Question

Offer an explanation for the following observations. (a) \(\mathrm{H}_{3} \mathrm{O}^{+}\)is a stronger acid than \(\mathrm{NH}_{4}^{+}\). (b) Nitric acid, \(\mathrm{HNO}_{3}\), is a stronger acid than nitrous acid, \(\mathrm{HNO}_{2}\). (c) Ethanol and water have approximately the same acidity. (d) Trifluoroacetic acid, \(\mathrm{CF}_{3} \mathrm{COOH}\), is a stronger acid than trichloroacetic acid, \(\mathrm{CCl}_{3} \mathrm{COOH}\).

Short answer

(b) \(\mathrm{HNO}_{3}\) or \(\mathrm{HNO}_{2}\)? (c) Ethanol or water? (d) \(\mathrm{CF}_{3} \mathrm{COOH}\) or \(\mathrm{CCl}_{3} \mathrm{COOH}\)? Answer: (a) \(\mathrm{H}_{3} \mathrm{O}^{+}\) is a stronger acid than \(\mathrm{NH}_{4}^{+}\). (b) \(\mathrm{HNO}_{3}\) is a stronger acid than \(\mathrm{HNO}_{2}\). (c) Ethanol and water have approximately the same acidity. (d) \(\mathrm{CF}_{3} \mathrm{COOH}\) is a stronger acid than \(\mathrm{CCl}_{3} \mathrm{COOH}\).

Step-by-step solution

(a) Compare \(\mathrm{H}_{3} \mathrm{O}^{+}\) and \(\mathrm{NH}_{4}^{+}\) Acid Strength

To compare the acid strength of \(\mathrm{H}_{3} \mathrm{O}^{+}\) and \(\mathrm{NH}_{4}^{+}\), we need to look at their conjugate bases, which are \(\mathrm{H}_{2} \mathrm{O}\) and \(\mathrm{NH}_{3}\) respectively. A stronger acid has a weaker and more stable conjugate base. The presence of more electronegative oxygen in \(\mathrm{H}_{2} \mathrm{O}\) makes it a more stable conjugate base than \(\mathrm{NH}_{3}\), where nitrogen is less electronegative. Therefore, \(\mathrm{H}_{3} \mathrm{O}^{+}\) is a stronger acid than \(\mathrm{NH}_{4}^{+}\).

(b) Compare \(\mathrm{HNO}_{3}\) and \(\mathrm{HNO}_{2}\) Acid Strength

Nitric acid (\(\mathrm{HNO}_{3}\)) and nitrous acid (\(\mathrm{HNO}_{2}\)) are oxyacids, and their acidity can be compared by looking at the stability of their conjugate bases. The conjugate base of \(\mathrm{HNO}_{3}\) is \(\mathrm{NO}_{3}^{-}\), while the conjugate base of \(\mathrm{HNO}_{2}\) is \(\mathrm{NO}_{2}^{-}\). In resonance structures, the negative charge delocalization in \(\mathrm{NO}_{3}^{-}\) is more efficient, as the negative charge is distributed amongst three oxygen atoms, whereas in \(\mathrm{NO}_{2}^{-}\), it is distributed amongst only two oxygen atoms. This makes the conjugate base \(\mathrm{NO}_{3}^{-}\) more stable and weaker than \(\mathrm{NO}_{2}^{-}\). Hence, \(\mathrm{HNO}_{3}\) is a stronger acid than \(\mathrm{HNO}_{2}\).

(c) Compare Ethanol and Water Acidity

Ethanol ( \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}\)) and water (\(\mathrm{H}_{2}\mathrm{O}\)) share similarities in their molecular structure: both contain an oxygen atom bonded to a hydrogen atom, which forms the acidic \(\mathrm{O-H}\) bond. The main difference between the two is the presence of the hydrocarbon chain in ethanol. However, the hydrocarbon chain in ethanol does not have a significant effect on the acidity of the \(\mathrm{O-H}\) bond, as it does not contribute to the stability of the conjugate base. Therefore, ethanol and water have approximately the same acidity.

