When 100 mL each of 2.0 × 10^-4 M Ag⁺(aq)and 2.0 × 10^-1 M CO₃^2-(aq)are mixed,what is the remaining Ag⁺(aq)ion concentration and is precipitation complete? The solubility product constant of Ag₂CO₃(s)is 8.5 × 10^-12.

Question

Quizplus · Accepted Answer

First, we need to write out the chemical equation for the reaction between AgS1U1P1+S1S1P0(aq)and COS1U1B13S1U1B0S1U1P12-S1S1P0(aq):

AgS1U1P1+S1S1P0(aq) + COS1U1B13S1U1B0S1U1P12-S1S1P0(aq) → AgS1U1B12S1U1B0COS1U1B13S1U1B0(s) + S1S1P0(aq)

Next, we can use an ICE table to determine the concentration of remaining AgS1U1P1+S1S1P0(aq):

|        | AgS1U1P1+S1S1P0(aq) | COS1U1B13S1U1B0S1U1P12-S1S1P0(aq) | AgS1U1B12S1U1B0COS1U1B13S1U1B0(s) | S1S1P0(aq) |
|--------|---------------------|---------------------------------|--------------------------------|------------|
| Initial | 2.0 × 10S1U1P1-4S1S1P0 | 2.0 × 10S1U1P1-1S1S1P0          | 0                              | 0          |
| Change | -x                | -x                              | +x                             | +x         |
| Equil.  | 2.0 × 10S1U1P1-4S1S1P0 - x | 2.0 × 10S1U1P1-1S1S1P0 - x     | x                              | x          |

We can assume that x << 2.0 × 10S1U1P1-4S1S1P0, so we can simplify:

2.0 × 10S1U1P1-4S1S1P0 - x ≈ 2.0 × 10S1U1P1-4S1S1P0

2.0 × 10S1U1P1-1S1S1P0 - x ≈ 2.0 × 10S1U1P1-1S1S1P0

x ≈ [S1S1P0]

Now we can substitute the equilibrium concentration of S1S1P0 into the expression for the solubility product constant, Ksp:

Ksp = [AgS1U1B12S1U1B0COS1U1B13S1U1B0(s)][S1S1P0]

8.5 × 10S1U1P1-12S1S1P0 = x²

x = sqrt(8.5 × 10S1U1P1-12S1S1P0) = 9.2 × 10S1U1P1-6 S1S1P0

Therefore, the remaining concentration of AgS1U1P1+S1S1P0(aq) is 2.0 × 10S1U1P1-4S1S1P0 - 9.2 × 10S1U1P1-6 S1S1P0 ≈ 2.0 × 10S1U1P1-4S1S1P0, and precipitation is not complete. The correct answer is C.

When 100 ML Each of 2