Question

Acid Strength and \(K_{\mathrm{a}}\) Classify each acid as strong or weak. If the acid is weak, write an expression for the acid ionization constant \(\left(K_{a}\right) .\) $$\begin{array}{l}{\text { a. HF }} \\ {\text { b. HCHO }} \\ {\text { c. } \mathrm{H}_{2} \mathrm{SO}_{4}} \\ {\text { d. } \mathrm{H}_{2} \mathrm{CO}_{3}}\end{array}$$

Short answer

a. HF is weak, Ka: \(K_{a} = \frac{[H^{+}][F^{-}]}{[HF]}\); b. HCHO is neither an acid nor a base in this context; c. \(H_{2}SO_{4}\) is strong, no Ka; d. \(H_{2}CO_{3}\) is weak, Ka1: \(K_{a1} = \frac{[H^{+}][HCO_{3}^{-}]}{[H_{2}CO_{3}]}\), Ka2: \(K_{a2} = \frac{[H^{+}][CO_{3}^{2-}]}{[HCO_{3}^{-}]}\).

Step-by-step solution

Identifying the strength of HF

Hydrofluoric acid (HF) is a weak acid because it does not dissociate completely in water. For weak acids, we write an expression for the acid ionization constant, Ka.

Writing the Ka expression for HF

The expression for the ionization constant Ka of HF is given by: \(K_{a} = \frac{[H^{+}][F^{-}]}{[HF]}\)

Identifying the strength of HCHO

Formaldehyde (HCHO) does not behave like a typical acid and it is not generally considered in the context of acid strength and ionization constants.

Identifying the strength of \(H_{2}SO_{4}\)

Sulfuric acid (\(H_{2}SO_{4}\)) is a strong acid and it dissociates completely in water. For strong acids, we do not write Ka expressions.

Identifying the strength of \(H_{2}CO_{3}\)

Carbonic acid (\(H_{2}CO_{3}\)) is a weak acid as it does not fully dissociate in water. We need to write an expression for its acid ionization constant.

Writing the Ka expression for \(H_{2}CO_{3}\)

The ionization constant expression for the first dissociation of \(H_{2}CO_{3}\) is: \(K_{a1} = \frac{[H^{+}][HCO_{3}^{-}]}{[H_{2}CO_{3}]}\). For the second dissociation: \(K_{a2} = \frac{[H^{+}][CO_{3}^{2-}]}{[HCO_{3}^{-}]}\)

Key concepts

Acid Strength

Understanding how to classify acids as strong or weak is fundamental in chemistry. Acid strength refers to an acid's propensity to donate a proton (H⁺) in an aqueous solution. Strong acids are characterized by their complete dissociation in water, meaning that they release all of their hydrogen ions when dissolved. Examples include hydrochloric acid (HCl), sulfuric acid (H₂SO₄), and nitric acid (HNO₃).

In contrast, weak acids only partially dissociate in water, resulting in an equilibrium between the undissociated acid and the ions produced. Acetic acid (CH₃COOH) and hydrofluoric acid (HF) are classic examples of weak acids. A good understanding of this concept assists in making predictions about the behavior of acids in various chemical reactions.

Ka Expression

The acid ionization constant (Ka) quantifies the strength of a weak acid. It's an equilibrium constant for the acid's ionization reaction. Specifically, the Ka expression relates to the concentrations of the products and reactants at equilibrium for a weak acid dissociating into its ions.

For example, for a generic weak acid HA, the ionization in water would be:
HA(aq) + H₂O(l) ⇌ H₃O⁺(aq) + A⁻(aq)

And the Ka expression is: \[ K_{a} = \frac{[\text{H}_3\text{O}^+][A^-]}{[HA]} \]

Here, \([HA]\) is the concentration of the undissociated weak acid, and \([\text{H}_3\text{O}^+]\) and \([A^-]\) represent the concentrations of the hydronium and the acid’s conjugate base, respectively. A higher Ka value implies a stronger acid, as it indicates a greater extent of dissociation.

Weak Acids

Exploring weak acids reveals why they only partially dissociate in water. This incomplete ionization results in a dynamic equilibrium between the undissociated molecules and the ions in solution. The position of this equilibrium is represented numerically by the acid ionization constant (Ka).

Due to this equilibrium, weak acids have unique properties. They are less conductive than strong acids, and pH levels in their solutions do not drop as dramatically. Examples of weak acids include hydrofluoric acid (HF) and carbonic acid (H₂CO₃). The Ka values for weak acids are typically less than 1, indicative of their lower tendency to lose a proton compared to strong acids.

Moreover, weak acids have various degrees of weakness. For instance, acetic acid (CH₃COOH) is a relatively stronger weak acid when compared to hydrocyanic acid (HCN), once again evidenced by their respective Ka values.

Strong Acids

Strong acids are characterized by their full dissociation in aqueous solution into hydronium ions (H₃O⁺) and the conjugate base anions. The complete ionization indicates that strong acids are highly effective proton donors.

Unlike weak acids, which have a Ka value that indicates their ionization degree, strong acids are considered to have an infinitely large Ka. This reflects the fact that the reaction of a strong acid with water goes to completion. Because all the acid molecules dissociate to release H⁺ ions, the resulting pH of a solution of a strong acid at a given concentration will be lower (more acidic) than that of a solution of a weak acid at the same concentration.

Due to their complete ionization, strong acids are also excellent conductors of electricity in solution. Examples include hydrochloric acid (HCl), hydrobromic acid (HBr), and perchloric acid (HClO₄). Understanding strong acids is crucial, especially in industrial applications and in predicting the outcome of acid-base reactions.