(d) Compare \(\mathrm{CF}_{3} \mathrm{COOH}\) and \(\mathrm{CCl}_{3} \mathrm{COOH}\) Acid Strength

Trifluoroacetic acid (\(\mathrm{CF}_{3} \mathrm{COOH}\)) and trichloroacetic acid (\(\mathrm{CCl}_{3} \mathrm{COOH}\)) are both carboxylic acids. To determine their relative acidity, we need to assess the influence of the attached atoms (F in \(\mathrm{CF}_{3}\) and Cl in \(\mathrm{CCl}_{3}\)) on the stability of their corresponding carboxylate conjugate bases (\(\mathrm{CF}_{3} \mathrm{COO}^{-}\) and \(\mathrm{CCl}_{3} \mathrm{COO}^{-}\)). Fluorine is more electronegative than chlorine and will have a higher inductive effect that stabilizes the negative charge on the carboxylate group. As a result, \(\mathrm{CF}_{3} \mathrm{COOH}\) has a more stable conjugate base, making it a stronger acid than \(\mathrm{CCl}_{3} \mathrm{COOH}\).

Key concepts

Conjugate Base Stability

When we discuss the strength of an acid, we inevitably encounter the concept of conjugate base stability. A fundamental tenet in acid-base chemistry is that the strength of an acid is inversely related to the stability of its conjugate base. The more stable the conjugate base, the stronger the acid. This principle helps explain why certain substances, such as e stable, leading to a strongly acidic . Conversely, the less electronegative element in makes its conjugate base less stable and thus weaker as an acid.

Factors that contribute to the stability of a conjugate base include the atom to which the negative charge is localized, the ability to delocalize that charge, and the overall energy of the molecule. For instance, the negative charge can be stabilized by resonance or by the inductive effect of adjacent electronegative atoms. Enhanced stability often leads to a lower tendency to re-associate with a proton, characterizing a strong acid.

Electronegativity

Electronegativity is a property of atoms that reflects their ability to attract electrons in a chemical bond. It is a critical factor in determining the strength of an acid. Generally, atoms with higher electronegativity stabilize negative charges more effectively. This is due to their strong attractivene for electrons, which pulls electron density towards themselves, dispersing the negative charge and increasing the stability of the conjugate base.

If we take the example of water () having a similar acidity to ethanol (), it's largely because the oxygen atom's electronegativity in both molecules is responsible for the acidity, with the hydrocarbon tail of ethanol having negligible effect. However, when differences in electronegativity are at play, such as with and , the different electronegativities of nitrogen and oxygen lead to differing conjugate base stabilities and thus different acid strengths.

Resonance in Acids

Resonance is the delocalization of electrons across multiple atoms, and it plays a key role in the acid strength of certain molecules, especially those that can form multiple, equivalent resonance structures. In oxyacids, such as and e, resonance stabilization of the conjugate base is a significant contributor to acid strength.

The ability of conjugate bases like to delocalize the negative charge over several oxygen atoms through resonance creates stability. The more extensive and effective this delocalization, the more stable the conjugate base will be. This property can be noted in the comparison of nitric and nitrous acids, where the former, with a conjugate base that can distribute a negative charge over three oxygen atoms, is stronger than the latter, which can only distribute the charge over two.

Inductive Effect on Acidity

The inductive effect is related to the ability of substituent groups within a molecule to donate or withdraw electron density through sigma bonds. Electronegative elements or groups exert an inductive effect that can pull electron density towards themselves, away from the rest of the molecule. This withdrawal of electron density can lead to an increased stabilization of a conjugate base and, consequ ently, increase the acid's strength.

This effect is illustrated in the comparison between and . The fluorine atoms in are highly electronegative and exert a stronger inductive effect than the chlorines in e. As a result, the conjugate base of is more stabilized by the withdrawal of electron density, making trifluoroacetic acid a stronger acid than trichloroacetic acid.