Question

Answer the following questions in a complete sentence or two: a. How do you know if an acid is strong or weak? b. How do you calculate the \(\mathrm{pH}\) of a strong acid solution? c. How do you calculate the \(\mathrm{pH}\) of a weak acid solution? d. If you know the \(K_{\mathrm{a}}\) of an acid, how do you determine the \(K_{\mathrm{b}}\) of its conjugate base? e. If you know [OH \(^{-}\) ] for a solution, how do you determine \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right] ?\)

Short answer

a. Acids are strong if they completely dissociate in water. b. Calculate pH of a strong acid with -log10([H+]). c. Calculate pH of a weak acid using the ICE table and Ka value. d. Determine conjugate base's Kb using Kb = Kw / Ka. e. Determine [H3O+] with [H3O+] = Kw / [OH-].

Step-by-step solution

Determining Acid Strength

An acid is considered strong if it completely dissociates in solution, meaning that all its molecules donate protons (H+ ions) when dissolved in water. To determine if an acid is strong or weak, you can check if it is listed among the common strong acids (e.g., HCl, HNO3, H2SO4, HClO4, HBr, HI) or its dissociation constant (Ka) value in water is very large, which suggests it almost completely dissociates. For weak acids, they only partially dissociate in solution, and they normally have a small Ka value.

Calculating pH of a Strong Acid

To calculate the pH of a strong acid solution, you first need the concentration of the acid (in moles per liter). Because strong acids completely dissociate, the concentration of hydrogen ions, [H⁺], is equal to the initial concentration of the acid. The pH is then calculated using the formula pH = -log10([H+]).

Calculating pH of a Weak Acid

For a weak acid, because it doesn't completely dissociate, you typically use its dissociation constant (Ka) and set up an equilibrium expression involving the concentrations of the acid (HA), the conjugate base (A-), and hydrogen ions (H+). This is often solved using the ICE table (Initial, Change, Equilibrium) method to find the equilibrium concentration of [H+] and then calculate pH using pH = -log10([H+]).

Determine the Kb of a Conjugate Base

To find the Kb for the conjugate base of an acid, use the relationship Ka * Kb = Kw, where Kw is the ion-product constant for water (1.0 x 10^-14 at 25°C). If you know the Ka of the acid, you can rearrange this formula to solve for Kb: Kb = Kw / Ka.

Determine the Concentration of Hydronium Ions

If you know the hydroxide ion concentration ([OH⁻]), you calculate the concentration of hydronium ions, [H3O⁺], using the relationship Kw = [H3O⁺][OH⁻], where Kw is the ion-product constant for water. Rearrange the formula to solve for [H3O⁺]: [H3O⁺] = Kw / [OH⁻].

Key concepts

Strong and Weak Acids

Understanding the difference between strong and weak acids is crucial when it comes to pH calculation.
A strong acid is one that completely dissociates into its ions in a solution. This means that every molecule of the acid releases a proton (H⁺), contributing to the hydrogen ion concentration of the solution. Examples include hydrochloric acid (HCl) and sulfuric acid (H₂SO₄).

In contrast, a weak acid only partially dissociates in solution, leaving several undissociated molecules in equilibrium with its ions. This creates a dynamic balance between the non-ionized acid and the ions produced. Acetic acid (CH₃COOH) is a classic example of a weak acid.

To identify the strength of an acid, one can refer to tables listing common strong acids or look at the magnitude of its acid dissociation constant (Ka). A large Ka value indicates a strong acid, as it implies a greater degree of dissociation.

Acid Dissociation Constant (Ka)

The acid dissociation constant, abbreviated as Ka, is a quantitative measure of an acid's strength. Specifically, it gives us the equilibrium constant for the dissociation reaction of the acid in water.

For a generic acid HA, the dissociation can be written as: \[ HA \rightleftharpoons H⁺ + A⁻ \]
The Ka expression is represented by: \[ K_a = \frac{[H⁺][A⁻]}{[HA]} \]
The higher the value of Ka, the stronger the acid as it indicates a greater shift of the equilibrium towards the ions, meaning more hydrogen ions are available to lower the pH of the solution.

Equilibrium Expression

The concept of an equilibrium expression is critical in understanding reactions that do not go to completion, such as the dissociation of weak acids. It quantifies the ratio of concentrations of products to reactants at equilibrium.

For the dissociation of a weak acid HA into H⁺ and its conjugate base A⁻, the equilibrium expression is:\[ K_a = \frac{[H⁺][A⁻]}{[HA]} \]
In this expression, [H⁺], [A⁻], and [HA] represent the molar concentrations of the hydrogen ions, the conjugate base, and the undissociated acid, respectively, at equilibrium. This expression is essential when calculating the pH of a weak acid solution.

Conjugate Bases

When an acid donates a proton, it forms a conjugate base. The strength of a conjugate base is directly related to the strength of its parent acid. When dealing with weak acids, understanding their conjugate bases becomes important for equilibrium calculations.

The acid dissociation constant (Ka) of a weak acid and the base dissociation constant (Kb) of its conjugate base are related inversely by the ion-product constant of water (Kw). This relationship is expressed as:\[ K_a \times K_b = K_w \]
Thus, if you know the Ka of a weak acid, you can determine the Kb of its conjugate base, which is crucial when dealing with the acid-base equilibrium in aqueous solutions.

Ion-Product Constant of Water (Kw)

The ion-product constant of water (Kw) is the product of the concentrations of hydrogen ions [H⁺] and hydroxide ions [OH⁻] in pure water. This constant is a fundamental concept in acid-base chemistry and has a value of \(1.0 \times 10^{-14}\) at 25°C.

For any aqueous solution at this temperature, the relationship holds:\[ [H_3O⁺][OH⁻] = K_w \]
Knowing the concentration of either hydroxide or hydronium ions will allow you to calculate the other, since Kw is a constant value at a given temperature. This is particularly useful when you need to determine the pH of a solution, starting with the hydroxide ion concentration.