Problem 7 - Chemistry An Atoms First Approach

Question

You have a solution of the weak acid HA and add some HCl to it. What are the major species in the solution? What do you need to know to calculate the \(\mathrm{pH}\) of the solution, and how would you use this information? How does the \(\mathrm{pH}\) of the solution of just the HA compare with that of the final mixture? Explain.

Step-by-Step Solution

Answer

The major species present in the solution of weak acid HA and strong acid HCl are HA, H+ (from both HA and HCl), A- (conjugate base of HA), and Cl- (from HCl). To calculate the pH of the solution, the initial concentrations of HA and HCl, as well as the dissociation constant Ka, are needed. After calculating the total initial concentration of H+ ions and using charge balance equation, we can find [H3O+] from the equilibrium equation and calculate the pH by applying the formula: \[\mathrm{pH} = -\log[H_3O^+]\]. The pH of the final mixture will be lower (more acidic) than the pH of the initial HA solution due to the increased concentration of H+ ions from HCl.

Step 1: Identify the major species in the solution

Initially, the weak acid HA will dissociate into its ions H+ and A-, and HCl, being a strong acid, will be fully dissociated into H+ and Cl-. Since HCl is a strong acid, it will donate H+ ions to the solution, which will further ionize HA molecules. Therefore, the major species present in the solution are: 1. HA (weak acid) 2. H+ (from HA and HCl) 3. A- (conjugate base of HA after dissociation) 4. Cl- (from the dissociation of HCl)

Step 2: Determine the information needed to calculate the pH of the solution

In order to calculate the pH of the solution, we need to know the following information: 1. The initial concentration of the weak acid HA ([HA]₀) 2. The initial concentration of the strong acid HCl ([HCl]₀) 3. The dissociation constant of the weak acid, Ka (which can be obtained from a table or using the pKa value)

Step 3: Using the information to calculate the pH

To calculate the pH of the solution, we can follow these steps: 1. Write the equilibrium expression for HA as it donates a proton to water: \[HA + H_2O \rightleftharpoons H_3O^+ + A^-\] 2. Write the Ka expression for HA: \[Ka = \frac{[H_3O^+][A^-]}{[HA]}\] 3. Calculate the total initial concentration of H+ ions due to both HA and HCl: \[[H_3O^+]_0 = [H^+]_{HA} + [H^+]_{HCl}\] 4. Use the charge balance equation to relate the concentrations of A- and H3O+: \[[A^-] = [H_3O^+] - [Cl^-]\] 5. Substitute the concentrations (in terms of initial concentrations) and Ka value into the Ka expression. 6. Calculate the [H3O+] from the equilibrium equation and find the pH using the formula: \[\mathrm{pH} = -\log[H_3O^+]\]

Step 4: Compare the pH of the HA solution with the final solution

The pH of the pure HA solution would be higher (meaning it is less acidic) than the final solution since the addition of HCl contributes to the increase of H+ ion concentration, making the solution more acidic. By finding the pH of the HA solution before the addition of HCl using the Ka expression and comparing it with the pH of the final mixture after adding HCl, one can observe the difference between the two pH values. The final mixture will have a lower pH than the initial HA solution.

Key Concepts

Weak Acid

A weak acid is an acid that only partially dissociates into its ions in water. This means that not all molecules of the weak acid break apart to release hydrogen ions (\(H^+\)). As a result, the pH of a weak acid solution is higher (less acidic) compared to a strong acid with the same concentration.

• Partial dissociation implies that in a weak acid solution, there will be a mix of undissociated acid molecules and ions.
• The extent of dissociation is characterized by the dissociation constant, denoted as \(K_a\).

For example, acetic acid (CH₃COOH) is a common weak acid that does not fully break down in solution, resulting in a balance between the molecules (CH₃COOH) and its ions (CH₃COO^- and H^+).
To calculate the pH of a solution containing a weak acid, you need its initial concentration and \(K_a\). These values help determine how many ions are present in solution at equilibrium.

Strong Acid

Strong acids, unlike weak acids, completely dissociate into their ions when dissolved in water. This means that each molecule of a strong acid releases a hydrogen ion (\(H^+\)) in solution.

• This complete dissociation leads to a higher concentration of \(H^+\) ions, making the solution more acidic, thus lowering its pH.
• Common examples of strong acids include hydrochloric acid (HCl), sulfuric acid (H₂SO₄), and nitric acid (HNO₃).

In a solution of a strong acid, the major species are the ions produced (H^+and the anion like Cl^- in the case of HCl) because strong acids do not remain in their molecular form.

Dissociation Constant

The dissociation constant, often denoted as \(K_a\) for acids, is a measure of how well an acid dissociates in solution. It is specifically the equilibrium constant for the dissociation reaction of the acid.

• A higher \(K_a\) value indicates a stronger acid as it implies more ions are produced from dissociation.
• Conversely, a lower \(K_a\) value signifies a weaker acid with fewer ions in solution.

The formula for calculating \(K_a\) for a weak acid represented as HA is:\[K_a = \frac{[H^+][A^-]}{[HA]}\]This equation relates the concentrations of the ions (\(H^+\) and \(A^-\)) to the undissociated acid (HA) at equilibrium.
Understanding the \(K_a\) helps in calculating the pH of a weak acid solution, as it indicates how much of the acid dissociates into ions.