Problem 59 - Chemistry

Question

A \(0.015-M\) solution of a monoprotic acid is 0.92 percent ionized. Calculate the ionization constant for the acid.

Step-by-Step Solution

Answer

The ionization constant \(K_a\) is approximately \(1.28 \times 10^{-6}\).

Step 1: Determine the Concentration of Ionized Acid

The solution is 0.92 percent ionized, which means 0.92 percent of the original concentration (0.015 M) of the acid is ionized. To find the concentration of the ionized acid, multiply 0.92 percent by the initial concentration.\[\text{Ionized concentration} = 0.0092 \times 0.015\, \text{M} = 0.000138\, \text{M}\]

Step 2: Write the Ionization Reaction

Since the acid is monoprotic, its ionization can be represented as:\[\text{HA} \rightleftharpoons \text{H}^+ + \text{A}^-\]

Step 3: Set Up the Equilibrium Expression

The equilibrium expression for the ionization of a monoprotic acid is:\[K_a = \frac{[\text{H}^+][\text{A}^-]}{[\text{HA}]}\]

Step 4: Determine Equilibrium Concentrations

At equilibrium, the concentration of \(\text{H}^+\) and \(\text{A}^-\) ions is equal to the ionized concentration: 0.000138 M each. The concentration of non-ionized HA is the original concentration minus the ionized concentration:\[[\text{HA}] = 0.015\, \text{M} - 0.000138\, \text{M} = 0.014862\, \text{M}\]

Step 5: Calculate the Ionization Constant

Substitute the equilibrium concentrations into the equilibrium expression to find the ionization constant \(K_a\):\[K_a = \frac{(0.000138)^2}{0.014862} \approx 1.28 \times 10^{-6}\]

Step 6: Confirm and Interpret the Result

The calculated ionization constant \(K_a = 1.28 \times 10^{-6}\) indicates the strength of the acid. A small \(K_a\) value suggests that the acid weakly ionizes in solution.

Key Concepts

Monoprotic Acid

A monoprotic acid is a type of acid that donates only one proton or hydrogen ion (\( \text{H}^+ \)) per molecule to an aqueous solution. This makes it different from polyprotic acids, which can donate more than one proton. For example, hydrochloric acid (HCl) and acetic acid (CH₃COOH) are both monoprotic acids. When a monoprotic acid ionizes in solution, it leads to the formation of one hydrogen ion and its conjugate base.

In the given exercise, the ionization of a monoprotic acid is represented by the chemical reaction:

- \( \text{HA} \rightleftharpoons \text{H}^+ + \text{A}^- \)

Here, \( \text{HA} \) stands for the monoprotic acid, \( \text{H}^+ \) is the proton donated, and \( \text{A}^- \) is the conjugate base formed during the dissociation. Understanding the specific behavior of monoprotic acids helps in simplifying the calculation of their ionization constants.

Equilibrium Expression

The equilibrium expression is a fundamental concept in chemistry that helps us understand how species are distributed at equilibrium in a reaction. For acids, this expression is termed the ionization constant, \( K_a \). This constant shows the ratio of the concentration of ionized parts of an acid to the concentration of the non-ionized form.

When setting up an equilibrium expression for a monoprotic acid, we use the formula:

- \( K_a = \frac{[\text{H}^+][\text{A}^-]}{[\text{HA}]} \)

Here, \([\text{H}^+]\) and \([\text{A}^-]\) are the concentrations of the ionized acid components at equilibrium, and \([\text{HA}]\) is the concentration of the non-ionized acid. Knowing how to set up this expression is crucial as it is the first step in calculating the ionization constant, which plays a vital role in predicting the acid's behavior in solution.

Acid Strength

Acid strength refers to the tendency of an acid to donate a proton (\( \text{H}^+ \)) in solution. The strength of an acid is determined by its ionization constant \( K_a \), which gives us a measure of the degree of ionization of the acid.

A stronger acid will have a higher percentage of its molecules dissociating into ions, implying a larger \( K_a \). Conversely, a small \( K_a \) indicates that the acid only weakly ionizes, meaning fewer molecules give up protons, thus translating into a weaker acid.

For example, in the exercise, the calculated \( K_a = 1.28 \times 10^{-6} \) reflects that the acid in question is a weak acid, as only a small fraction of the acid molecules ionize in the solution. Understanding acid strength through \( K_a \) is essential for predicting how an acid will behave in different chemical environments.

Chemical Equilibrium

Chemical equilibrium is a state in a chemical reaction where the concentrations of reactants and products no longer change over time. This dynamic state means that while individual molecules may still be reacting, the overall concentrations remain constant.

In the context of the ionization of a monoprotic acid, the equilibrium implies that the rates of the forward and reverse reactions are equal, resulting in no net change in concentrations. This can be observed in the reaction:

- \( \text{HA} \rightleftharpoons \text{H}^+ + \text{A}^- \)

At equilibrium, the concentration of \( \text{H}^+ \) and \( \text{A}^- \) remains constant, and any changes in the acid or conjugate base's concentrations occur at the same rate as their production. This understanding is critical because it allows chemists to predict and control reactions in laboratory and industrial processes. Calculating the ionization constant and setting up equilibrium expressions are practical applications of the principles of chemical equilibrium.