You are interested in using lactic acid $($pKa $=3\mathrm{.}1)$ as a buffer for your biochemical experiment.

It was found that out of a pH of $2,4,6$ that a pH of $4$ was the best pH to go with and when deciding to use lactic acid to make $1\mathrm{.}5$ L of $50\mathrm{.}0$ mM buffer at the pH of $4$ the results for the concentrations of lactic acid and its conjugate base are $44.$mM

c$)$ In making the buffer you described in part b$,$ you find that you can buy $12$ M lactic acid from a chemical company.

i$)$ What volume of $12$ M lactic acid should you start with?

ii$)$ Would you make your desired buffer by adding strong acid $(4\mathrm{.}0$ M HCl$)$ or strong base

$(4\mathrm{.}0$ M NaOH$)?$ Explain your answer.

iii$)$ How many mL of either the strong acid or strong base would you need to add?