Titration and Buffers (5A) Practice Test

A 20.0 mL sample of 0.200 M formic acid is titrated with 0.200 M NaOH at 25°C:

$\mathrm{HCOOH + OH^- \rightarrow HCOO^- + H_2O}$

Given $pK_a(\mathrm{HCOOH}) = 3.75$. Consider two points on the titration: Point P occurs when 5.0 mL of NaOH has been added; Point Q occurs when 19.0 mL of NaOH has been added. Assume volume changes are not negligible for pH but focus on conceptual species dominance.

Which statement best explains why the solution at one of these points has greater buffer capacity against added base?

A laboratory technician must prepare 500 mL of a buffer at pH 7.40 using the $\mathrm{H_2PO_4^- / HPO_4^{2-}}$ system at 25°C:

$\mathrm{H_2PO_4^- \rightleftharpoons H^+ + HPO_4^{2-}}$, $pK_a = 7.21$.

They can choose between two stock solutions: (i) 0.10 M $\mathrm{NaH_2PO_4}$ and 0.10 M $\mathrm{Na_2HPO_4}$, or (ii) 0.010 M $\mathrm{NaH_2PO_4}$ and 0.010 M $\mathrm{Na_2HPO_4}$. The pH will be set by mixing appropriate volumes of the acid and base stocks; no other acids/bases will be added. The goal is not only to reach pH 7.40 but also to maximize buffer capacity.

Which choice is most consistent with achieving the desired pH with the highest buffer capacity, assuming both options can be mixed to the same base:acid ratio?