Problem 85 - Introductory Chemistry Atoms First

Question

True or false? Because carbonic acid, \(\mathrm{H}_{2} \mathrm{CO}_{3}\), is diprotic, it is a stronger acid than \(\mathrm{HCl}\), which is only monoprotic. Explain your answer.

Step-by-Step Solution

Answer

The statement is false. Although carbonic acid (\(\mathrm{H}_{2}\mathrm{CO}_{3}\)) is diprotic, it is a weaker acid than hydrochloric acid (\(\mathrm{HCl}\)), which is monoprotic. The strength of an acid depends on its acidity constant (K_a) rather than the number of protons it can donate. In this case, the K_a of the first dissociation step of carbonic acid is smaller than that of hydrochloric acid, making carbonic acid a weaker acid.

Step 1: Understand diprotic and monoprotic acids

A diprotic acid is an acid that has two hydrogen ions (protons) available for donation, while a monoprotic acid has only one hydrogen ion available for donation. In this case, carbonic acid, \(\mathrm{H}_{2}\mathrm{CO}_{3}\), is diprotic because it has two hydrogen atoms in its chemical formula, while hydrochloric acid, \(\mathrm{HCl}\), is monoprotic because it only has one hydrogen atom in its formula.

Step 2: Compare the acidity constants

To determine the strength of an acid, we need to look at the acidity constants. A larger acidity constant (K_a) indicates a stronger acid. The K_a values for the first dissociation step of carbonic acid (\(\mathrm{H}_{2}\mathrm{CO}_{3}\)) and hydrochloric acid (\(\mathrm{HCl}\)) are: \[\mathrm{H}_{2}\mathrm{CO}_{3}\:K_{a1} = 4.3 \times 10^{-7}\] \[\mathrm{HCl}\: K_{a} = 1.3 \times 10^{6}\]

Step 3: Compare the acid strengths

Since the acidity constant for the first dissociation step of carbonic acid (\(\mathrm{H}_{2}\mathrm{CO}_{3}\), K_a1) is smaller than the acidity constant of hydrochloric acid (\(\mathrm{HCl}\), K_a), it indicates that carbonic acid is a weaker acid than hydrochloric acid. The fact that carbonic acid is diprotic does not necessarily make it stronger than monoprotic hydrochloric acid.

Step 4: Conclusion

The statement is false. Although carbonic acid (\(\mathrm{H}_{2}\mathrm{CO}_{3}\)) is diprotic, it is a weaker acid than hydrochloric acid (\(\mathrm{HCl}\)), which is monoprotic. The strength of an acid depends on its acidity constant (K_a) rather than the number of protons it can donate.

Key Concepts

Diprotic Acids

Diprotic acids are unique in that they have the ability to donate two protons (hydrogen ions) during their dissociation processes. This is an important feature that differentiates diprotic acids from other types of acids.
An example of a diprotic acid is carbonic acid (\(\text{H}_2\text{CO}_3\)). It dissociates in two steps: first by releasing one hydrogen ion to form bicarbonate (\(\text{HCO}_3^-\)), and second by releasing another hydrogen ion to form carbonate (\(\text{CO}_3^{2-}\)). This staged dissociation means diprotic acids can exhibit slightly different behaviors in terms of acid strength.

• Dissociation 1: \(\text{H}_2\text{CO}_3 \rightarrow \text{H}^+ + \text{HCO}_3^-\)
• Dissociation 2: \(\text{HCO}_3^- \rightarrow \text{H}^+ + \text{CO}_3^{2-}\)

Despite having two dissociations, the strength of a diprotic acid is not determined by the number of protons it can donate, but rather by its first dissociation constant \(K_{a1}\). This is why a diprotic acid is not necessarily stronger than a monoprotic one.

Monoprotic Acids

Monoprotic acids contain just one hydrogen ion which they can donate during dissociation in water. This is perhaps the simplest form of acid, often leading to fewer steps in chemical reactions.
Hydrochloric acid (\(\text{HCl}\)) is a well-known example of a monoprotic acid. Upon dissolving in water, it completely dissociates into hydrogen ions and chloride ions:

• Dissociation: \(\text{HCl} \rightarrow \text{H}^+ + \text{Cl}^-\)

The complete nature of this dissociation means that \(\text{HCl}\) is a strong acid, and its acid strength is reflected in its acidity constant \(K_{a}\). This property reflects not only how readily \(\text{HCl}\) donates its proton, but also how it affects the pH of a solution.
Contrary to what one might assume, the number of protons (like in diprotic acids) doesn't necessarily indicate greater acid strength. It's all about the ease with which the proton is donated.

Acidity Constant (K_a)

The acidity constant \(K_a\) is a crucial factor in determining the strength of an acid. It represents the equilibrium constant for the dissociation of an acid into its ions in an aqueous solution.
A higher \(K_a\) value indicates that the acid dissociates more completely in water, resulting in a stronger acid, whereas lower \(K_a\) values suggest weaker acids.
For example:

• The \(K_{a1}\) for carbonic acid (\(\text{H}_2\text{CO}_3\)) is \(4.3 \times 10^{-7}\), which is relatively low, indicating it's a weaker acid.
• On the other hand, \(\text{HCl}\) has a \(K_a\) of \(1.3 \times 10^6\), reflecting its complete ionization and thus, its status as a strong acid.

When comparing the strength between diprotic and monoprotic acids, it's essential to focus on their \(K_a\) values rather than merely the number of protons they can donate.

Carbonic Acid vs Hydrochloric Acid

The comparison between carbonic acid (\(\text{H}_2\text{CO}_3\)) and hydrochloric acid (\(\text{HCl}\)) provides a clear illustration of how \(K_a\) values are more indicative of acid strength rather than the number of hydrogen ions an acid can donate.
Despite being diprotic, carbonic acid has a much lower \(K_a1\) at \(4.3 \times 10^{-7}\). This indicates that it does not dissociate as effectively as hydrochloric acid, whose \(K_a\) is \(1.3 \times 10^6\).

• \(\text{Carbonic Acid: } \text{H}_2\text{CO}_3 \rightarrow \text{H}^+\) poorly
• \(\text{Hydrochloric Acid: } \text{HCl} \rightarrow \text{H}^+\) fully

Thus, although carbonic acid can donate two protons, its partial ionization makes it considerably weaker than \(\text{HCl}\). This demonstrates that the strength of an acid is dependent more on its dissociation properties than simply its diprotic or monoprotic nature.