophiles typically initiate a reaction by attacking electrophiles. Always consider the electron configuration and charge of the species to determine nucleophilicity.

Base strength comparison

Base strength can be compared by considering the ability to donate an electron pair. The strength of a base is influenced by its molecular structure, the stability of its conjugate acid, and its environment.
The ethoxide ion, \(\mathrm{C}_2\mathrm{H}_5\mathrm{O}^-\), is a strong base due to the electron-donating ethyl group. However, when compared to the hydroxide ion, \(\mathrm{OH}^-\), it is weaker.

• \(\mathrm{OH}^-\) is strong due to its small size and high charge density, providing less steric hindrance and more effective electron pair donation.
• Electronegativity plays a role—oxygen is more electronegative than carbon, contributing to \(\mathrm{OH}^-\) being a stronger base.

By comparing these characteristics, one can predict base strength and understand reactions involving bases.