Question

A chemistry student needs to prepare a buffer solution of pH 5.0 using acetic acid and acetate ions. If the student has 0.3 M acetic acid and 0.2 M acetate ions, what volume of acetic acid and acetate ions should he/she mix to prepare a solution with a total volume of 500 mL?

Answer 1

To solve this problem, we will use the Henderson-Hasselbalch equation:pH = pKa + log  [A-]/[HA] For acetic acid, the pKa is 4.74. We are given the pH  5.0  and the concentrations of acetic acid  [HA] = 0.3 M  and acetate ions  [A-] = 0.2 M . We need to find the volume of acetic acid and acetate ions to mix to prepare a 500 mL solution.First, let's rearrange the Henderson-Hasselbalch equation to solve for the ratio of [A-]/[HA]:log  [A-]/[HA]  = pH - pKalog  [A-]/[HA]  = 5.0 - 4.74log  [A-]/[HA]  = 0.26Now, find the ratio of [A-]/[HA]:[A-]/[HA] = 10^0.26  1.82Let x be the volume of 0.3 M acetic acid solution and y be the volume of 0.2 M acetate ion solution. We have two equations:1. x + y = 500 mL  total volume 2.  0.2y / 0.3x  = 1.82  ratio of [A-]/[HA] Now, we can solve for x and y:From equation 1, y = 500 - xSubstitute this into equation 2: 0.2 500 - x  / 0.3x  = 1.82Simplify and solve for x:100 - 0.2x = 0.54x100 = 0.74xx  135 mLNow, find y:y = 500 - 135y  365 mLThe student should mix approximately 135 mL of 0.3 M acetic acid solution and 365 mL of 0.2 M acetate ion solution to prepare a 500 mL buffer solution with a pH of 5.0.