Question

The data below compare the strength of acetic acid with a related series of acids, where the H atoms of the \(\mathrm{CH}_{3}\) group in acetic acid are successively replaced by Br. $$\begin{array}{ll}\text { Acid } & \mathrm{p} K_{\mathrm{a}} \\\\\hline \mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{H} & 4.74 \\\\\mathrm{BrCH}_{2} \mathrm{CO}_{2} \mathrm{H} & 2.90 \\\\\mathrm{Br}_{2} \mathrm{CHCO}_{2} \mathrm{H} & 1.39 \\ \mathrm{Br}_{3} \mathrm{CCO}_{2} \mathrm{H} & -0.147 \\\\\hline\end{array}$$ (a) What trend in acid strength do you observe as \(\mathrm{H}\) is successively replaced by Br? Can you suggest a reason for this trend? (b) Suppose each of the acids above was present as a \(0.10 \mathrm{M}\) aqueous solution. Which would have the highest pH? The lowest pH?

Short answer

Acid strength increases with more bromine substitutions. The acetic acid (\(\text{CH}_3\text{CO}_2\text{H}\)) has the highest pH, while \(\text{Br}_3\text{CCO}_2\text{H}\) has the lowest pH.

Step-by-step solution

Analyzing the Acid Strength Trend

Observing the given data, we see that the \( pK_a\) values decrease as hydrogen atoms in \( \text{CH}_3\text{CO}_2\text{H} \) are replaced by bromine. \( pK_a \) values are decreasing from 4.74 to -0.147. This indicates that the acid strength increases with more bromine substitutions.

Explaining the Acid Strength Trend

The trend of increasing acid strength (decreasing \( pK_a \) value) as hydrogens are replaced by bromines can be explained by the electron-withdrawing nature of bromine. Bromine atoms stabilize the negative charge on the carboxylate anion (formed after deprotonation) through inductive effects, making the acid more willing to donate protons.

Determining Highest pH for 0.10 M Solutions

A higher \( pK_a \) value indicates a weaker acid, which means its dissociation in solution is less, leading to a higher pH. \( \text{CH}_3\text{CO}_2\text{H} \) with the highest \( pK_a \) of 4.74, is the weakest acid and will have the highest pH among these solutions.

Determining Lowest pH for 0.10 M Solutions

Conversely, a lower \( pK_a \) value corresponds to a stronger acid, which dissociates more in solution, resulting in a lower pH. \( \text{Br}_3\text{CCO}_2\text{H} \) with the lowest \( pK_a \) of -0.147 is the strongest acid and will produce the lowest pH in a 0.10 M solution.

Key concepts

pKa values

The concept of pKa values is crucial in understanding acid strength. pKa is a numerical value that indicates the strength of an acid. It represents the negative logarithm of the acid dissociation constant (\( K_a \)). Simply put, the lower the pKa value, the stronger the acid because it readily donates hydrogen ions in solution.

• High pKa values suggest weak acids.
• Low pKa values suggest strong acids.

The data from the exercise shows a decrease in pKa from 4.74 to -0.147 as more hydrogens in acetic acid are replaced by bromines. This indicates that the acidity increases, meaning these acids release protons more easily as the pKa values drop.

electron-withdrawing effects

Electron-withdrawing effects play a significant role in influencing the strength of acids. Elements or groups that are electron-withdrawing pull electron density away from other parts of the molecule. This can stabilize the negatively charged species formed after the acid donates a proton.
Bromine is an example of an electron-withdrawing element. In the context of the provided exercise, as bromine atoms replace hydrogens in acetic acid, they enhance the electron-withdrawing effects:

• This stabilization makes it easier for the acid to lose a proton, thereby increasing its strength.
• Increased electron-withdrawing effects correlate with lower pKa values and stronger acids.

bromine substitution

Bromine substitution is a process where bromine atoms replace hydrogen atoms in a molecule. This can significantly alter the chemical properties of the initial molecule. In the studied acids:

• Each substitution of bromine for hydrogen in acetic acid leads to stronger acid properties due to the reasons mentioned in electron-withdrawing effects.
• The data shows that more bromine substitutions lead to a progressive increase in acidity, indicated by decreasing pKa values.

Thus, bromine substitution greatly enhances acid strength due to bromine's ability to stabilize the negative charge on the carboxylate anion through inductive effects.

inductive effects

Inductive effects are crucial for explaining how electron-withdrawing groups like bromine influence the stability of anions formed after acids dissociate. These effects result from the shifting of electron density through sigma bonds within the molecule.

• Through inductive effects, bromines withdraw electron density from the carboxyl group, stabilizing the carboxylate anion.
• Inductive effects are more pronounced when the electron-withdrawing group is closer to the highly electronegative atom, such as oxygen in the carboxyl group.

These properties explain why acidic strength increases with more bromine atoms, as seen by more negative pKa values.

carboxylate anion

The carboxylate anion is the negatively charged species formed when a carboxylic acid donates a proton. Its stability is a determining factor in the acid's strength.

• The more stable the carboxylate anion, the stronger the acid.
• Stabilization often comes from electron-withdrawing effects, as observed in the case of brominated acetic acids.

In these acids, as bromine atoms substitute for hydrogens, the electron-withdrawing power of bromine stabilizes the carboxylate anion.
This reduces the energy needed for the acid to lose a proton, thereby enhancing acid strength.