Problem 11 - Chemistry: The Central Science

Question

Rank the following acids in order of increasing acidity: \(\mathrm{CH}_{3} \mathrm{COOH}, \mathrm{CH}_{2} \mathrm{ClCOOH}, \mathrm{CHCl}_{2} \mathrm{COOH}, \mathrm{CCl}_{3} \mathrm{COOH}\) \(\mathrm{CF}_{3} \mathrm{COOH}\). [Section 16.10]

Step-by-Step Solution

Answer

The order of increasing acidity for the given acids is: \(CH_3COOH < CH_2ClCOOH < CHCl_2COOH < CCl_3COOH < CF_3COOH\). This is based on the stability of their conjugate bases and the electron-withdrawing effects of the surrounding atoms, with fluorine having a stronger electron-withdrawing effect than chlorine.

Step 1: Write the conjugate bases of each acid

After losing a proton (H+) from each acid, their conjugate bases are as follows: \(CH_3COO^{-}\), \(CH_2ClCOO^{-}\), \(CHCl_2COO^{-}\), \(CCl_3COO^{-}\), and \(CF_3COO^{-}\).

Step 2: Determine the effect of electron-withdrawing groups on acidity

In each acid, chlorine attached to the carbon atoms serves as electron-withdrawing groups due to their high electronegativity. They increase the stability of the conjugate base by withdrawing electron density from the negatively charged oxygen atom in the conjugate base. The more chlorines present, the more electron-withdrawing effect, and therefore, higher acidity.

Step 3: Compare the effect of the electron-withdrawing groups of each acid

Each acid has a different number of Cl atoms, which results in different electron-withdrawing effects and acidity. Rank them in order of increasing acidity based on the number of Cl atoms present: 1. \(CH_3COOH\) (no Cl atoms) 2. \(CH_2ClCOOH\) (one Cl atom) 3. \(CHCl_2COOH\) (two Cl atoms) 4. \(CCl_3COOH\) (three Cl atoms)

Step 4: Evaluate the effect of fluorine in \(CF_3COOH\) on acidity

Fluorine is more electronegative than chlorine. In \(CF_3COOH\), the electron-withdrawing effect of the three F atoms is even stronger than the effect of three chlorine atoms in \(CCl_3COOH\). As a result, \(CF_3COOH\) will have a higher acidity than \(CCl_3COOH\).

Step 5: Rank the acids in order of increasing acidity

Based on our comparisons, the order of increasing acidity is: 1. \(CH_3COOH\) 2. \(CH_2ClCOOH\) 3. \( CHCl_2COOH\) 4. \(CCl_3COOH\) 5. \(CF_3COOH\)

Key Concepts

Conjugate Bases

In the context of acidity, a conjugate base is the species that remains after an acid donates its proton (H⁺). Conjugate bases play a pivotal role in determining the strength of their parent acids. Acids with stable conjugate bases tend to be stronger because the base is better able to accommodate the negative charge left behind when the proton is donated.

Stability in a conjugate base can come from a variety of factors, such as the presence of electron-withdrawing groups, resonance stabilization, and the overall size and electronegativity of the atoms involved. In the provided exercise, by comparing the resulting conjugate bases after acid deprotonation, students can infer which acids are strongest by evaluating which conjugate bases would be most stable.

Electron-Withdrawing Groups

The presence of electron-withdrawing groups (EWGs) can greatly influence the acidity of a molecule. EWGs are atoms or groups of atoms that pull electron density toward themselves due to their high electronegativity. This ability can stabilize a negative charge on a nearby atom, such as the oxygen on a conjugate base, by dispersing that charge.

In our exercise, chlorine (Cl) and fluorine (F) are such groups. As each chlorine atom is added to the acetic acid molecule, the electron-withdrawing capability increases, leading to a more stable conjugate base and thus a stronger acid. However, because fluorine is even more electronegative than chlorine, acids with fluorine as an EWG, like trifluoroacetic acid (CF_3COOH), will typically be stronger than comparable acids with chlorine.

Electronegativity

Electronegativity is a measure of an atom's ability to attract and hold onto electrons. In the scope of acid strength, the more electronegative atoms attached to the vicinity of the acidic proton, the more acidic the compound generally is.

This is relevant because electronegative atoms adjacent to an acidic proton can draw electron density away from the bond between the acidic proton and its parent molecule, making it easier for the proton to be released. Also, they stabilize the conjugate base left behind after deprotonation. For instance, fluorine's high electronegativity in CF_3COOH makes its conjugate base very stable and thus makes the acid very strong.

Stability of Conjugate Base

The stability of conjugate base is crucial for understanding the strength of an acid. A high level of stability means that the base can effectively distribute or diminish the negative charge resulted from the donation of a proton. Factors contributing to this stability include resonance, inductive effects, hybridization, and the size of the atom bearing the negative charge.

In the exercise, we see that as the number of chloride atoms increases, so too does the stability of the conjugate base due to the induction effect, where electron density is pulled towards these electronegative groups, spreading out the negative charge. Out of the acids listed, the one with the trifluoromethyl group (CF_3COO-) has the most stable conjugate base leading to the strongest acid.