A solution contains [Ba²⁺] = 5.0 × 10^-5 M, [Ag⁺] = 3.0 × 10^-5 M, and [Zn²⁺] = 2.0 × 10^-7 M. Sodium oxalate is slowly added so that [C₂O₄^2-] increases.
What is the concentration of the first cation to precipitate when the second cation just begins to precipitate?

Question

A solution contains [Ba²⁺] = 5.0 × 10^-5 M, [Ag⁺] = 3.0 × 10^-5 M, and [Zn²⁺] = 2.0 × 10^-7 M. Sodium oxalate is slowly added so that [C₂O₄^2-] increases.

A solution contains [Ba<sup>2+</sup>] = 5.0 × 10<sup>-5</sup> M, [Ag<sup>+</sup>] = 3.0 × 10<sup>-5</sup> M, and [Zn<sup>2+</sup>] = 2.0 × 10<sup>-7</sup> M. Sodium oxalate is slowly added so that [C<sub>2</sub>O<sub>4</sub><sup>2-</sup>] increases. What is the concentration of the first cation to precipitate when the second cation just begins to precipitate? A) 1.3 × 10<sup>-6</sup> B) 2.2 × 10<sup>-6</sup> C) 5.0 × 10<sup>-5</sup> D) 1.35 × 10<sup>-9</sup> E) 1.1 × 10<sup>-11</sup>

What is the concentration of the first cation to precipitate when the second cation just begins to precipitate?

Quizplus · Accepted Answer

The first cation to precipitate will be the one with the lowest Ksp value. We can calculate the Ksp values using the given concentrations:

Ksp BaSO4 = [BaS1U1P12+S1S1P0][CS1U1B12S1U1B0OS1U1B14S1U1B0S1U1P12-S1S1P0] = (5.0 × 10^-5)(x)

Ksp Ag2Ox = [AgS1U1P1+S1S1P0][CS1U1B12S1U1B0OS1U1B14S1U1B0S1S1P0]^2 = (3.0 × 10^-5)(x^2)

Ksp ZnC2O4 = [ZnS1U1P12+S1S1P0][CS1U1B12S1U1B0OS1U1B14S1U1B0S1U1P12-S1S1P0] = (2.0 × 10^-7)(x)

where x is the concentration of sodium oxalate.

At the point where the second cation just begins to precipitate, the concentration of the ion with the higher Ksp value will reach its solubility product. So we can set the Ksp expression for Ag2Ox equal to its Ksp value and solve for x:

Ksp Ag2Ox = (3.0 × 10^-5)(x^2) = 5.5 × 10^-13

x = 2.2 × 10^-6 M

Now we can calculate the ion concentrations at this point:

[BaS1U1P12+S1S1P0] = (5.0 × 10^-5)(2.2 × 10^-6) / (1.5 × 10^-12) = 7.3 × 10^-3 M

[AgS1U1P1+S1S1P0] = 3.0 × 10^-5 M

[ZnS1U1P12+S1S1P0] = (2.0 × 10^-7)(2.2 × 10^-6) / (1.5 × 10^-12) = 2.9 × 10^-2 M

Therefore, the first cation to precipitate is Ba2+ and its concentration at this point is 7.3 × 10^-3 M, which is closest to choice B: 2.2 × 10^-6.

A Solution Contains [Ba2+] = 5

A Solution Contains [Ba²⁺] = 5