# Solutions of Polyprotic Acid/Base Systems, Problem A

### In-class Problem Set #3

**1. Calculate the pH of a 0.127 M solution of ascorbic acid. **

Groups quickly see that ascorbic acid has two pKa values.

*What does it mean if something has two pK _{a} values? What two chemical expressions represent the two equilibria that are occurring?*

Students may be tempted at first to ignore the presence of a second p*K _{a}* value, but encourage them to investigate what it implies about the acid. Once they have realized that there are two dissociable protons, ask them to write the correct chemical expressions making sure to include the proper charges. This should take about ten minutes. Some groups then use Ka1 to solve for a concentration of H3O+ and Ka2 to solve for a second value of H3O+. If they do so, they realize that the second value is much smaller than the first. But they also apparently have a solution with two different concentrations of H3O+.

*What do we know about [H _{3}O^{+}] in the two expressions? *

Remind the students that since only one pH value can be measured, the concentration of H_{3}O^{+} in the two equations must be equal.

*Write an expression for [H _{3}O^{+}] in terms of the ascorbic acid species.*

Students should have no trouble recognizing that for every one mole of ascorbic acid that is deprotonated, one mole of H_{3}O^{+} is produced, but they may have some trouble understanding that for every one mole of the fully deprotonated ascorbate formed, two moles of H_{3}O^{+} are formed.

*What is x for the K _{a1} expression?*

*What is x for the K _{a2} expression? What does this tell us about the second reaction?*

Students should realize very quickly that the second *x* value is equal to the *K _{a2}*. With an

*x*value this small, they should recognize that the second reaction is insignificant and that solving for the pH using just the p

*K*is sufficient. Spend several minutes talking about the general differences between p

_{a1}*K*values and when the second one can be ignored. Make sure students are clear that this was an example that began with the fully protonated species of a polyprotic acid.

_{a}*What is the pH of the solution?*