What is the pH of a buffer that results when 0.50 mole of H₃PO₄ is mixed with 0.75 mole of NaOH and diluted with water to 1.00 L? (The acid dissociation constants of phosphoric acid are K_a1 = 7.5 $\times$ 10^-3,K_a2 = 6.2 $\times$ 10^-8,and K_a3 = 3.6 $\times$ 10^-13) A) 1.82 B) 2.12 C) 6.91 D) 7.21 E) 12.44

Question

Quizplus · Accepted Answer

To calculate the pH of a buffer solution, we need to determine the pKa values and the moles of the acid and conjugate base. In this case, we are given the acid dissociation constants of phosphoric acid and the initial moles of the acid and added base. The balanced chemical equation for the reaction is:

H3PO4 + 3NaOH → Na3PO4 + 3H2O

We can use the moles of the acid and added base to determine the moles of the conjugate base:

moles of H3PO4 = 0.50
moles of NaOH = 0.75

Since the reaction is 1:3 between the acid and base, the limiting reactant is H3PO4, so all of the moles of NaOH will react with H3PO4 to form 0.75/3 = 0.25 moles of the conjugate base (H2PO4-).

Next, we can use the acid dissociation constants to determine the pKa values. Since phosphoric acid has 3 dissociable protons, it has 3 pKa values:

pKa1 = 2.12
pKa2 = 6.25
pKa3 = 10.37

From this, we can determine that H3PO4 is a weak acid and will partially dissociate in water to form H+ and H2PO4-. H2PO4- is the conjugate base of H3PO4 and will have a basic character.

The Henderson-Hasselbalch equation can be used to calculate the pH:

pH = pKa + log([A-]/[HA])

where [A-] is the concentration of the conjugate base (H2PO4-) and [HA] is the concentration of the weak acid (H3PO4).

We can determine the concentrations of the acid and conjugate base by using the initial moles and the final volume:

[A-] = moles of conjugate base / volume = 0.25 / 1.00 L = 0.25 M
[HA] = moles of acid / volume = 0.50 / 1.00 L = 0.50 M

Finally, we can plug in the values to get the pH:

pH = pKa2 + log([A-]/[HA])
pH = 6.25 + log(0.25/0.50)
pH = 7.21

Therefore, the pH of the buffer solution is 7.21, so the best choice is D.

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