Question

2. The acidity constants for citric acid are \(\mathrm{p} K_{a 1}=3.13, \mathrm{pK}_{a 2}=4.72,\) and \(\mathrm{p} K_{a 3}=6.33\)

a. Write expressions for \(\alpha_{0}, \alpha_{1}, \alpha_{2},\) and \(\alpha_{3}\) as a function of the \(K_{a}\) values and \(\left\{\mathrm{H}^{+}\right\}\)

b. Identify the region where each species is dominant.

c. Determine which terms in the denominators for the \(\alpha\) values are significant at \(\mathrm{pH} 7.5\) (terms contributing less than \(5 \%\) to the summation can be considered negligible). For a solution with \(10^{-1} M\) total citrate, write out an approximate equation of the form \(\log C_{i}=\) constant \(+n(\mathrm{pH})\) for each citrate species at \(\mathrm{pH}\) 7.5, approximating the dominant species' concentration as TOTCit.

d. Draw a log \(C\) -pH diagram for a solution with \(10^{-1} M\) TOTCit. Include the \(\mathrm{pH}\) range \(1.0<\mathrm{pH}<8.0\).

e. Find the \(\mathrm{pH}\) of the following solutions:

i. \(10^{-1} \mathrm{M} \mathrm{H}_{3} \mathrm{Cit}+\) water.

ii. \(10^{-1} M \mathrm{Na}_{2} \mathrm{HCit}+\) water.

iii. \(0.05 \mathrm{M} \mathrm{Na}_{3} \mathrm{Cit}+0.05 \mathrm{M} \mathrm{NaH}_{2} \mathrm{Cit}+\) water.