What is the concentration of silver(I) ion in a saturated solution of silver(I) carbonate containing 0.0092 M Na2CO3? For Ag2CO3, Ksp = 8.6 × 10–12.
Ag2CO3 ==> 2Ag^+ + CO3^-2
Ksp = (Ag^+)^2(CO3^-2) = 8.6 x 10^-12
Substitute00092 for CO3^-2, calculate Ag^+.
To determine the concentration of silver(I) ion (Ag⁺) in a saturated solution of silver(I) carbonate (Ag₂CO₃), we can use the solubility product constant (Ksp) and the stoichiometry of the reaction.
The balanced chemical equation for the dissociation of Ag₂CO₃ is as follows:
Ag₂CO₃(s) ⇌ 2Ag⁺(aq) + CO₃²⁻(aq)
According to the stoichiometry, for every 1 mol of Ag₂CO₃ that dissolves, 2 mol of Ag⁺ ions are produced. Therefore, if we let 'x' represent the concentration of Ag⁺ ions, the concentration of CO₃²⁻ ions will also be 'x' (since they have a 1:1 stoichiometric ratio).
Using the Ksp expression, we have:
Ksp = [Ag⁺]²[CO₃²⁻]
Ksp = (2x)²(x) = 8.6 × 10⁻¹²
Simplifying the equation gives:
4x³ = 8.6 × 10⁻¹²
Solving for 'x' gives:
x = (8.6 × 10⁻¹² / 4)^(1/3) = 3.656 × 10⁻⁴ M
Therefore, the concentration of silver(I) ion (Ag⁺) in the saturated solution of silver(I) carbonate is approximately 3.656 × 10⁻⁴ M.