Final answer:
The concentrations of Ga and CO₃ in a saturated solution of Ga₂(CO₃)₃ at 25°C with a given Ksp of 1.7 x 10⁻¹¹ is [Ga₃⁺] = 2s and [CO₃²⁻] = 3s.
Step-by-step explanation:
To determine the concentration of Ga and CO₃ in a saturated solution of Ga₂(CO₃)₃, we can use the solubility product constant (Ksp) provided, which is 1.7 x 10⁻¹¹. The dissolution of gallium carbonate can be represented by the equation:
Ga₂(CO₃)₃ (s) ⇌ 2Ga₃⁺ (aq) + 3CO₃²⁻ (aq)
Let the solubility of Ga₂(CO₃)₃ be 's' moles/liter. Therefore, at equilibrium, [Ga₃⁺] will be 2s and [CO₃²⁻] will be 3s. Substituting these into the expression for Ksp:
Ksp = [2s]²[3s]³
1.7 x 10⁻¹¹ = 108s5
s = (1.7 x 10⁻¹¹ / 108)1/5
Once we find 's', we can then find the concentrations:
[Ga₃⁺] = 2s
[CO₃²⁻] = 3s