What is the remaining concentration of the cation that precipitates first, when the other cation just begins to precipitate? consider a solution that is 2.3×10−2 m in fe2+ and 2.0×10−2 m in mg2+?

Ksp for FeCO₃ is 3.07 x 10⁻¹¹
Ksp for MgCO₃ is 6.82 x 10⁻⁶
So Fe²⁺ will precipitated first as solubility product of FeCO₃ is lower than solubility product of MgCO₃
Ksp FeCO₃ = [Fe²⁺][CO₃²⁻] 
3.07 x 10⁻¹¹ = (2.3 x 10⁻²) [CO₃²⁻]
[CO₃²⁻] = 1.33 x 10⁻⁹ M to precipitate Fe²⁺ ions

Ksp MgCO₃ = [Mg²⁺][CO₃²⁻]
6.82 x 10⁻⁶ = (2.0 x 10⁻²) [CO₃²⁻]
[CO₃²⁻] = 3.4 x 10⁻⁴ M to precipitate the Mg²⁺ ions

Ksp FeCO₃ = [Fe²⁺][CO₃²⁻]
3.07 x 10⁻¹¹ = [Fe²⁺] (3.4 x 10⁻⁴)
[Fe²⁺] = 9 x 10⁻⁸ M when Mg²⁺ ions precipitate

The activity series is shown in the attached picture. if the element is below the other, then you can displace the other. following the activity series as a guide, the reactions are as follows: nickel and aluminum chloride3 ni + 2 alcl₃  → 3 nicl₂ + 2 albarium and copper bromideba + cubr  →  no reaction because cu is less oxidizable than bapotassium nitrate and aluminum3 kno₃ + al  → al(no₃)₃ + 3 ksodium phosphate and zincnaso₄ + zn  → znso₄ + na