If a solution is prepared by dissolving 1.6 mol Na₂CrO₄ in 1.0 L of a buffer at pH 8.24, what will be [Cr₂O₇^2-] in the solution? The resultant equilibria are: HCrO₄^- ⇌ H⁺ + CrO₄^2- Ka = 3.2 × 10^-7
2 HCrO₄^-⇌ Cr₂O₇^2-+ H₂O K = 33

Question

Quizplus · Accepted Answer

First, we need to set up an ICE table for the first equilibrium:
HCrOS1U1B14S1U1B0S1U1P1-S1S1P0 ⇌ HS1U1P1+S1S1P0 + CrOS1U1B14S1U1B0S1U1P12-S1S1P0
I:  0          0              1.6
C:   -x        +x            +x
E:  0-x        x             1.6+x
Using the Ka expression and solving for x, we get x = 1.159 × 10S1U1P1-6S1S1P0 M
Next, we need to set up another ICE table for the second equilibrium:
2 HCrOS1U1B14S1U1B0S1U1P1- S1S1P0⇌ CrS1U1B12S1U1B0OS1U1B17S1U1B0S1U1P12-S1S1P0+ HS1U1B12S1U1B0O
I:    0                           0                    1.6
C:   +2x                        -x                    -x
E:   2x                         0                     1.6-x
Using the K expression and the values from the ICE table, we get:
33 = (CrS1U1B12S1U1B0OS1U1B17S1U1B0S1U1P12-S1S1P0)(HS1U1B12S1U1B0O)/(HCrOS1U1B14S1U1B0S1U1P1-S1S1P0)S1S1P0 = (1.6-x)(x)/(2x)S1S1P0
Simplifying and solving for x, we get x = 2.9 × 10S1U1P1-28S1S1P0 M
Finally, we need to calculate the concentration of CrS1U1B12S1U1B0OS1U1B17S1U1B0S1U1P12-S1S1P0 using the ICE table for the first equilibrium:
[CrS1U1B12S1U1B0OS1U1B17S1U1B0S1U1P12-S1S1P0] = 1.6+x = 1.6 + 2.9 × 10S1U1P1-28S1S1P0 = 8.9 × 10S1U1P1-9S1S1P0 M
Therefore, the answer is choice E.

If a Solution Is Prepared by Dissolving 1