A phosphate buffer solution (25.00 mL sample) used for a growth medium was titrated with 0.1000 M hydrochloric acid. The components of the buffer were sodium monohydrogen phosphate and sodium dihydrogen phosphate. The first endpoint occurred at a volume of 10.32 mL; the second occurred after an additional 18.62 mL was added, for a total volume of 28.94 mL. What was the approximate ratio of HPO₄²^- to H₂PO₄^-in the buffer?

Question

Quizplus · Accepted Answer

First, we need to determine the pKa values for the two components of the buffer (sodium monohydrogen phosphate and sodium dihydrogen phosphate). The pKa values can be calculated using the Henderson-Hasselbalch equation for each endpoint:

pKa1 = pH + log([H2PO4-]/[HPO42-]) where pH is the pH at the first endpoint and [H2PO4-]/[HPO42-] is the ratio of the concentrations of the two species.

pKa2 = pH + log([HPO42-]/[PO43-]) where pH is the pH at the second endpoint and [HPO42-]/[PO43-] is the ratio of the concentrations of the two species.

Using the given volumes and concentrations, we can calculate the initial concentrations of the two species:

[V1] [C1] = [V2] [C2] where V1 and C1 are the volume and concentration of the HCl used in the first endpoint, and V2 and C2 are the volume and concentration of the buffer solution.

For the first endpoint, we have:

10.32 mL * 0.1000 M HCl = 25.00 mL * [H2PO4-]/[HPO42-] + 0.00 mL * [HPO42-]/[H2PO4-]

Simplifying, we get:

[H2PO4-]/[HPO42-] = 0.413

For the second endpoint, we have:

18.62 mL * 0.1000 M HCl = 25.00 mL * [HPO42-]/[PO43-] + 10.32 mL * [H2PO4-]/[HPO42-]

Simplifying, we get:

[H2PO4-]/[HPO42-] = 1.196

Since the ratio of [H2PO4-]/[HPO42-] changes from 0.413 to 1.196, the pH must also change from around the pKa1 value to around the pKa2 value. The pKa1 value is approximately 7.21, and the pKa2 value is approximately 12.27. Therefore, the pH at the first endpoint is acidic (below 7.21) and the pH at the second endpoint is basic (above 12.27).

Now we can calculate the ratio of the two components based on their pKa values and the pH range of the buffer:

[H2PO4-]/[HPO42-] = 10^(pKa-pH)

At the first endpoint:

[H2PO4-]/[HPO42-] = 10^(7.21-pH) = 0.413

At the second endpoint:

[H2PO4-]/[HPO42-] = 10^(12.27-pH) = 1.196

Solving for pH at each endpoint, we get:

pH1 = 6.91

pH2 = 12.44

So the ratio of [H2PO4-]/[HPO42-] changes from 0.413 to 1.196 over a pH range of 6.91 to 12.44. This means that the buffer is most likely a mixture of primarily HPO42- with some H2PO4- to create a pH range of around 7.0-12.5. The approximate ratio of HPO42- to H2PO4- is:

[HPO42-]/[H2PO4-] = 1/[H2PO4-]/[HPO42-]

[HPO42-]/[H2PO4-] = 1/0.413 = 2.42

Therefore, the best choice is D) 5:4, which is the closest answer choice to 2.42 in a 5:4 ratio.

A Phosphate Buffer Solution (25