Calculate the pH after 0.010 mol of gaseous HCl is added to...

Calculate the pH after 0.010 mol of gaseous HCl is added to 250.0 mL of each of the following buffered solutions.
a. $0.050 \mathrm{M} \mathrm{NH}_3$ and $0.15 \mathrm{M} \mathrm{NH}_4 \mathrm{Cl}$
b. $0.50 \mathrm{M} \mathrm{NH}_3$ and $1.50 \mathrm{M} \mathrm{NH}_4 \mathrm{Cl}$

Key Concepts

Reaction Stoichiometry

Reaction stoichiometry involves calculating the change in moles of reactants and products when a reaction takes place. In the context of buffer solutions, it is essential to determine how the addition of an acid or base alters the concentrations of the buffer components, which can then be used in the Henderson-Hasselbalch equation to evaluate the resulting pH.

Acid-Base Reaction in Buffers

When a strong acid is added to a buffer, the acidic proton reacts with the weak base component of the buffer to form its conjugate acid. This reaction consumes the added acid while producing more of the weak acid, maintaining the pH of the solution relatively constant, provided that the buffer has sufficient capacity.

Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation provides a simplified way to calculate the pH of a buffer solution by relating the pH to the pKa of the weak acid and the ratio of the concentrations of the conjugate base to the weak acid. It is expressed as pH = pKa + log([base]/[acid]), and is particularly useful when analyzing the effect of adding small amounts of acid or base to a buffer.

Buffer Solutions

Buffer solutions are mixtures of a weak acid and its conjugate base, or a weak base and its conjugate acid, that resist changes in pH when small amounts of strong acid or base are added. Their ability to moderate pH shifts is due to the equilibrium established between the acid and base components, which can absorb added hydrogen or hydroxide ions.

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