Final answer:
To find the volume of 5.0-M sodium borate needed to achieve a pH of 9.6 in a 200-mL solution of 50 mM boric acid, use the Henderson-Hasselbalch equation to determine the ratio of conjugate base to acid. Then calculate the volume using molarity and volume relationships.
Step-by-step explanation:
To determi0-M solution of sodium borate must be added to a 200-mL solution of 50 mM boric acid to achieve a pH one how many mL of a 5.f 9.6, we must understand the concept of buffer solutions and Henderson-Hasselbalch equation. The sodium borate and boric acid system create a buffer solution. The Henderson-Hasselbalch equation is pH = pKa + log([A-]/[HA]), where [A-] is the concentration of the conjugate base, and [HA] is the concentration of the acid.
in this case, we're targeting a pH of 9.6, and the pKa of boric acid is typically around 9.24. We can rearrange the equation to solve for the ratio of [A-] to [HA]:
[base]/[acid] = 10^(pH - pKa)
After calculating the ratio, we can find the volume of the 5.0 M sodium borate solution needed by using molarity and volume relationships. The answer would be one of the given choices after performing the correct calculations.