[Radu]

      I have a problem: 0,01 moles of Ag₃PO₄ are placed in 1 L of pure water. Knowing k_sAgOH=4*10^-16, k_sAg3PO4=2.7*10^-18, Ka₁=10^-2, ka₂=10^-7, ka₃=10^-2 (for H₃PO₄), calculate:
   a) the constant of the reaction: Ag₃PO₄+ 3H₂O 3AgOH + H₃PO₄.
   b)  find pH, [PO₄^3-], and [Ag⁺] at equilibrium in the resulting solution
   c) ignoring the hydrolisis of Ag⁺, calculate the pH of the solution.
 
    Here's my approach:

         a) I obtain easily k=4.2*10⁷.
         b) Having this big constant for the hydrolisis of the salt, I can assume that all silver phosphate has dissolved, and, at equilibrium, that : [Ag⁺]=k_sAgOH/[OH^-]., and C_H3PO4≈0.01M. Given we expect to have a basic solution, I do the charge balance: [PO₄^3-]*3+ [HPO₄^2-]*2+[HO^-]=[H₃O⁺] + k_sAgOH/[HO^-]. Multiplying the relation with [HO^-], I obtain: some terms + [HO^-]²= K_w + k_sAgOH≈kw. some terms=kw-[HO^-]², which means that [OH^-]<10^-7 ( acidic medium)  Is this actually correct? Does silver phosphate hydrolisis create acidity? The correct answers are [Ag⁺]=6.5*10^-14M, [PO₄^3-]=3.8*10^-3, pH=11.792. If you look at these, you'll notice k_sAgOH has been reached, and that all Ag₃PO₄ has been dissolved
c) it is very similar to the phosphoric acid problem(IChO-see "Back with the phosphoric acid" topic), but applying the same method I obtain pH= 9.8. They obtain pH=10.62. One thing that strikes is that this pH, which is achieved theoretically, by neglecting Ag⁺ hydrolisis, is smaller than the one where Ag⁺ lowers the pH by forming the insoluble hydroxide). What might be wrong, and how can this problem be treated?

[Big-Daddy]

      I have a problem: 0,01 moles of Ag₃PO₄ are placed in 1 L of pure water. Knowing k_sAgOH=4*10^-16, k_sAg3PO4=2.7*10^-18, Ka₁=10^-2, ka₂=10^-7, ka₃=10^-2 (for H₃PO₄), calculate:
   a) the constant of the reaction: Ag₃PO₄+ 3H₂O 3AgOH + H₃PO₄.
   b)  find pH, [PO₄^3-], and [Ag⁺] at equilibrium in the resulting solution
   c) ignoring the hydrolisis of Ag⁺, calculate the pH of the solution.
 
    Here's my approach:

         a) I obtain easily k=4.2*10⁷.
         b) Having this big constant for the hydrolisis of the salt, I can assume that all silver phosphate has dissolved, and, at equilibrium, that : [Ag⁺]=k_sAgOH/[OH^-]., and C_H3PO4≈0.01M. Given we expect to have a basic solution, I do the charge balance: [PO₄^3-]*3+ [HPO₄^2-]*2+[HO^-]=[H₃O⁺] + k_sAgOH/[HO^-]. Multiplying the relation with [HO^-], I obtain: some terms + [HO^-]²= K_w + k_sAgOH≈kw. some terms=kw-[HO^-]², which means that [OH^-]<10^-7 ( acidic medium)  Is this actually correct? Does silver phosphate hydrolisis create acidity? The correct answers are [Ag⁺]=6.5*10^-14M, [PO₄^3-]=3.8*10^-3, pH=11.792. If you look at these, you'll notice k_sAgOH has been reached, and that all Ag₃PO₄ has been dissolved
c) it is very similar to the phosphoric acid problem(IChO-see "Back with the phosphoric acid" topic), but applying the same method I obtain pH= 9.8. They obtain pH=10.62. One thing that strikes is that this pH, which is achieved theoretically, by neglecting Ag⁺ hydrolisis, is smaller than the one where Ag⁺ lowers the pH by forming the insoluble hydroxide). What might be wrong, and how can this problem be treated?

You mean Ag₃PO₄ (s) + 3H₂O (l) 3AgOH (s) + H₃PO₄ (aq)? I want to be careful to avoid ambiguity.

If the constant is that high for this equilibrium, it is implied that most PO₄^3- ends up as H₃PO₄ and most Ag⁺ as AgOH. So how does the answer give a decently high PO₄^3-? Of course it is implied that K_sp(AgOH) is reached anyway, otherwise your equilibrium constant does not hold since this equilibrium: Ag₃PO₄ (s) + 3H₂O (l) 3AgOH (s) + H₃PO₄ (aq) does not exist unless AgOH saturation has been reached.

Where did you get the problem?

[Guvanch]

Is it from icho?

[kaya67]

Look up Woodward's Nobel lecture from 1966 I think it was published in Science.