The acid- dissociation constants of phosphoric acid (H₃PO₄) are K_a1= 7.5 × 10^-³, K_a2= 6.2 × 10^-⁸, and K_a3= 4.2 × 10^-¹³at 25.0 °C. What is the molar concentration of phosphate ion in a 2.5 M aqueous solution of phosphoric acid?

Question

Quizplus · Accepted Answer

Phosphoric acid can dissociate in three stages as follows:

HS1U1B13S1U1B0POS1U1B14S1U1B0 → H+ + H2S1U1B1O4S1U1B1O- (Ka1)
H2S1U1B1O4S1U1B1O- → H+ + HS1U1B13S1U1B0PO4S1U1B13-S1U1B0 (Ka2)
HS1U1B13S1U1B0PO4S1U1B13-S1U1B0 → H+ + S1U1B12S1U1B0PO4S1U1B2- (Ka3)

In the first stage, only a small fraction of the acid will dissociate. Let x be the concentration of H+ ions produced by the dissociation of the first proton. The concentration of H2S1U1B1O4S1U1B1O- will be (2.5 – x) M. Then, we can calculate the concentration of H+ ions produced by the dissociation of the second proton.

Ka2 = [H+][HS1U1B13S1U1B0PO4S1U1B13-S1U1B0]/[H2S1U1B1O4S1U1B1O-]
6.2 × 10S1U1P1-S1S1P0S1U1P18S1S1P0 = x^2/(2.5 – x)

Since x is much smaller than 2.5, we can simplify the expression as:

6.2 × 10S1U1P1-S1S1P0S1U1P18S1S1P0 = x^2/2.5

Solving for x, we get:

x = 3.3 × 10S1U1P1- S1S1P0S1U1P12S1S1P0

At equilibrium, the concentration of HS1U1B13S1U1B0PO4S1U1B13-S1U1B0 will be (2.5 – x – y) M, where y is the concentration of H+ ions produced by the dissociation of the third proton. We can use a similar approach as before to calculate y:

Ka3 = [H+][HS1U1B13S1U1B0PO4S1U1B13-S1U1B0]/[S1U1B12S1U1B0PO4S1U1B2-]
4.2 × 10S1U1P1-S1S1P0S1U1P113S1S1P0 = y^2/ [2.5 – (3.3 × 10S1U1P1- S1S1P0S1U1P12S1S1P0) – y]

Simplifying, we get:

4.2 × 10S1U1P1-S1S1P0S1U1P113S1S1P0 = y^2/(2.2 – y)

Solving for y, we get:

y = 1.8 × 10S1U1P1- S1S1P0S1U1P11S1S1P0

The concentration of phosphate ion is:

[PO4S1U1B33-] = [S1U1B12S1U1B0PO4S1U1B2-] + [HS1U1B13S1U1B0PO4S1U1B13-S1U1B0] + [H2S1U1B1O4S1U1B1O-]
= y + (2.5 – x – y) + (2.5 – x)
= 5.0 – 2x
= 5.0 – 6.6 × 10S1U1P1- S1S1P0S1U1P12S1S1P0

Therefore, the best choice is C.

The Acid- Dissociation Constants of Phosphoric Acid (H3PO4) Are Ka1

The Acid- Dissociation Constants of Phosphoric Acid (H₃PO₄) Are K_a1