To determine which mineral will precipitate from the solution, we need to compare the solubility products (Ksp) of calcite (CaCO3), dolomite (CaMg(CO3)2), and magnesite (MgCO3). The mineral with the lowest solubility product will precipitate first.
The solubility product expressions for the three minerals are as follows:
Calcite: Ksp(calcite) = [Ca2+][CO32-]
Dolomite: Ksp(dolomite) = [Ca2+][Mg2+][CO32-]^2
Magnesite: Ksp(magnesite) = [Mg2+][CO32-]
Given that the concentration of each ion (Mg2+, Ca2+, and CO32-) is 8 × 10^-3 M, we can calculate the ion activities, assuming molar concentrations are equal to ion activities.
Since the concentrations of Ca2+ and Mg2+ are the same, the activity terms for these ions will cancel out when comparing the solubility products. Therefore, we only need to compare the activity of the carbonate ion, CO32-.
In a solution of water, the activity of water is typically assumed to be approximately 1. So, we can write:
Ksp(calcite) = (8 × 10^-3)(1)
Ksp(dolomite) = (8 × 10^-3)(8 × 10^-3)(1)^2
Ksp(magnesite) = (8 × 10^-3)(1)
Calculating the values:
Ksp(calcite) ≈ 8 × 10^-3
Ksp(dolomite) ≈ 6.4 × 10^-6
Ksp(magnesite) ≈ 8 × 10^-3
Comparing the solubility products, we find that dolomite (CaMg(CO3)2) has the lowest solubility product, suggesting that dolomite will precipitate from the solution first. Therefore, dolomite would be the expected precipitate in this case.