Final answer:
To determine [Ag+] and [SO4 2-] concentrations after the addition of AgNO3, we calculate the shift in equilibrium from the solubility product constant (Ksp) for Ag2SO4 and consider the Ag+ provided by the added AgNO3.
Step-by-step explanation:
The student asked about calculating the concentrations of silver ions [Ag+] and sulfate ions [SO4 2-] in a saturated solution of Ag2SO4 after adding AgNO3. The Ksp for Ag2SO4 at 25o C is given as 1.2 x 10-5.
To find the concentrations, we'd start with the dissociation equation for Ag2SO4:
Ag2SO4 (s) ⇌ 2 Ag+ (aq) + SO4 2- (aq)
Let 's' represent the solubility of Ag2SO4, which means [Ag+] = 2s and [SO4 2-] = s. Thus, the Ksp expression is:
Ksp = [Ag+]2[SO4 2-] = (2s)2s = 4s3 = 1.2 x 10-5
However, because AgNO3 is a strong electrolyte and will completely dissociate in the solution, the added Ag+ ions from the dissociation of AgNO3 will affect the initial concentration of Ag+ in the solution and possibly shift the equilibrium.
0.755 g of AgNO3 is equivalent to:
0.755 g AgNO3 * (1 mol AgNO3 / 169.87 g/mol) = 4.44 x 10-3 mol AgNO3
Since the final volume is 500.0 mL, the molarity of AgNO3 added is:
4.44 x 10-3 mol / 0.500 L = 8.88 x 10-3 M
Given the Ksp expression and the stoichiometry of the dissociation, the concentration of sulfate at equilibrium will not change significantly due to the common ion effect provided by additional Ag+ ions, thus we only calculate the shift in equilibrium concerning the added Ag+ ions. The final concentration of Ag+ ions will be the concentration from Ag2SO4 plus the concentration from AgNO3. Alternatively, a detailed equilibrium calculation would be needed if AgNO3 addition caused a significant perturbation in the initial solubility equilibrium, but assuming the changes are negligible, the final concentration of Ag+ in the solution would be primarily from AgNO3.