Question

Suggest reasons for the following trend in \(\mathrm{p} K_{\mathrm{a}}\) values: EtOH, p \(K_{\mathrm{a}}=16.0 ; \mathrm{Me}_{3} \mathrm{COH}, \mathrm{p} K_{\mathrm{a}}=18.0\) \\[ \mathrm{CF}_{3} \mathrm{CH}_{2} \mathrm{OH}, \mathrm{p} K_{\mathrm{a}}=12.4 ;\left(\mathrm{CF}_{3}\right)_{3} \mathrm{COH}, \mathrm{p} K_{\mathrm{a}}=5.4 \\]

Short answer

Electron-withdrawing groups like fluorines stabilize the conjugate base, making alcohols with such groups more acidic.

Step-by-step solution

Understanding pKa Values

The pKa value is a measure of the acidity of a substance. A lower pKa value indicates a stronger acid. Conversely, a higher pKa value suggests a weaker acid.

Analyze Ethanol and tert-Butanol

For ethanol (EtOH), the \( \mathrm{p}K_{a} \) is 16.0, and for tert-butanol (\( \mathrm{Me}_3 \mathrm{COH} \)), the \( \mathrm{p}K_{a} \) is 18.0. Ethanol is more acidic than tert-butanol. This is because ethanol can form a slightly more stable conjugate base due to the lack of steric hindrance, which facilitates solvation of the alkoxide ion.

Evaluate Trifluoroethanol and Trifluoro-tert-butanol

For trifluoroethanol (\( \mathrm{CF}_3 \mathrm{CH}_2 \mathrm{OH} \)), the \( \mathrm{p}K_{a} \) is 12.4, showing it's more acidic than ethanol. The electron-withdrawing trifluoromethyl group increases the stability of the conjugate base by delocalizing negative charge, leading to stronger acidity.

Assess Tris-trifluoromethyl-methanol

Tris-trifluoromethyl-methanol (\( (\mathrm{CF}_3)_3 \mathrm{COH} \)) has a \( \mathrm{p}K_{a} \) of 5.4, making it the most acidic. The three trifluoromethyl groups have a very strong electron-withdrawing effect, greatly stabilizing the negative charge on the conjugate base, reducing the overall \( \mathrm{p}K_{a} \), and increasing acidity.

Summarizing the Trends

The trend from least to most acidic based on \( \mathrm{p}K_{a} \) values is: tert-butanol \(<\) ethanol \(<\) trifluoroethanol \(<\) tris-trifluoromethyl-methanol. The general trend can be explained by the electron-withdrawing fluorine atoms increasing acidity by stabilizing the conjugate base.

Key concepts

Understanding pKa Values

In organic chemistry, the pKa value of a compound is a crucial indicator of its acidity. It is important to grasp that the pKa is the negative logarithm of the acid dissociation constant (K_a). Therefore, a low pKa value corresponds to a high K_a, indicating a strong acid. Conversely, a high pKa value indicates a weak acid.
To put it simply, an acid donates a proton (H\(^+\)) more readily if it has a lower pKa value. This is because its conjugate base is more stable, allowing the forward reaction (proton donation) to be favored. For instance, in the series of compounds discussed, the pKa values help in comparing their relative acid strengths, illustrating how structural differences can impact acidity.

Conjugate Base Stability

The stability of the conjugate base is a key factor in determining the acidity of a compound. When an acid donates a proton, it leaves behind a conjugate base. If this base is stable, the acid is more likely to release its proton, thus behaving as a stronger acid. There are several factors that contribute to the stability of the conjugate base:

• Steric hindrance: Bulky groups near the negatively charged site of a conjugate base can interfere with solvation, reducing stability. This is why tert-butanol has a higher pKa compared to ethanol—ethanol's conjugate base is less hindered and thus more stable.


• Resonance: Delocalization of electrons through resonance can greatly stabilize a conjugate base. Although not explicitly discussed in the exercise compounds, it's a critical concept to remember.


• Distribution of charge: Polar groups, especially those containing electronegative atoms, help stabilize the conjugate by distributing negative charge.

By understanding how these factors affect conjugate base stability, we gain valuable insights into why certain compounds exhibit stronger or weaker acidic properties.

Electron-Withdrawing Groups

Electron-withdrawing groups (EWGs) are functional groups in a molecule that pull electron density away from other areas, typically due to their high electronegativity. This feature can have significant effects on the acidity of compounds. EWGs stabilize the conjugate base by reducing the electron density at the atom that has accepted the proton, leading to more stable ions.
In the case of trifluoroethanol and tris-trifluoromethyl-methanol, the trifluoromethyl groups (CF\(_3\)) are strong electron-withdrawing groups. Their presence in these compounds greatly increases the acidity compared to their non-fluorinated counterparts. As shown in the provided trend, compounds with more electron-withdrawing groups like tris-trifluoromethyl-methanol have a significantly lower pKa, making them much stronger acids.
Understanding EWGs provides a clear explanation for changes in acidity, emphasizing how molecular structure directly influences reactivity and stability in organic chemistry.