Consider a solution that is 2.0*10-2 M in Fe2 + and 1.8*10-2 M in Mg2+. (Ksp for FeCO3 is 3.07*10-11 and Ksp for MgCO3 is 6.82*10-6.)

-What minimum concentration of K2CO3 is required to cause the precipitation of the cation that precipitates first?

Express your answer using two significant figures.

The minimum concentration of K₂CO₃ is (1.5 x 10⁻⁹ M) that is required to cause the the precipitation of FeCO₃ firstly.

Explanation:

Firstly, we should know that the precipitate is formed when the ionic product of the ions is higher than the solubility product.

FeCO₃ is formed when: [Fe²⁺][CO₃⁻²] > Ksp of FeCO₃.

MgCO₃ is formed when: [Mg²⁺][CO₃⁻²] > Ksp of MgCO₃.

1) For FeCO₃:

∵ Ksp (FeCO₃) = [Fe²⁺][CO₃⁻²]

(3.07 * 10⁻¹¹) = (2.0 * 10²⁻) [CO₃⁻²]

∴ [CO₃⁻²] = (3.07 * 10⁻¹¹) / (2.0 * 10²⁻) = 1.5 x 10⁻⁹ M.

2) For MgCO₃:

∵ Ksp (MgCO₃) = [Mg²⁺][CO₃⁻²]

(6.82 * 10⁻⁶) = (1.8 * 10²⁻) [CO₃⁻²]

∴ [CO₃⁻²] = (6.82 * 10⁻⁶) / (1.8 * 10²⁻) = 3.8 x 10⁻⁴ M.

The concentration of K₂CO₃ is (1.5 x 10⁻⁹ M) that is required to cause the the precipitation of FeCO₃ is much less than the concentration of K₂CO₃ (3.8 x 10⁻⁴ M) that is required to cause the the precipitation of MgCO₃.

So, The minimum concentration of K₂CO₃ is (1.5 x 10⁻⁹ M) that is required to cause the the precipitation of FeCO₃ firstly.