Question

What is the \(\mathrm{p} K_{\mathrm{a}}\) of an acid? As the \(\mathrm{p} K_{\mathrm{a}}\) value increases, does acid strength increase or decrease? Explain.

Short answer

The pKa of an acid is the negative logarithm of its acid dissociation constant (Ka), given by the equation \(pKa = -\log_{10}(Ka)\). It indicates the relative strength of an acid in a solution by quantifying its tendency to donate protons. As the pKa value increases, the acid strength decreases, making it a weaker acid. Conversely, as the pKa value decreases, the acid strength increases, making it a stronger acid.

Step-by-step solution

Define pKa

The pKa value of an acid represents the negative logarithm of the acid dissociation constant (Ka). It is expressed as: \(pKa = -\log_{10}(Ka)\). The pKa value gives us an idea of the relative strength of an acid in a solution by quantifying how readily the acid donates a proton (H+) in the solution.

Understand acid dissociation constant (Ka)

Ka is the acid dissociation constant, which is a measure of the tendency of an acid to dissociate into its conjugate base and a proton in the solution. For a general acid HA, the equilibrium reaction in a solution can be represented as: \[HA \rightleftharpoons A^- + H^+\] The equilibrium constant of this reaction is represented by Ka: \[Ka = \frac{[A^-][H^+]}{[HA]}\] where [HA], [A^-], and [H^+] are the equilibrium concentrations of the acid, its conjugate base, and the proton, respectively.

Explain the relationship between pKa and acid strength

As the pKa value increases, the Ka value decreases since \(pKa = -\log_{10}(Ka)\). A lower Ka value indicates a lower degree of dissociation, which in turn implies a weaker acid, as it is less likely to donate a proton in the solution. Therefore, as the pKa value of an acid increases, its strength decreases, i.e., the acid becomes weaker. Conversely, when the pKa value decreases, the acid's strength increases, making it a stronger acid.

Summary

In conclusion, the pKa value of an acid represents the negative logarithm of its acid dissociation constant (Ka), which indicates the degree of dissociation and thus the strength of the acid in the solution. As the pKa value increases, the acid strength decreases, making it a weaker acid. Conversely, as the pKa value decreases, the acid strength increases, making it a stronger acid.

Key concepts

Acid Dissociation Constant

In chemistry, we often use the acid dissociation constant, denoted as \(K_a\), to understand how well an acid gives up its proton in a solution. This value is crucial because it tells us about the acid's ability to release hydrogen ions \(H^+\) into the solution. When an acid, say \(HA\), is dissolved in water, it dissociates into its conjugate base \(A^-\) and hydrogen ions \(H^+\). The equation for this equilibrium reaction is:

• \(HA \rightleftharpoons A^- + H^+\)

The \(K_a\) value is defined as:

• \(K_a = \frac{[A^-][H^+]}{[HA]}\)

Here, \([HA]\), \([A^-]\), and \([H^+]\) are the concentrations of the acid, the conjugate base, and the hydrogen ions at equilibrium, respectively.
This concept is fundamental because it helps us quantify how much the acid dissociates in water, thus revealing how strong or weak an acid is.

Acid Strength

Acid strength is a measure of an acid's capacity to donate protons in a solution. A stronger acid dissociates more in water, producing more hydrogen ions \(H^+\), while a weaker acid dissociates less, producing fewer hydrogen ions. We gauge the strength of an acid using its \(K_a\) and \(pK_a\) values. A higher \(K_a\) means a stronger acid because it dissociates more easily. However, we often refer to the \(pK_a\), which is simply the negative logarithm of the \(K_a\):

• \(pK_a = -\log_{10}(K_a)\)

A smaller \(pK_a\) means a stronger acid and vice versa. Therefore, as the \(pK_a\) decreases, the acid strength increases.
Understanding these values helps us predict how the acid will behave in different chemical reactions and environments.

Equilibrium Reaction

Equilibrium reactions are a major concept in chemistry that explains how reversible reactions reach a state where the reactants and products form at the same rate. In the case of acids, we examine the equilibrium between the undissociated acid \(HA\) and its dissociated forms \(A^-\) and \(H^+\). At equilibrium, the rate of the forward reaction (acid dissociating) equals the rate of the reverse reaction (acid and base recombining).The equation for the dissociation of an acid in water is central to understanding this balance:

• \(HA \rightleftharpoons A^- + H^+\)

Here, equilibrium is essential because it tells us the ratio of \([A^-][H^+]/[HA]\). This ratio is equal to \(K_a\), the acid dissociation constant.
Understanding equilibrium reactions allows chemists to determine how changes in conditions, such as concentration or temperature, shift the balance of products and reactants. In the context of acids, this determines how much of the acid will dissociate and how strong the acid really is at equilibrium.