Problem 28 - Chemistry and Chemical Reactivity

Question

Which is the stronger of the following two acids? (a) acetic acid, \(\mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{H}, K_{\mathrm{a}}=1.8 \times 10^{-5}\) (b) chloroacetic acid, \(\mathrm{ClCH}_{2} \mathrm{CO}_{2} \mathrm{H}, \mathrm{p} K_{\mathrm{a}}=2.85\)

Step-by-Step Solution

Answer

Chloroacetic acid is the stronger acid, with a higher \(K_a\) value.

Step 1: Understanding Acid Strength

The strength of an acid is determined by its ability to donate protons, which is quantified by the acid dissociation constant \(K_a\). A stronger acid has a higher \(K_a\) value.

Step 2: Converting \(pK_a\) to \(K_a\) for Chloroacetic Acid

To compare \(K_a\) values, convert chloroacetic acid's \(pK_a\) to \(K_a\) using the formula: \[ K_a = 10^{-pK_a} \] where \(pK_a = 2.85\). So, \[ K_a = 10^{-2.85} \approx 1.41 \times 10^{-3} \].

Step 3: Comparing \(K_a\) Values

Now compare the \(K_a\) values of both acids. Acetic acid has \(K_a = 1.8 \times 10^{-5}\) and chloroacetic acid has \(K_a \approx 1.41 \times 10^{-3}\). Since \(1.41 \times 10^{-3} > 1.8 \times 10^{-5}\), chloroacetic acid is the stronger acid.

Key Concepts

Acid Dissociation Constant

The acid dissociation constant, abbreviated as \(K_a\), is a measure of the strength of an acid in solution. It represents the equilibrium constant for the dissociation of an acid into its corresponding proton \((H^+)\) and anion. An acid's \(K_a\) value is a crucial indicator of how readily it gives up its proton, and thus, its strength.

• A large \(K_a\) value means that the acid dissociates completely in solution, indicating a strong acid.
• A small \(K_a\) value suggests a weak acid that does not donate its protons as readily.

Understanding \(K_a\) allows chemists to predict the behavior of acids in various environments and is essential for comparing the relative strength of different acids.

Equilibrium Constant

In the context of acids, the equilibrium constant \(K_a\) governs the balance of the forward and reverse reactions in acid dissociation. At equilibrium, the rate of formation of products \(H^+\) and anion equals the rate of their recombination to create the acid.
Understanding equilibrium is essential because:

• It helps to establish the concentration of each species at a point where the reaction seems "at rest".
• The position of equilibrium can tell us more about the nature of the solution - acidic, neutral, or basic.
• It determines how changes in concentration, pressure, temperature, or presence of catalysts can affect the\( \)dissociation process.

By knowing the equilibrium constant, one can manipulate reactions to favor either the formation of more product (dissociated ions) or more reactant (undissociated acid).

pKa

\(pK_a\) is the negative logarithm of the acid dissociation constant \(K_a\). It offers a more convenient way to compare the strengths of acids, especially when \(K_a\) values differ by several orders of magnitude. Here's why \(pK_a\) is handy:

• \(pK_a\) compresses the wide range of \(K_a\) values into a more manageable numeric scale, usually between 0 and 14 for most acids.
• Lower \(pK_a\) values correspond to stronger acids, which have a higher tendency to give up protons.
• For calculating the \(K_a\) from \(pK_a\), simply take the antilogarithm: \( K_a = 10^{-pK_a} \). This is crucial for comparing acids using standardized data.

Remember, because \(pK_a\) and \(K_a\) are inversely related, a strong grasp of both concepts enables a better prediction of acid behavior.

Proton Donation

The ability of an acid to donate a proton \((H^+)\) is central to its definition and its strength. Acids that easily give up protons are considered strong acids, while those that hold onto their protons tightly are termed weak acids.
There are a few important notes about proton donation:

• Proton donation is often driven by the surrounding solvent, temperature, and other present ions.
• When an acid donates a proton, it forms what is known as its conjugate base, which can sometimes re-associate with the proton under different conditions.
• Consequently, the nature of the conjugate base can also affect the overall tendency for proton donation, influencing the \(K_a\) and \(pK_a\) values.

Overall, recognizing how proton donation affects acid strength is necessary for predicting and understanding chemical reactions involving acids.