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What is the combination of the safe?

  1. Mar 21, 2005 #1
    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.
  2. jcsd
  3. Mar 21, 2005 #2
    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 Ka before you can find its pH. How can you do this using information about solution B? Keep the hint in mind.
  4. Mar 22, 2005 #3
    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?
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