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.
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To determine the concentration of silver(I) ions (Ag⁺) in a saturated solution of silver(I) carbonate (Ag2CO3), we need to use the solubility product expression (Ksp) and the stoichiometry of the balanced equation.
The balanced chemical equation for the dissociation of silver(I) carbonate is:
Ag2CO3 ↔ 2Ag⁺ + CO3²⁻
The Ksp expression for this reaction is:
Ksp = [Ag⁺]²[CO3²⁻]
Given Ksp = 8.6 × 10⁻¹² and the concentration of sodium carbonate (Na2CO3) as 0.0092 M, we can use the stoichiometry of the balanced equation to determine the concentration of Ag⁺.
Since 1 mole of Ag2CO3 yields 2 moles of Ag⁺, the change in concentration of Ag⁺ is twice the change in concentration of CO3²⁻. Therefore, we need to divide the concentration of Na2CO3 by 2 to find the concentration of CO3²⁻.
CO3²⁻ concentration = 0.0092 M / 2 = 0.0046 M
Now, let's Substitute the values into the Ksp expression and solve for [Ag⁺]:
Ksp = [Ag⁺]²[CO3²⁻]
8.6 × 10⁻¹² = [Ag⁺]² * 0.0046
Rearranging the equation to solve for [Ag⁺]:
[Ag⁺]² = (8.6 × 10⁻¹²) / 0.0046
[Ag⁺]² = 1.8696 × 10⁻⁹
Finally, taking the square root of both sides to solve for [Ag⁺]:
[Ag⁺] = √(1.8696 × 10⁻⁹)
[Ag⁺] ≈ 4.32 × 10⁻⁵ M
Therefore, the concentration of silver(I) ion (Ag⁺) in the saturated solution of silver(I) carbonate is approximately 4.32 × 10⁻⁵ M.