Problem 59 - A Complete Resource Book in Chemistry for JEE Main

Question

pKa values of three acids \(\mathrm{A}, \mathrm{B}\) and \(\mathrm{C}\) are \(4.3,3.3\) and 5\. 5 respectively. Which of the following represents the correct order of acid strength? (a) \(\mathrm{A}>\mathrm{B}>\mathrm{C}\) (b) \(\mathrm{C}>\mathrm{A}>\mathrm{B}\) (c) \(\mathrm{B}>\mathrm{A}>\mathrm{C}\) (d) \(\mathrm{C}>\mathrm{B}>\mathrm{A}\)

Step-by-Step Solution

Answer

(c) B > A > C

Step 1: Understanding pKa and Acid Strength

The pKa value of an acid is a negative logarithmic measure of its acid dissociation constant \((K_a)\). It indicates how easily an acid donates protons \((H^+)\). The lower the pKa value, the stronger the acid, as it implies a larger \(K_a\).

Step 2: Ranking the Acids by pKa Values

We have three acids with pKa values: \(pKa_A = 4.3\), \(pKa_B = 3.3\), and \(pKa_C = 5.5\). To determine acid strength, compare their pKa values. \(pKa_B = 3.3\) is the smallest, indicating that Acid B is the strongest. \(pKa_A = 4.3\) is the next smallest, making Acid A the next strongest. \(pKa_C = 5.5\) is the largest, meaning Acid C is the weakest.

Step 3: Arrange Acids According to Strength

Based on pKa values: \(pKa_B < pKa_A < pKa_C\), the order of acid strength from strongest to weakest is \(B > A > C\). Therefore, the correct order is \(\) **B > A > C**.

Key Concepts

pKa values

The pKa value is an essential concept in understanding the strength of an acid. It is the negative logarithm of the acid dissociation constant, often denoted as \( K_a \). This value helps us determine how readily an acid releases its hydrogen ions, or protons (H⁺).
Lower pKa values mean stronger acids because they easily dissociate to give up protons. Conversely, higher pKa values indicate weaker acids that hold onto their protons more tightly.
When comparing acids, remember: \( ext{pKa} = - ext{log}(K_a) \). By understanding this relationship, you can quickly gauge the relative strength of different acids.

acid dissociation constant

The acid dissociation constant, \( K_a \), is a quantitative measure of the strength of an acid in solution. It represents the equilibrium constant for the dissociation of an acid into its constituent ions: a hydrogen ion and the conjugate base.
For instance, in water, the dissociation of an acid \( HA \) can be written as:
\[ HA \leftrightarrow H^+ + A^- \]
This equilibrium is governed by the \( K_a \) value. A large \( K_a \) indicates a strong acid that dissociates readily, producing more hydrogen ions in the solution. A small \( K_a \) suggests a weak acid that does not dissociate as easily. This is why a strong acid has a smaller pKa; the relationship is inverse due to the logarithmic calculation of pKa from \( K_a \).

proton donation

Proton donation is a fundamental characteristic of acids. When an acid donates a proton (H⁺), it is effectively undergoing dissociation. The ease with which an acid donates protons is indicative of its strength.
Strong acids, like hydrochloric acid, donate protons readily and completely dissociate in water. Weak acids, such as acetic acid, only partially dissociate.
This process is critical because the strength of an acid in donating protons determines many chemical properties and reactions. Understanding proton donation helps when considering acid-base reactions, acid strength, and calculating pKa values for different substances.

acid ranking

Acid ranking is the process of ordering acids from strongest to weakest based on their ability to donate protons, which we can evaluate through their pKa values. A smaller pKa value indicates a stronger acid, as it suggests greater proton donation ability.
To rank acids effectively:

• Compare pKa values; lower values denote stronger acids.
• Use the acid dissociation constant \( K_a \) if available, where a larger \( K_a \) equates to a stronger acid.
• Consider both chemical structure and environmental conditions, as these can impact acid behavior.

Ultimately, understanding these principles allows for the correct ranking of acids and better prediction of their behavior in various chemical settings.