Caffeine (C8H10N4O2) is a weak base with a pKb of 10.4. Calculate the pH of a solution containing a caffeine concentration of 435 mg/L.

• A. pH = 7.0
• B. pH = 5.2
• C. pH = 8.6
• D. pH = 9.8

Answer: (C)

Verified step by step guidance

1. Convert the concentration of caffeine from mg/L to mol/L. First, calculate the molar mass of caffeine (C8H10N4O2) by adding the atomic masses of its constituent elements: Carbon (C), Hydrogen (H), Nitrogen (N), and Oxygen (O).
2. Use the molar mass to convert the given concentration from mg/L to mol/L. This is done by dividing the mass concentration (in mg/L) by the molar mass (in g/mol) and converting mg to g.
3. Recognize that caffeine is a weak base and use the given pKb value to find the Kb (base dissociation constant) using the formula: Kb = 10^(-pKb).
4. Set up an equilibrium expression for the dissociation of caffeine in water: C8H10N4O2 + H2O ⇌ C8H10N4O2H+ + OH-. Use an ICE table (Initial, Change, Equilibrium) to express the concentrations of the species at equilibrium.
5. Solve for the hydroxide ion concentration [OH-] using the Kb expression: Kb = [C8H10N4O2H+][OH-] / [C8H10N4O2]. Then, calculate the pOH from [OH-] and use the relationship pH + pOH = 14 to find the pH of the solution.