Question

(a) Which of the following is the stronger Bronsted-Lowry acid, \(\mathrm{HClO}_{3}\) or \(\mathrm{HClO}_{2} ?\) (b) Which is the stronger Bronsted-Lowry base, \(\mathrm{HS}^{-}\) or \(\mathrm{HSO}_{4}^{-}\) ?

Short answer

The stronger Brønsted-Lowry acid is \(\mathrm{HClO}_{3}\) and the stronger Brønsted-Lowry base is \(\mathrm{HS}^{-}\).

Step-by-step solution

Identify their conjugate bases

The conjugate base of an acid is formed by subtracting a proton (H+) from the acid. So, for \(\mathrm{HClO}_{3}\) and \(\mathrm{HClO}_{2}\), we will find their respective conjugate bases. \[ \mathrm{HClO}_{3} \rightarrow \mathrm{ClO}_{3}^{-} + \mathrm{H}^{+} \] \[ \mathrm{HClO}_{2} \rightarrow \mathrm{ClO}_{2}^{-} + \mathrm{H}^{+} \] Conjugate bases of these acids are \(\mathrm{ClO}_{3}^{-}\) and \(\mathrm{ClO}_{2}^{-}\), respectively.

Evaluate the stability of the conjugate bases

The stability of the conjugate bases is affected by the presence of oxygen atoms in these species. Oxygen atoms have a higher electronegativity, and therefore they are better at stabilizing negative charges. More oxygen atoms in the conjugate base will increase its stability. \(\mathrm{ClO}_{3}^{-}\) has more oxygen atoms (3) than \(\mathrm{ClO}_{2}^{-}\) (2). Thus, the increased oxygen presence in \(\mathrm{ClO}_{3}^{-}\) allows it to better stabilize the negative charge, making it a more stable conjugate base.

Determine the stronger acid

A stronger acid will have a more stable conjugate base. Since \(\mathrm{ClO}_{3}^{-}\) is more stable than \(\mathrm{ClO}_{2}^{-}\), the stronger Brønsted-Lowry acid is \(\mathrm{HClO}_{3}\). (b) Comparing the strength of \(\mathrm{HS}^{-}\) and \(\mathrm{HSO}_{4}^{-}\) as Bronsted-Lowry bases:

Identify their conjugate acids

The conjugate acid of a base is formed by adding a proton (H+) to the base. So, for \(\mathrm{HS}^{-}\) and \(\mathrm{HSO}_{4}^{-}\), we will find their respective conjugate acids. \[ \mathrm{HS}^{-} + \mathrm{H}^{+} \rightarrow \mathrm{H}_{2}\mathrm{S} \] \[ \mathrm{HSO}_{4}^{-} + \mathrm{H}^{+} \rightarrow \mathrm{H}_{2}\mathrm{SO}_{4} \] Conjugate acids of these bases are \(\mathrm{H}_{2}\mathrm{S}\) and \(\mathrm{H}_{2}\mathrm{SO}_{4}\), respectively.

Evaluate the stability of the conjugate acids

The presence of oxygen atoms in the conjugate acids affects their stability due to the electron-withdrawing inductive effect. A conjugate acid with more oxygen atoms will destabilize the positive charge on the acidic hydrogen more effectively. \(\mathrm{H}_{2}\mathrm{SO}_{4}\) has more oxygen atoms (4) than \(\mathrm{H}_{2}\mathrm{S}\) (0). Thus, the increased oxygen presence in \(\mathrm{H}_{2}\mathrm{SO}_{4}\) allows it to better stabilize the positive charge, making it a more stable conjugate acid.

Determine the stronger base

A stronger base will have a less stable conjugate acid. Since \(\mathrm{H}_{2}\mathrm{S}\) is less stable than \(\mathrm{H}_{2}\mathrm{SO}_{4}\), the stronger Brønsted-Lowry base is \(\mathrm{HS}^{-}\). So, the answers are (a) \(\mathrm{HClO}_{3}\) is a stronger Bronsted-Lowry acid, and (b) \(\mathrm{HS}^{-}\) is a stronger Bronsted-Lowry base.

Key concepts

Conjugate Acids and Bases

In the Brønsted-Lowry acid-base theory, acids and bases come in conjugate pairs. When an acid donates a proton ( H+ ), it forms its conjugate base. Similarly, when a base accepts a proton, it forms its conjugate acid. For example, as shown in the exercise, HClO_3 becomes ClO_3^{-} after donating a proton, making ClO_3^{-} the conjugate base of HClO_3 . Meanwhile, H_2S is the conjugate acid of HS^{-} because H_2S forms when HS^{-} accepts a proton. Understanding conjugate pairs is crucial for predicting acid and base behavior in reactions.

Acid Strength

The strength of an acid is determined by its ability to donate a proton. Stronger acids readily lose protons and form more stable conjugate bases. In our example, HClO_3 is stronger than HClO_2 because its conjugate base, ClO_3^{-} , is more stable due to the presence of more oxygen atoms. These oxygen atoms stabilize the negative charge more effectively, enabling easier proton donation by the acid. A stronger acid often correlates with a more stable conjugate base.

Base Stability

Base stability relates to the stability of its conjugate acid. A base is stronger when its conjugate acid is less stable. For instance, HS^{-} is a stronger base than HSO_4^{-} . This is because H_2S , the conjugate acid of HS^{-} , is less stable compared to H_2SO_4 , the conjugate acid of HSO_4^{-} . A less stable conjugate acid means the base does not readily hold onto additional protons, improving its basicity.

Electronegativity

Electronegativity plays a crucial role in the stability of conjugate bases and acids. It is the ability of an atom to attract shared electrons. Elements with higher electronegativity pull electrons more strongly, helping to stabilize negative charges in conjugate bases. For instance, oxygen's high electronegativity is why ClO_3^{-} , which has more oxygen atoms, is more stable than ClO_2^{-} . As electronegativity increases, the ability to stabilize negative charges also increases, influencing acid and base strengths.

Oxygen's Impact on Stability

Oxygen significantly impacts the stability of both conjugate acids and bases. Its high electronegativity and ability to engage in strong electron-withdrawing effects make it crucial for stabilizing negative charges. In conjugate bases, like ClO_3^{-} , each additional oxygen atom increases stability by better supporting the negative charge. In conjugate acids, oxygen atoms can draw electrons away, enhancing acidity by making the release of protons easier. Hence, acids like HClO_3 with more oxygen atoms are stronger due to this stability.