Sketch the titration curves for a diprotic acid titrated by a strong base and a triprotic acid titrated by a strong base. List the major species present at various points in each curve. In each curve, label the halfway points to equivalence. How do you calculate the pH at these halfway points?

For a diprotic acid, the titration curve will have two equivalence points and two buffer regions, while for a triprotic acid, the titration curve will have three equivalence points and three buffer regions. In both cases, the curve will start from a relatively low pH and end at a higher pH, as the strong base reacts with each acidic group one at a time.

Throughout the titration, several species will be present depending on the degree of reaction with the base: - At the beginning of the titration, the major species will be the unreacted diprotic/triprotic acid (H2A or H3A). - At the first buffer region, the major species will be a mixture of the first deprotonated species (HA- or H2A-) and the corresponding acid. - At the second buffer region for diprotic and first buffer region for triprotic acids, the major species will be a mixture of the second deprotonated species (A2- or HA2-) and the corresponding acid. - For triprotic acids, at the third buffer region, the major species will be a mixture of the third deprotonated species (A3-) and the corresponding acid. - At the final point of the titration, the major species will be the completely deprotonated species (A2- or A3-).

The halfway points are where half of the acidic groups have reacted with the strong base. We can calculate these points by finding the ratio of moles of base to moles of acid: - For diprotic acids: - Halfway to the first equivalence point: moles of base = 0.5 * moles of acid - Halfway to the second equivalence point: moles of base = 1.5 * moles of acid - For triprotic acids: - Halfway to the first equivalence point: moles of base = 0.5 * moles of acid - Halfway to the second equivalence point: moles of base = 1.5 * moles of acid - Halfway to the third equivalence point: moles of base = 2.5 * moles of acid

At the halfway points, the pH is equal to the pKa value of the corresponding acidic group. To calculate the pH at these points, use the formula: \( pH = pKa = -\log_{10}(Ka) \) where Ka is the acid dissociation constant for the particular acidic group.