In an acid-base experiment at 25.0°C, a sodium hydroxide solution was

standardized against KHP. The average value for the concentration of the sodium
hydroxide solution was calculated to be 0.0125 M. This solution was used to titrate
the phosphoric acid present in coke. The first two equivalence points were clearly
visible in the titration curve of the coke sample. However, the third equivalence point
could not be seen. Using calculations, demonstrate whether half of the HPO4^2- (aq) (Ka = 4.79 x 10-13) can be deprotonated.

To determine whether half of the HPO4^2- (aq) can be deprotonated, we can use the Henderson-Hasselbalch equation.

The Henderson-Hasselbalch equation is given by:
pH = pKa + log ([A^-]/[HA])

Where:
- pH is the acidity of the solution
- pKa is the negative logarithm of the acid dissociation constant
- [A^-] is the concentration of the deprotonated form (HPO4^2- in this case)
- [HA] is the concentration of the protonated form (H2PO4^- in this case)

Using the given Ka value (4.79 x 10^-13), we can calculate the pKa as follows:
pKa = -log(Ka) = -log(4.79 x 10^-13) = 12.32

Now, let's assume that half of the HPO4^2- (aq) can be deprotonated. This means that the concentration of HPO4^2- would be double the concentration of H2PO4^-. Let's say the concentration of H2PO4^- is "x" M. Then, the concentration of HPO4^2- would be "2x" M.

Plugging these values into the Henderson-Hasselbalch equation, we get:
pH = 12.32 + log (2x/x)
pH = 12.32 + log 2

Using a calculator, log 2 is approximately 0.3010:
pH = 12.32 + 0.3010
pH ≈ 12.62

Therefore, if half of the HPO4^2- (aq) can be deprotonated, the pH of the solution would be approximately 12.62.

If the third equivalence point couldn't be seen in the titration curve, it indicates that the pH is still acidic and has not reached the pH of approximately 12.62. Therefore, it can be concluded that only a fraction, less than half, of the HPO4^2- has been deprotonated in the solution.

To determine whether half of the HPO4^2- (aq) can be deprotonated, you need to calculate the concentration of HPO4^2- and H2PO4^- at the pH corresponding to the third equivalence point.

The Ka expression for the deprotonation reaction of HPO4^2- is:

Ka = [H2PO4^-][OH^-] / [HPO4^2-]

Since the third equivalence point has been reached, which means all HPO4^2- has been converted to H2PO4^-:

[HPO4^2-] = 0
[H2PO4^-] = initial concentration of HPO4^2-

Knowing the initial concentration of HPO4^2- in the coke sample is crucial to determine whether half of it has been deprotonated. Unfortunately, the given information does not provide the initial concentration of HPO4^2- in the coke sample. Therefore, it's not possible to make the calculation and determine whether half of the HPO4^2- has been deprotonated.

If you have the initial concentration of HPO4^2- in the coke sample, you can calculate the concentration of H2PO4^- at the third equivalence point and compare it with the concentration of HPO4^2-. If the concentration of H2PO4^- is approximately half of the initial concentration of HPO4^2-, then half of the HPO4^2- has been deprotonated.