Question

The \(\mathrm{p} K_{\mathrm{a}}\) values of two monoprotic acids \(\mathrm{HA}\) and \(\mathrm{HB}\) are 5.9 and 8.1 , respectively. Which of the two is the stronger acid?

Short answer

HA is the stronger acid because it has a lower pKa value.

Step-by-step solution

Understand the pKa Concept

The \(\mathrm{p} K_{\mathrm{a}}\\) value is a measure of the strength of an acid in solution. It is the negative logarithm of the acid dissociation constant \(K_{\mathrm{a}}\\). A lower \(\mathrm{p} K_{\mathrm{a}}\\) value indicates a stronger acid because the acid dissociates more completely.

Compare the pKa Values

Given are the \(\mathrm{p} K_{\mathrm{a}}\\) values for acids \(\mathrm{HA}\\) and \(\mathrm{HB}\\): 5.9 and 8.1, respectively. The acid with the lower \(\mathrm{p} K_{\mathrm{a}}\\) value is the stronger acid since it indicates greater ionization in solution.

Determine the Stronger Acid

Since the \(\mathrm{p} K_{\mathrm{a}}\\) value for \(\mathrm{HA}\\) is 5.9, which is lower than the \(\mathrm{p} K_{\mathrm{a}}\\) of 8.1 for \(\mathrm{HB}\\), this implies that \(\mathrm{HA}\\) is the stronger acid.

Key concepts

Acid Strength

Acid strength refers to the acid's ability to donate protons (H⁺ ions) to a solution. The stronger the acid, the more readily it donates these protons. This is often assessed through the acid's dissociation behavior in water. When an acid dissociates completely, it implies a strong acid, as it releases more protons into the solution. Conversely, a weak acid only partially dissociates, releasing fewer protons.
Understanding the strength of acids is crucial because it influences their behavior and reactivity in chemical reactions. For example, strong acids are typically more reactive and can catalyze reactions that weaker acids cannot. Knowing whether an acid is strong or weak helps predict the outcome of chemical reactions and the conditions needed to achieve them.

• Strong acids have low pKa values.
• This means they dissociate completely in solution.
• Weak acids have higher pKa values, indicating partial dissociation.

Acid Dissociation Constant

The acid dissociation constant, denoted as \( K_{a} \), is a quantitative measure of how easily an acid releases its hydrogen ion in solution. This constant gives insight into the equilibrium reached between an acid and its dissociated ions in solution. A high \( K_{a} \) value means the acid dissociates extensively, indicating strong acid behavior. Conversely, a low \( K_{a} \) value indicates limited dissociation, which is characteristic of a weak acid.
To bridge the understanding of \( K_{a} \) with intuitive numbers, chemists often use \( pK_{a} \), which is the negative logarithm of \( K_{a} \). This converts exponential \( K_{a} \) values into manageable numerics. Simply put, the smaller the \( pK_{a} \), the stronger the acid. This is because a smaller \( pK_{a} \) corresponds to a larger \( K_{a} \), indicating a higher degree of ionization.
Key points about \( pK_{a} \) and \( K_{a} \):

• \( K_{a} \) is a measure of acid strength in terms of ionization.
• \( pK_{a} \) is the logarithmic measure of that strength.
• Smaller \( pK_{a} \) means stronger acids due to greater ionization.

Monoprotic Acids

Monoprotic acids are a category of acids that can donate one hydrogen ion per molecule to a solution. This property differentiates them from polyprotic acids, which can release two or more protons. Common examples of monoprotic acids include hydrochloric acid (HCl) and acetic acid (CH₃COOH).
In terms of acid strength and pKa, monoprotic acids offer a simpler system as they involve only one ionizable hydrogen. This makes them easier to study and compare, such as in exercises where acids HA and HB are evaluated based on their pKa values.
For monoprotic acids, concepts of dissociation constants become straightforward, helping students and chemists alike understand the acid-base balance in solutions.
Essential insights about monoprotic acids include:

• They donate one proton per molecule.
• They have one pKa value corresponding to their sole hydrogen ion.
• They simplify the study of acid-base equilibria, focusing solely on one dissociation event.