Final answer:
To determine the pH in acid-base reactions, one must apply the Henderson-Hasselbalch equation for buffers and consider the stoichiometry of the reactions. Including the pKa values and the concentrations of the acids, bases, and their conjugate species, we are able to find the desired pH values in the solution.
Step-by-step explanation:
To calculate the pH in the given scenarios, we must consider the reactions between acids and bases and apply the Henderson-Hasselbalch equation for buffer solutions. In the first case, the neutralization of benzoic acid with NaOH is considered, which will require the understanding of stoichiometry to find the concentrations of species in a buffer system. In the second case, the reaction of NH₃ with HCl forms the NH₄⁺ ion, and we use the equilibrium constant for the ammonium ion to find the pH. Proper use of the equilibrium constant expressions and the stoichiometry of the reactions will allow us to solve for the unknown pH values in these solutions.
For the buffer solution calculations, the Henderson-Hasselbalch equation should be applied, which relates the pH of a buffer solution to the pKa of the acid and the ratio of the concentrations of the conjugate base and the acid:
pH = pKa + log([A⁻]/[HA])
For example, if we have a 0.333 M solution of benzoic acid and a 0.252 M solution of sodium benzoate, the pH can be found using the Henderson-Hasselbalch equation with the given pKa of benzoic acid, which is 4.20. This comprises a buffer system, so the pH will be stable even with some addition of strong acid or base.