Question

Given below are the dissociation constant values of few acids. Arrange them in order of increasing acidic strength. \(\mathrm{H}_{2} \mathrm{SO}_{3}=1.3 \times 10^{-2}, \mathrm{HNO}_{2}=4 \times 10^{-4}\) \(\mathrm{CH}_{3} \mathrm{COOH}=1.8 \times 10^{-5}, \mathrm{HCN}=4 \times 10^{-10}\) (a) \(\mathrm{HCN}<\mathrm{CH}_{3} \mathrm{COOH}<\mathrm{HNO}_{2}<\mathrm{H}_{2} \mathrm{SO}_{3}\) (b) \(\mathrm{CH}_{3} \mathrm{COOH}<\mathrm{HNO}_{2}<\mathrm{HCN}<\mathrm{H}_{2} \mathrm{SO}_{3}\) (c) \(\mathrm{CH}_{3} \mathrm{COOH}<\mathrm{HCN}<\mathrm{H}_{2} \mathrm{SO}_{3}<\mathrm{HNO}_{2}\) (d) \(\mathrm{HNO}_{2}<\mathrm{H}_{2} \mathrm{SO}_{3}<\mathrm{CH}_{3} \mathrm{COOH}<\mathrm{HCN}\)

Short answer

\(\mathrm{HCN}<\mathrm{CH}_{3} \mathrm{COOH}<\mathrm{HNO}_{2}<\mathrm{H}_{2} \mathrm{SO}_{3}\)

Step-by-step solution

Understanding Acidic Strength and Dissociation Constant

The strength of an acid correlates with its dissociation constant (Ka). A higher Ka value indicates a stronger acid, as it dissociates more in solution, releasing more hydrogen ions (H+). To arrange the acids in order of increasing acidic strength, we will align them in order of increasing Ka values.

Listing Given Ka values

List the dissociation constant (Ka) values for the given acids: For \(\mathrm{H}_{2} \mathrm{SO}_{3}\), Ka = \(1.3 \times 10^{-2}\), for \(\mathrm{HNO}_{2}\), Ka = \(4 \times 10^{-4}\), for \(\mathrm{CH}_{3} \mathrm{COOH}\), Ka = \(1.8 \times 10^{-5}\), and for \(\mathrm{HCN}\), Ka = \(4 \times 10^{-10}\).

Arranging Acids by Increasing Ka Values

Arrange the given Ka values in ascending order to determine the increasing order of acidic strength: \(\mathrm{HCN} < \mathrm{CH}_{3} \mathrm{COOH} < \mathrm{HNO}_{2} < \mathrm{H}_{2} \mathrm{SO}_{3}\). Here, the smallest Ka value belongs to HCN and the largest to \(\mathrm{H}_{2} \mathrm{SO}_{3}\), indicating the former is the weakest and the latter is the strongest acid among those given.

Key concepts

Dissociation Constant

The dissociation constant, represented as Ka, is a fundamental concept in chemistry that quantifies the strength of an acid in a solution. In essence, it measures the extent to which an acid can separate into its ions when dissolved in water. The precise definition of the dissociation constant is the ratio of the concentration of the dissociated forms of the acid to the concentration of the undissociated form.

Mathematically, for a generic acid HA dissociating to H+ (a proton) and A- (the conjugate base), the dissociation constant can be written as:
\[\begin{equation}Ka = \frac{[H^+][A^-]}{[HA]}\end{equation}\]where [H+], [A-], and [HA] represent the molar concentrations of the hydrogen ions, the conjugate base, and the undissociated acid, respectively.

The size of the Ka value gives insight into the acid's propensity to lose a proton; a larger Ka indicates a stronger acid capable of ionizing more completely. When comparing acids, if one has a Ka value that is orders of magnitude greater than another, it is safe to assume that the former is significantly stronger as an acid than the latter.

Acid Strength Ranking

Acid strength ranking involves placing acids in order based on their relative strengths, which is crucial when predicting reaction outcomes and understanding chemical equilibrium. Acids with higher dissociation constants (Ka) are considered stronger because they release more hydrogen ions into the solution, thereby lowering the pH.

The ranking can be counterintuitive because it's an inverse relationship; lower pH values correspond to higher acid strengths, which in turn align with higher Ka values. When presented with a list of Ka values, as seen in the exercise, an acid with a smaller Ka (indicating lower acidity) would be placed before one with a larger Ka (indicating higher acidity).

For example, from the given Ka values, hydrocyanic acid (\(HCN\)) has the smallest Ka and is thus the weakest acid listed, while sulfuric acid (\(\mathrm{H}_2\mathrm{SO}_3\)) with the largest Ka value is the strongest. By understanding how to rank acids based on their Ka, students can more effectively determine the likely direction and extent of chemical reactions involving acids.

Acid Dissociation in Solution

Acid dissociation in solution is the process wherein an acid releases hydrogen ions (H+) and forms its conjugate base. This process is central to understanding the behavior of acids in aqueous solutions. The degree to which an acid dissociates is described by its dissociation constant, Ka. Complete dissociation, characteristic of strong acids, results in all acid molecules releasing their hydrogen ions. Conversely, weak acids only partially dissociate, maintaining a larger proportion of undissociated molecules.

Take acetic acid (\(\mathrm{CH}_3\mathrm{COOH}\)) as an example. It is a weak acid, and in water, it only partially dissociates into hydrogen ions (\(H^+\)) and acetate ions (\(\mathrm{CH}_3\mathrm{COO}^-\)). This partial dissociation is reflected in its relatively low Ka value compared to strong acids like sulfuric acid (\(\mathrm{H}_2\mathrm{SO}_3\)), which dissociates significantly more as indicated by a higher Ka value.

Students should note that while strong acids release more hydrogen ions, rendering the solution more acidic, the concentration of the undissiated acid will be lower in comparison to weak acids at equilibrium. Understanding this behavior is key to mastering concepts like pH calculations, buffer systems, and equilibrium constants in the study of acid-base chemistry.