Problem 58 - Chemistry The Molecular Nature of Matter

Question

$$ \begin{aligned} &\text { Choose the stronger acid and give your reason: }\\\ &\text { (a) } \mathrm{HIO}_{3}\\\ &\text { or } \mathrm{HIO}_{4} \text { , (b) } \mathrm{H}_{3} \mathrm{AsO}_{4} \text { or } \mathrm{H}_{3} \mathrm{As} \mathrm{O}_{3} \text { . } \end{aligned} $$

Step-by-Step Solution

Answer

The stronger acid between \(HIO_3\) and \(HIO_4\) is \(HIO_4\) due to its higher oxidation state, and between \(H_3AsO_4\) and \(H_3AsO_3\), \(H_3AsO_4\) is stronger because it has more oxygen atoms contributing to a higher oxidation state.

Step 1: Understanding Acid Strength

The strength of an acid depends on the stability of the conjugate base after deprotonation, and the ability of the acid to distribute and stabilize the negative charge. Acids that can distribute negative charge over a greater volume or number of atoms, or that have elements with higher electronegativity, tend to be stronger.

Step 2: Analyzing Acids Based on Oxidation States and Electronegativity

Analyze the given acids according to the number of oxygen atoms they contain and their oxidation states. Acids with higher oxidation states of the central atom tend to be stronger because they can better stabilize the negative charge resulting from deprotonation.

Step 3: Comparison of \(HIO_3\) and \(HIO_4\)

Compare \(HIO_3\) (iodic acid) with \(HIO_4\) (periodic acid). Since \(HIO_4\) has a higher oxidation state for iodine and one more oxygen atom than \(HIO_3\), it can better delocalize the negative charge from the deprotonation. Therefore, \(HIO_4\) is the stronger acid.

Step 4: Comparison of \(H_3AsO_4\) and \(H_3AsO_3\)

Compare \(H_3AsO_4\) (arsenic acid) with \(H_3AsO_3\) (arsenous acid). \(H_3AsO_4\) has more oxygen atoms than \(H_3AsO_3\), indicating a higher oxidation state of arsenic in \(H_3AsO_4\). As a result, \(H_3AsO_4\) is able to distribute negative charge more effectively and is the stronger acid.

Key Concepts

Conjugate Base Stability

When it comes to understanding acid strength, the concept of conjugate base stability is paramount. After an acid donates a proton (\textbf{H+}), it forms what is called a conjugate base. A key indicator of a strong acid is the conjugate base being more stable after this deprotonation process.

Stability for conjugate bases arises from their ability to delocalize the negative charge remaining after the acid loses a proton. The more effectively a conjugate base can spread this charge across its structure — either through resonance or the induction effect — the less reactive it will be, thus more stable.

Revisiting our exercise, we compared \textbf{HIO}\(_3\) (iodic acid) and \textbf{HIO}\(_4\) (periodic acid), analyzing which holds the highest stability within their conjugate bases. Since \textbf{HIO}\(_4\) has more oxygen atoms to distribute the negative charge, its conjugate base is inherently more stable, confirming that \textbf{HIO}\(_4\) is the stronger acid.

Oxidation States

The oxidation state of an atom in a molecule gives us insight into its electron control and can hint at the molecule's reactivity. When determining the strength of an acid, we should consider the oxidation state of the central atom. Typically, a higher oxidation state corresponds to a stronger acid.

In the comparison of \textbf{HIO}\(_3\) and \textbf{HIO}\(_4\), we look at iodine’s oxidation state in each. With every additional oxygen atom, the oxidation state increases, reflecting a greater ability to withdraw electron density and stabilize the negative charge. Therefore, with \textbf{HIO}\(_4\) having one more oxygen than \textbf{HIO}\(_3\), iodine’s oxidation state is higher in periodic acid, contributing to its more acidic nature.

This is also evident in the comparison of \textbf{H}\(_3\)\textbf{AsO}\(_4\) with \textbf{H}\(_3\)\textbf{AsO}\(_3\). Arsenic’s higher oxidation state in \textbf{H}\(_3\)\textbf{AsO}\(_4\) makes it the stronger acid of the two, as it can more effectively favor the distribution of negative charge after deprotonation.

Electronegativity

The electronegativity of an atom is a measure of its ability to attract shared electrons in a chemical bond. In the realm of acid strength, electronegativity plays a critical role in stabilizing the negative charge that emerges once an acid donates a proton. The higher the electronegativity of the atoms surrounding the remaining negative charge, the more stable the conjugate base will be, increasing the acid's strength.

For instance, oxygen is a highly electronegative element, which is why acids like \textbf{HIO}\(_4\) and \textbf{H}\(_3\)\textbf{AsO}\(_4\), with more oxygen atoms around the central atom, are stronger. These atoms effectively pull electron density toward themselves, helping to disperse and hence stabilize the negative charge across the molecule.

Therefore, both the quantity of electronegative atoms and their placement within a molecule can significantly impact the overall acid strength, as seen in our textbook exercise comparisons.