To solve this problem, we will use the Henderson-Hasselbalch equation:pH = pKa + log [A-]/[HA] We are given the pH 7.5 , pKa 4.5 , and initial concentration of HA 0.2 M . We need to find the concentrations of A- and HA in the final buffer solution.7.5 = 4.5 + log [A-]/[HA] Rearranging the equation to solve for the ratio of [A-]/[HA]:log [A-]/[HA] = 7.5 - 4.5log [A-]/[HA] = 3Now, we can remove the log:[A-]/[HA] = 10^3[A-] = 1000 * [HA]Since the total volume of the buffer solution is 500 mL, we can write the following equations for the moles of A- and HA:moles of A- = 1000 * moles of HANow, we need to find the total moles of HA and A- in the 500 mL buffer solution. We know that the initial concentration of HA is 0.2 M, so:moles of HA = 0.2 M * 0.5 L = 0.1 molesNow we can find the moles of A-:moles of A- = 1000 * moles of HA = 1000 * 0.1 = 100 molesNow that we have the moles of A- and HA, we can find the mass of each component. To do this, we need the molar mass of HA and A-. However, since the problem does not provide the molar mass of HA and A-, we will express the mass in terms of their molar masses:mass of HA = moles of HA * molar mass of HA = 0.1 moles * M_HAmass of A- = moles of A- * molar mass of A- = 100 moles * M_A-So, to prepare 500 mL of a buffer solution with a pH of 7.5 using a weak acid HA and its conjugate base A-, you would need to mix 0.1 moles * M_HA of HA and 100 moles * M_A- of A-.