Final answer:
To find the required masses of bromoacetic acid and sodium bromoacetate, use the Henderson-Hasselbalch equation with the given pH and pKa to calculate their concentration ratio in the buffer solution, then determine individual concentrations within the total concentration of 0.200 M, and finally calculate the masses for a 1.00 L solution.
Step-by-step explanation:
The question revolves around preparing a specific pH buffer solution using bromoacetic acid and sodium bromoacetate. To calculate the required masses, we must first consider the Henderson-Hasselbalch equation which relates pH, pKa, and the ratio of the concentrations of the acid and its salt (conjugate base). For bromoacetic acid (which has a pKa of approximately 2.90), the equation is:
$$ pH = pKa + \log \left(\frac{{[\text{Conjugate Base}]}}{{[\text{Acid}]}}\right) $$
Given a pH of 5 and a pKa of 2.90, the ratio of the concentrations of sodium bromoacetate to bromoacetic acid is determined. Using this ratio and the total concentration (0.200 M), we can find the individual concentrations of bromoacetic acid and sodium bromoacetate. Once we have the concentrations, we can calculate the masses by using the molar mass of each compound and the volume of the solution (1.00 L).