Final answer:
To calculate the solubility product constant (Ksp) for Ag₂CO₃, we need to determine the concentration of Ag⁺ ions and CO₃²⁻ ions in the solution. The solubility of Ag₂CO₃ is given as 0.035 g/L at 25 °C. Using this information, we can calculate the concentrations of Ag⁺ and CO₃²⁻ ions and substitute them into the expression for Ksp.
Step-by-step explanation:
To calculate the solubility product constant (Ksp) for Ag₂CO₃, we need to determine the concentration of Ag⁺ ions and CO₃²⁻ ions in the solution. The solubility of Ag₂CO₃ is given as 0.035 g/L at 25 °C.
Using this information, we can calculate the concentrations of Ag⁺ and CO₃²⁻ ions and substitute them into the expression for Ksp.
The balanced equation for the dissolution of Ag₂CO₃ is:
Ag₂CO₃ ⇌ 2Ag⁺ + CO₃²⁻
From the equation, we can see that the concentration of Ag⁺ ions ([Ag⁺]) is equal to twice the solubility of Ag₂CO₃, and the concentration of CO₃²⁻ ions ([CO₃²⁻]) is equal to the solubility of Ag₂CO₃.
Therefore, [Ag⁺] = 2(0.035 g/L)
= 0.07 g/L and
[CO₃²⁻] = 0.035 g/L.
Now, we convert the concentrations from grams per liter to molarity by dividing by the molar mass of Ag and CO₃.
The molar mass of Ag is 107.87 g/mol, and the molar mass of CO₃ is 60.01 g/mol.
Thus, [Ag⁺] = 0.07 g/L / 107.87 g/mol
= 6.48 × 10⁻⁴ M and
[CO₃²⁻] = 0.035 g/L / 60.01 g/mol
= 5.83 × 10⁻⁴ M.
Finally, we substitute these concentrations into the expression for Ksp:
Ksp = [Ag⁺]²[CO₃²⁻]
= (6.48 × 10⁻⁴ M)²(5.83 × 10⁻⁴ M)
≈ 2.1 × 10⁻¹⁰