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

None of the statements are correct.

Step 1: Analyze statement (a)

Statement (a) claims that \( \mathrm{pK}_{\mathrm{a}} + \mathrm{pK}_{\mathrm{b}} = \mathrm{pK}_{\mathrm{w}} \) at all temperatures. This is incorrect. The equation \( \mathrm{pK}_{\mathrm{a}} + \mathrm{pK}_{\mathrm{b}} = \mathrm{pK}_{\mathrm{w}} \) is valid only at a particular temperature, typically 25°C. As the ion-product of water, \( K_{w} \), changes with temperature, so do \( \mathrm{pK}_{\mathrm{a}} \) and \( \mathrm{pK}_{\mathrm{b}} \), and their sum is equal to the \( \mathrm{pK}_{w} \) value at only that specific temperature.

Step 2: Evaluate statement (b)

Statement (b) suggests that acetic acid behaves like a strong acid in \( \mathrm{NH}_3 \). This is incorrect as well. Acetic acid is a weak acid, and in a basic solvent such as \( \mathrm{NH}_3 \), it will not behave like a strong acid. Instead, it will become a bit more acidic relative to in water, due to higher basicity of \( \mathrm{NH}_3 \), but it will not transform into a strong acid.

Step 3: Check statement (c)

Statement (c) claims \( \mathrm{H}_3\mathrm{O}^+ \) is a strong nucleophile. This is incorrect, since \( \mathrm{H}_3\mathrm{O}^+ \) is actually a very poor nucleophile because it is a hydronium ion, which is commonly seen as an acid (a proton donor) rather than a nucleophile.

Step 4: Assess statement (d)

Statement (d) suggests that \( \mathrm{C}_2\mathrm{H}_5\mathrm{O}^- \) is a weaker base than \( \mathrm{OH}^- \). This is also incorrect. \( \mathrm{C}_2\mathrm{H}_5\mathrm{O}^- \) or ethoxide ion, is actually a stronger base than \( \mathrm{OH}^- \) due to the presence of the ethyl group which increases electron density on the oxygen, enhancing its basicity.

Key Concepts

pKa and pKb relationship

The relationship between pKa and pKb is a fundamental concept in acid-base chemistry. For any acid-base conjugate pair, their respective pKa and pKb values are related to the auto-ionization constant of water, denoted as Kw. This relationship can be summarized by the equation: \[ \mathrm{pK_a} + \mathrm{pK_b} = \mathrm{pK_w} \]However, this equation is conditional to a particular temperature, commonly at 25°C. At this temperature, water's ion-product constant, Kw, is approximately \(1.0 \times 10^{-14}\), which gives a pKw of 14. Therefore, the sum of the pKa and pKb for a conjugate acid-base pair equals 14 at 25°C.

• As the temperature changes, Kw also changes, altering both pKa and pKb.
• This means that the sum of pKa and pKb equals the pKw value only at a given temperature.

Hence, it is crucial to remember that the equality \( \mathrm{pK_a} + \mathrm{pK_b} = \mathrm{pK_w} \) is not universally applicable across all temperatures.

Temperature effect on Kw

Temperature has a significant impact on the ion-product constant of water, denoted as Kw. Kw is the equilibrium constant for the self-ionization of water into hydroxide and hydronium ions:\[ 2\,\mathrm{H}_2\mathrm{O} \rightleftharpoons \mathrm{H}_3\mathrm{O}^+ + \mathrm{OH}^- \]

• As temperature increases, Kw generally increases because the self-ionization reaction is endothermic.
• This implies an increase in both \([\mathrm{H}_3\mathrm{O}^+]\) and \([\mathrm{OH}^-]\) concentrations at higher temperatures.

The effect of temperature on Kw has practical implications for the calculations of pH, as well as for reactions where precise control of acidity or basicity is necessary. Understanding how Kw varies with temperature helps in applying acid-base principles accurately across different contexts.

Nucleophilicity

Nucleophilicity refers to the tendency of a species to donate an electron pair to form a chemical bond in reaction with an electrophile. It is a critical concept in understanding reaction mechanisms in organic and inorganic chemistry.

• Nucleophiles are usually negatively charged or neutral with lone pairs of electrons ready to donate.
• Strong bases often make strong nucleophiles since they can donate electrons efficiently.

For example, while hydroxide ions (\(\mathrm{OH}^-\)) are strong bases and good nucleophiles, hydronium ions (\(\mathrm{H}_3\mathrm{O}^+\)) are considered poor nucleophiles. The hydronium ion, being positively charged and an electron pair acceptor, is more suited for acidic reactions rather than nucleophilic attacks.

Factors Affecting Nucleophilicity:

• Charge: Negatively charged species are generally more nucleophilic.
• Electronegativity: Less electronegative atoms donate electrons more readily.
• Steric hindrance: Bulkier groups can impede nucleophilic attacks.

Basicity comparison

Basicity refers to the ability of a substance to act as a base, which is quantified by its ability to accept protons. It's crucial in comparing different bases, especially when predicting the outcome of chemical reactions.In comparing bases like hydroxide (\(\mathrm{OH}^-\)) and ethoxide (\(\mathrm{C}_2\mathrm{H}_5\mathrm{O}^-\)), understanding the influence of the molecular structure is key:

• \(\mathrm{C}_2\mathrm{H}_5\mathrm{O}^-\), or ethoxide, is a stronger base than \(\mathrm{OH}^-\).
• Ethoxide's increased basicity is attributed to the alkyl (ethyl) group which donates electron density.
• This donation stabilizes the negative charge more effectively, making it a stronger base.

The increased electron density around the oxygen atom in \(\mathrm{C}_2\mathrm{H}_5\mathrm{O}^-\) enhances its ability to bond with protons, thus illustrating a higher basicity compared to \(\mathrm{OH}^-\). Understanding these concepts helps in choosing appropriate bases for chemical reactions.