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) \(\mathrm{C}>\mathrm{B}>\mathrm{A}\)

Short answer

The correct order is (c) \( \mathrm{B} > \mathrm{A} > \mathrm{C} \).

Step-by-step solution

Understanding pKa and Acid Strength

The pKa value of an acid indicates its acid dissociation constant. A lower pKa value means a stronger acid, as it dissociates more readily in solution to release protons.

Compare the pKa Values

We are given pKa values as follows: \( \text{pKa of } A = 4.3 \), \( \text{pKa of } B = 3.3 \), and \( \text{pKa of } C = 5.5 \). To determine acid strength, identify which acid has the lowest pKa.

Rank the Acids by Strength

Since a lower pKa value indicates a stronger acid, we can rank the acids from strongest to weakest: \( \mathrm{B} (3.3) > \mathrm{A} (4.3) > \mathrm{C} (5.5) \).

Select the Correct Answer

Based on the ranking, the correct order of acid strength is \( \mathrm{B} > \mathrm{A} > \mathrm{C} \). The corresponding answer choice is (c).

Key concepts

Acid Dissociation Constant

The acid dissociation constant, often represented as Ka, is a crucial concept in understanding how acids behave in solution. It quantitatively measures the strength of an acid in terms of its ability to donate protons (hydrogen ions) to the surrounding medium. A higher acid dissociation constant indicates that the acid dissociates more readily, releasing more protons and, consequently, acting as a stronger acid. This strength of an acid is important in many chemical reactions, especially those in biological systems or industrial processes, where precise control over acidity and alkalinity is necessary. The dissociation constant provides insight into the extent of ionization of the acid under equilibrium conditions. This helps chemists and students quickly determine an acid's potency and predict its behavior in various chemical environments.

Comparing pKa Values

The pKa value is a logarithmic scale that provides a simple way to compare the strength of different acids. It is derived from the acid dissociation constant using the relationship: \[\text{pKa} = -\log_{10}(K_a)\]Since the pKa is calculated using a negative logarithm, a lower pKa value directly corresponds to a stronger acid. This is counterintuitive at first glance, as one might assume that a higher number indicates a stronger acid. Thus, it is essential for students to remember that in the context of pKa, smaller numbers indicate a more robust ability to donate protons.In comparing acids, simply lining up their pKa values in ascending order is a quick way to identify their relative strengths. This is because the logarithmic scale compresses large disparities in acid strength into easily comparable figures, helping chemists make rapid and accurate assessments.

Ranking Acids by Strength

To determine the strength of acids, one must rank them based on their pKa values, grouping them from the strongest to the weakest acid. This ranking provides a clear hierarchy, allowing one to understand which acid will more readily give up protons in a chemical reaction. For instance, when given pKa values like in this exercise - 3.3 for B, 4.3 for A, and 5.5 for C - one should note that B, with the lowest pKa, is the strongest acid. The importance of ranking lies in its ability to predict how acids will react in mixtures. If a stronger acid is present, it will dissociate first and impact the overall pH of the solution more significantly compared to a weaker acid. This context is crucial in processes such as buffering, titrations, and metabolic reactions within living organisms. Understanding this hierarchy helps foster an appreciation for the nuanced chemistry that underlies acid-base reactions, an essential concept for both beginner and advanced students alike.