Step-by-step explanation:
Silver hydroxide is almost an insoluble compound, its solubility product is 2*10^(-8). When it is in solution it dissolves like this way.
AgOH ----> Ag⁺ + OH⁻ Ksp = 2 * 10^(-8)
The expression for the solubilty product will be:
Ksp = [Ag+] * [OH-]
We are trying to dissolve the silver hydroxide in the silver nitrate solution. They have one ion in common, the silver cation (Ag+). Since the amount of silver hydroxide that can be dissolved is really small (because it is almost insoluble) we can consider that the concentration of the silver ion is governed by the concentration of the silver nitrate solution.
AgNO₃ ----> Ag+ + NO₃-
Since one molecule of silver nitrate has one nitrate ion we can say that the concentration of the silver ion will be the same as the concentration of the silver nitrate solution.
[AgNO₃] = [Ag+] = 0.270 M
Now that we know the concentration of the silver ion and the ksp, we can replace these values and find the concentration of the hydroxide ion.
Ksp = [Ag+] * [OH-]
[OH-] = Ksp/[Ag+]
[OH-] = 2 * 10^(-8)/(0.270 M)
[OH-] = 7.41 *10^(-8) M = [AgOH]
Answer: the maximum amount of silver hydroxide that will dissolve it 7.41*10^(-8) M