Answer :
Final answer:
The pH of a saturated solution of silver hydroxide can be calculated using the Ksp value and the concentration of hydroxide ions. With a Ksp of 1.57×10-8, the concentration of OH- in the solution is 1.25×10-4 M. Using the relationship between OH- and H+, the pH can be calculated to be 10.9.
Explanation:
The pH of a saturated solution of silver hydroxide can be determined by calculating the concentration of hydroxide ions (OH-) in the solution. We can use the solubility product constant (Ksp) to find the concentration of OH-. The equation for the dissociation of silver hydroxide is AgOH(s) ⇌ Ag+(aq) + OH-(aq).
Given that the Ksp of silver hydroxide is 1.57×10-8, we can set up an equilibrium expression:
Ksp = [Ag+][OH-]
Since the solubility of AgOH determines the concentration of Ag+ and OH-, and the solubility is equal to the concentration in a saturated solution, we can say that [Ag+] = [OH-] = x (assuming the solubility is x).
Substituting the concentrations into the equilibrium expression, we get:
1.57×10-8 = x * x
Solving the equation for x, we find:
x = 1.25×10-4
So, the concentration of OH- in a saturated solution of silver hydroxide is 1.25×10-4 M. Now, we can calculate the pH of the solution using the formula pH = -log[H+]. Since OH- and H+ are related by the equation H+ * OH- = Kw (the dissociation constant of water), we can find the concentration of H+ using the concentration of OH-.
pH = -log[H+] = -log(Kw/OH-) = -log(1.0×10-14/1.25×10-4) = 10.9
Therefore, the pH of a saturated solution of silver hydroxide is 10.9.
