(a) Calculate the pH of a buffer that is 0.12 \(\mathrm{M}\) in lactic acid and 0.11 \(\mathrm{M}\) in sodium lactate. (b) Calculate the pH of a buffer formed by mixing 85 mL of 0.13 M lactic acid with 95 mL of 0.15\(M\) sodium lactate.

Lactic acid has a chemical formula: \(\mathrm{CH_3CH(OH)COOH}\). The dissociation of lactic acid can be presented by the following equation: \(\mathrm{CH_3CH(OH)COOH} \rightleftharpoons \mathrm{H^+ + CH_3CH(OH)COO^-} \) The acid dissociation constant (K_a) for lactic acid is approximately \(1.4 \times 10^{-4}\). We will use this value to find the pKa of lactic acid: \(pK_a = -\log_{10}{K_a} = -\log_{10}(1.4 \times 10^{-4})\) We can plug this value into a calculator to find out the pKa.

Now that we have the pKa of lactic acid, we can use the Henderson-Hasselbalch equation to find the pH of the first buffer: \(pH = pK_a + \log{\frac{[\mathrm{A^-}]}{[\mathrm{HA}]}}\) The concentration of lactic acid (HA) is 0.12 M, and the concentration of sodium lactate (A-) is 0.11 M. Plugging these values and the pKa of lactic acid into the equation, we find the pH.

For the second part of the problem, we need to find the pH of the buffer system formed by mixing volumes of lactic acid and sodium lactate. We will use the given volumes and concentrations to find the overall concentration of lactic acid and sodium lactate in the final buffer and then apply the Henderson-Hasselbalch equation. Amount of lactic acid (in moles) = volume of lactic acid \(\times\) concentration of lactic acid = \((85 \times 10^{-3})L \times 0.13 M = 0.01105\) moles. Amount of sodium lactate (in moles) = volume of sodium lactate \(\times\) concentration of sodium lactate = \((95\times 10^{-3})L \times 0.15 M = 0.01425\) moles. Total volume of the buffer = volume of lactic acid + volume of sodium lactate = \((85 + 95) mL = 180 mL = 0.18 L\) Now we can find the final concentrations in the mixed buffer: Concentration of lactic acid, \(\mathrm{[HA]} = \frac{0.01105 \, \text{moles}}{0.18L}\) Concentration of sodium lactate, \(\mathrm{[A^-]} = \frac{0.01425\, \text{moles}}{0.18L}\) We will use these concentrations to calculate the pH using the Henderson-Hasselbalch equation: \(pH = pK_a + \log{\frac{[\mathrm{A^-}]}{[\mathrm{HA}]}}\) Plug in the pKa of lactic acid and the calculated concentrations for lactic acid, and sodium lactate into the equation to find the pH.