Question

(a) Which of the following is the stronger Brønsted-Lowry acid, \(\mathrm{HClO}_{3}\) or \(\mathrm{HClO}_{2} ?\) (b) Which is the stronger Brønsted-

Short answer

(a) \(\mathrm{HClO}_{3}\) is the stronger Brønsted-Lowry acid. (b) \(\mathrm{ClO}^{-}_{2}\) is the stronger Brønsted-Lowry base.

Step-by-step solution

1. Identify the conjugate acids and bases

To determine the strength of the given Brønsted-Lowry acids and bases, first, we need to identify their conjugate acids or bases. When an acid donates a proton, it forms its conjugate base, and when a base accepts a proton, it forms its conjugate acid. (a) For the acids \(\mathrm{HClO}_{3}\) and \(\mathrm{HClO}_{2}\): - \(\mathrm{HClO}_{3}\) donates a proton to form its conjugate base: \(\mathrm{ClO}_{3}^-\) - \(\mathrm{HClO}_{2}\) donates a proton to form its conjugate base: \(\mathrm{ClO}_{2}^-\) (b) For the bases \(\mathrm{ClO}^{-}_{3}\) and \(\mathrm{ClO}^{-}_{2}\): - \(\mathrm{ClO}^{-}_{3}\) accepts a proton to form its conjugate acid: \(\mathrm{HClO}_{3}\) - \(\mathrm{ClO}^{-}_{2}\) accepts a proton to form its conjugate acid: \(\mathrm{HClO}_{2}\)

2. Analyze stability of conjugate bases (part a)

The strength of a Brønsted-Lowry acid depends on the stability of its conjugate base. The more stable the conjugate base, the stronger the acid will be. Comparing the conjugate bases of the given acids in part (a): - \(\mathrm{ClO}_{3}^-\) has three oxygen atoms with -1 formal charge each, whereas \(\mathrm{ClO}_{2}^-\) has two oxygen atoms with -1 formal charge each. - The extra oxygen in \(\mathrm{ClO}_{3}^-\) helps to spread the negative charge over more atoms, which increases the stability by reducing its electron density.

3. Determine the stronger acid (part a)

As the conjugate base, \(\mathrm{ClO}_{3}^-\), is more stable than \(\mathrm{ClO}_{2}^-\), the corresponding acid, \(\mathrm{HClO}_{3}\), is the stronger Brønsted-Lowry acid compared to \(\mathrm{HClO}_{2}\). Answer for part (a): \(\mathrm{HClO}_{3}\) is the stronger Brønsted-Lowry acid.

4. Analyze stability of conjugate acids (part b)

To determine the strength of the given Brønsted-Lowry bases, we should look at the stability of their conjugate acids. The more stable the conjugate acid, the stronger the original base will be. Comparing the conjugate acids of the given bases in part (b): - The conjugate acid of \(\mathrm{ClO}^{-}_{3}\) is \(\mathrm{HClO}_{3}\) - The conjugate acid of \(\mathrm{ClO}^{-}_{2}\) is \(\mathrm{HClO}_{2}\) From part (a), we already know that \(\mathrm{HClO}_{3}\) is stronger than \(\mathrm{HClO}_{2}\).

5. Determine the stronger base (part b)

Since \(\mathrm{HClO}_{3}\) is a stronger acid than \(\mathrm{HClO}_{2}\), its conjugate base, \(\mathrm{ClO}^{-}_{3}\), is weaker than the conjugate base of \(\mathrm{HClO}_{2}\), which is \(\mathrm{ClO}^{-}_{2}\). So, the stronger Brønsted-Lowry base is \(\mathrm{ClO}^{-}_{2}\). Answer for part (b): \(\mathrm{ClO}^{-}_{2}\) is the stronger Brønsted-Lowry base.

Key concepts

Conjugate Base

In the Brønsted-Lowry theory, a conjugate base is formed when an acid donates a proton (H⁺). Every acid has its corresponding conjugate base that retains the electrons from the acid's proton. Consider the acids

• the possible phenomenon is evident, and understanding this will enable you to easily follow how these interactions determine the behavior and strength of acids.Initially, if we take \( \mathrm{HClO}_3 \) and \( \mathrm{HClO}_2 \),they will form conjugate bases: \( \mathrm{ClO}_3^- \) and \( \mathrm{ClO}_2^- \), respectively.When \( \mathrm{HClO}_3 \) donates a proton, the electrons left behind are now more evenly distributed over the oxygen atoms,resulting in the formation of \( \mathrm{ClO}_3^- \). Similarly, \( \mathrm{HClO}_2 \) forms \( \mathrm{ClO}_2^- \), with electrons distributed over lesser oxygen atoms connecting ionic stability.This dominant notion of balancing out electrons is what makes conjugate bases integral to understanding acids' reactions and strengths.

Stability of Conjugate Bases

The stability of a conjugate base plays a crucial role in determining the strength of its corresponding acid. When an acid donates a proton, the leftover electrons must be stabilized in its conjugate base form. How this stabilization happens can differ based on the structure and electronegativity of the atoms within the conjugate base.

• An example to understand is the stabilization of \( \mathrm{ClO}_3^- \) over \( \mathrm{ClO}_2^- \). Here, \( \mathrm{ClO}_3^- \) has an additional oxygen atom.
• This extra oxygen helps distribute the negative charge more evenly across its structure, reducing the overall electron density.
• The spreading of the negative charge leads to higher stability, making \( \mathrm{ClO}_3^- \) more stable than \( \mathrm{ClO}_2^- \).

By lowering electron concentration at any one point, the conjugate base becomes less reactive, allowing the acid from which it forms to be stronger. Stability makes it easier for acids to consistently donate protons, enhancing their acidic strength.

Acid Strength Comparison

When comparing acid strength, the stability of the formed conjugate bases is a primary factor. Stronger acids tend to have more stable conjugate bases because the ability to readily stabilize their additional electrons after donating protons makes them more eager to lose these protons.

• For instance, in the comparison between \( \mathrm{HClO}_3 \) and \( \mathrm{HClO}_2 \):
• The more stable conjugate base, \( \mathrm{ClO}_3^- \), corresponds to a stronger acid \( \mathrm{HClO}_3 \).
• On the other hand, \( \mathrm{ClO}_2^- \) is less stable, making \( \mathrm{HClO}_2 \) a weaker acid.

Thus, by examining how well a conjugate base is able to stabilize itself, we can make clear deductions on the respective strengths of acids. Factors like the presence, absence, or position of additional atoms in the molecular structure greatly influence how bases stabilize themselves and therefore affect the acid's ability to donate protons.