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

Statements (b) is correct. Statements (a), (c), and (d) are incorrect.

Step 1: Analyze Statement (a)

Statement (a) claims that \( \mathrm{pK}_{\mathrm{a}}+\mathrm{pK}_{\mathrm{b}}=\mathrm{pK}_{\mathrm{w}} \) at all temperatures. \( \mathrm{pK}_{\mathrm{a}} \) and \( \mathrm{pK}_{\mathrm{b}} \) are the acid and base dissociation constants, respectively, and \( \mathrm{pK}_{\mathrm{w}} \) is the ion product of water. This relationship holds true only at 25°C where \( \mathrm{pK}_{\mathrm{w}} = 14 \). The statement is false as written since it implies the relationship holds at all temperatures.

Step 2: Analyze Statement (b)

Statement (b) claims that acetic acid behaves like a strong acid in \( \mathrm{NH}_{3} \). Since \( \mathrm{NH}_{3} \) is a much weaker acid than acetic acid, acetic acid will indeed donate protons more readily in the presence of ammonia, enhancing its acidity characteristics relative to the weak nature of the solvent \( \mathrm{NH}_{3} \). Therefore, the statement is true.

Step 3: Analyze Statement (c)

Statement (c) suggests \( \mathrm{H}_{3} \mathrm{O}^{+} \) is a strong nucleophile. Nucleophilicity refers to the ability of a species to donate a pair of electrons. \( \mathrm{H}_{3} \mathrm{O}^{+} \), being a strong acid and devoid of free electron pairs ready for donation, is a poor nucleophile. The statement is false.

Step 4: Analyze Statement (d)

Statement (d) claims \( \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{O}^{-} \) is a weaker base than \( \mathrm{OH}^{-} \). \( \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{O}^{-} \) (ethoxide ion) is actually a stronger base than \( \mathrm{OH}^{-} \) due to the additional electron-donating ethyl group. The statement is false.

Key Concepts

pKa and pKb Relationship

The relationship between the acid dissociation constant (\( \mathrm{pK_{a}} \)) and the base dissociation constant (\( \mathrm{pK_{b}} \)) is an important concept in acid-base equilibrium. Together, \( \mathrm{pK_{a} + pK_{b} = pK_{w}} \), where \( \mathrm{pK_{w}} \) is the ion product constant of water. However, it is crucial to note that this relationship is temperature-dependent. At 25°C, \( \mathrm{pK_{w} = 14} \), and the equation holds true. Yet, at different temperatures, \( \mathrm{pK_{w}} \) varies, which means that \( \mathrm{pK_{a} + pK_{b}} \) will also change accordingly. Thus, it is incorrect to say this relationship holds at all temperatures, as it only applies accurately at specific standard conditions.

Here's what to keep in mind about pKa and pKb:

• They are logarithmic and derived from the equilibrium constants of acids and bases.
• The lower the \( \mathrm{pK_{a}} \), the stronger the acid.
• The lower the \( \mathrm{pK_{b}} \), the stronger the base.

Understanding the pKa and pKb relationship aids in comprehending the balance between acids and bases in different solutions and how they interact.

Acid Strength in Different Solvents

Acids may exhibit different strengths depending on the solvent in which they are dissolved. This concept allows us to understand why acetic acid appears stronger in ammonia (\( \mathrm{NH_{3}} \)) even though it's a weak acid. \( \mathrm{NH_{3}} \) acts as a much weaker acid compared to acetic acid, thus making acetic acid release more protons when dissolved in it.

Factors influencing acid strength in solvents:

• Solvent's basicity plays a role; the more basic the solvent, the more likely the acid will donate protons.
• Solvent's ability to stabilize ions formed during the dissociation of the acid.
• The solvent environment impacts the degree of dissociation of the acid.

Therefore, understanding the acid strength in different solvents is essential for predicting the behavior of acids in various chemical environments and explains why acetic acid appears stronger in ammonia than in water.

Nucleophilicity and Acidity

Nucleophilicity and acidity are closely related but essentially different concepts. A nucleophile is a species that donates an electron pair in a chemical reaction, while an acid is a species that donates a proton. The hydronium ion (\( \mathrm{H_{3}O^{+}} \)), often mistaken as a potential nucleophile, is actually a strong acid.

Key points about nucleophilicity and acidity:

• Nucleophiles typically have available electron pairs they can donate.
• Acids like \( \mathrm{H_{3}O^{+}} \) lack these free electron pairs, therefore, they cannot act as nucleophiles.
• Nucleophilicity is often confused with basicity, but while both involve electron pairs, basicity directly relates to how readily a species accepts protons.

It's important to distinguish between these two properties because they fundamentally influence how molecules behave and react in different chemical contexts.

Comparison of Base Strengths

Comparing the strengths of bases can be insightful for predicting their reactivity and behavior in chemical reactions. A common comparison is between the ethoxide ion (\( \mathrm{C_{2}H_{5}O^{-}} \)) and hydroxide ion (\( \mathrm{OH^{-}} \)). Though similar in function, the additional ethyl group in ethoxide enhances its base strength.

Key factors affecting base strengths:

• The presence of electron-donating groups, like an ethyl group, can increase base strength by increasing electron density.
• Basicity is related to a molecule's ability to accept protons; thus, the availability of electrons plays a significant role.
• Larger anions tend to be more basic due to their ability to delocalize charge distribution, which stabilizes the ion.

Ultimately, these differences in base strength affect chemical processes and the overall reactivity of these species in various reactions, making the understanding of these characteristics invaluable in chemistry.