Question

A student needs to prepare a buffer solution with a pH of 4.5 using acetic acid (pKa = 4.76) and its conjugate base sodium acetate. The student has 100 mL of 0.1 M acetic acid and has access to sodium acetate. What mass of sodium acetate (in grams) should the student add to the solution to achieve the desired pH?

Answer 1

To solve this problem, we can use the Henderson-Hasselbalch equation:pH = pKa + log  [A-]/[HA] where pH is the desired pH of the buffer solution, pKa is the acid dissociation constant of the weak acid, [A-] is the concentration of the conjugate base  sodium acetate , and [HA] is the concentration of the weak acid  acetic acid .We are given the pH  4.5 , pKa  4.76 , and the concentration of acetic acid  0.1 M . We need to find the concentration of sodium acetate  [A-] .4.5 = 4.76 + log  [A-]/0.1 Rearranging the equation to solve for [A-]:log  [A-]/0.1  = 4.5 - 4.76log  [A-]/0.1  = -0.26Now, we can find the ratio of [A-] to 0.1:[A-]/0.1 = 10^-0.26 [A-] = 0.1 * 10^-0.26 Calculating the concentration of sodium acetate:[A-]  0.1 * 0.55[A-]  0.055 MNow, we need to find the mass of sodium acetate needed to achieve this concentration in 100 mL of solution:moles of sodium acetate = 0.055 moles/L * 0.100 Lmoles of sodium acetate  0.0055 molesThe molar mass of sodium acetate  CH3COONa  is approximately 82.03 g/mol. Therefore, the mass of sodium acetate needed is:mass of sodium acetate = 0.0055 moles * 82.03 g/molmass of sodium acetate  0.451 gThe student should add approximately 0.451 grams of sodium acetate to the solution to achieve the desired pH of 4.5.