What is the combination of the safe?

[chjopl]

Captain Kirk, of the Starship Enterprise, has been told by his superiors that only a chemist can be trusted with the combination to the safe containing the dilithium crystals that power the ship. The combination, which consists of four numbers, is the pH of solution A described below, followed by the pH of solution C. (Example: If the pH of solution A is 3.47 and that of solution C is 8.15, then the combination to the safe is 3-47-8-15.) The chemist must find the combination using only the information below. All solutions are at 25C.

Solution A is 50.0 mL of a 0.100 M solution of the weak monoprotic acid HX.

Solution B is a 0.0500 M solution of the salt NaX. It has a pH of 10.02.

Solution C is made by adding 15.0 mL of 0.225 M KOH to solution A.

What is the combination of the safe?

Hint: You don't need to know the identity of X, except that the X in solution A is the same as in solution B.

 

[Sirus]

You need to show us some work first. You will information about solution A before you can find any about solution C, so leave that last one out for now. Since A is a weak acid, you need to find its K_a before you can find its pH. How can you do this using information about solution B? Keep the hint in mind.

 

[chjopl]

For solution b I took -log x= 10.02 so i got x to be 9.55*10^-11. Then i took K_b=(9.55*10^-11)^2/(.5-9.55*10^-11) and got the K_b to be 1.82*10^-20. I think i messed up there because when i take K_w/K_b=K_a i get the K_a to be a very large number. Where did I go wrong?