The active ingredient in aspirin is acetylsalicylic acid 1HC9H7O42, a monoprotic acid with Ka = 3.3 * 10^-4 at 25 °C. What is the pH of a solution obtained by dissolving two extra-strength aspirin tablets, each containing 500 mg of acetylsalicylic acid, in 250 mL of water?

Verified step by step guidance

1. Calculate the total mass of acetylsalicylic acid by multiplying the mass of one tablet by the number of tablets.
2. Convert the total mass of acetylsalicylic acid to moles using its molar mass (180.16 g/mol).
3. Determine the concentration of acetylsalicylic acid in the solution by dividing the number of moles by the volume of the solution in liters.
4. Set up the expression for the acid dissociation constant (Ka) for acetylsalicylic acid: \( Ka = \frac{[H^+][A^-]}{[HA]} \), where [HA] is the initial concentration of the acid, and [H^+] and [A^-] are the concentrations of the hydrogen ion and the acetate ion at equilibrium.
5. Assume that the initial concentration of [H^+] and [A^-] is negligible, and solve for [H^+] using the approximation \( [H^+] = \sqrt{Ka \times [HA]} \), then calculate the pH using \( pH = -\log[H^+] \).

Key Concepts

Monoprotic Acids

A monoprotic acid is an acid that can donate only one proton (H+) per molecule in an aqueous solution. This characteristic simplifies the calculation of pH, as the dissociation can be represented by a single equilibrium expression. Acetylsalicylic acid, the active ingredient in aspirin, is a monoprotic acid, which means it will dissociate in water to release one hydrogen ion, affecting the solution's acidity.

Acid Dissociation Constant (Ka)

The acid dissociation constant (Ka) quantifies the strength of an acid in solution, indicating how well it donates protons. A lower Ka value signifies a weaker acid, while a higher value indicates a stronger acid. For acetylsalicylic acid, with a Ka of 3.3 x 10^-4, this means it is a weak acid, and its dissociation in water will not be complete, necessitating the use of the Ka value to calculate the pH.

pH Calculation

pH is a measure of the hydrogen ion concentration in a solution, calculated using the formula pH = -log[H+]. In the case of weak acids, the concentration of H+ ions can be determined from the equilibrium expression involving Ka. For the aspirin solution, the total concentration of acetylsalicylic acid must be calculated first, followed by applying the Ka value to find the concentration of H+ ions, which will then be used to determine the pH.