What is the maximum concentration of carbonate ions that will precipitate BaCO₃ but not MgCO₃ from a solution that is M each in Mg²⁺ and Ba²⁺? For MgCO₃,K_sp = 1.0 × 10^-5 and for BaCO₃,K_sp = 2.6 × 10^-9. A) M B) M C) M D) M E)2.6 × 10^-14 M

Question

Quizplus · Accepted Answer

The solubility product constant for BaCO3 is much smaller than that for MgCO3 (2.6 × 10^-9 vs. 1.0 × 10^-5), which means that BaCO3 is much less soluble than MgCO3. To find the maximum concentration of carbonate ions that will precipitate BaCO3 but not MgCO3, we need to determine when the ion product of BaCO3 (i.e. [Ba2+][CO32-]) equals the solubility product constant:

Ksp = [Ba2+][CO32-] = (2.6 × 10^-9)

Assuming that x M of carbonate ions react with both Mg2+ and Ba2+ ions, the concentrations of the ions in the solution will be:

[Mg2+] = [S2-] = 11ea7a3a_9f32_f4f6_a82d_376001f78d3f_TB2288_11 M
[Ba2+] = [S2-] = 11ea7a3a_9f32_f4f6_a82d_376001f78d3f_TB2288_11 M

[CO32-] = x M

We can then write the ion product expressions for MgCO3 and BaCO3:

[Mg2+][CO32-] = (1.0 × 10^-5)x
[Ba2+][CO32-] = (2.6 × 10^-9)x

Since we want to find the maximum concentration of carbonate ions that will precipitate BaCO3 but not MgCO3, we want to find the value of x that makes [Ba2+][CO32-] equal to the solubility product constant, but [Mg2+][CO32-] less than the solubility product constant. This means that:

[Mg2+][CO32-] < Ksp
(1.0 × 10^-5)x < (2.6 × 10^-9)

Solving for x gives:

x < 2.6 × 10^-4

Since this is the maximum concentration of carbonate ions that will not cause MgCO3 to precipitate, it is also the maximum concentration of carbonate ions that will cause BaCO3 to precipitate. Therefore, the answer is choice A: 11ea7a3a_9f32_f4f7_a82d_f37f9e4fd8d2_TB2288_11 M.

What Is the Maximum Concentration of Carbonate Ions That Will