Find the Combination to the Safe with Only the Given Info

[JRAMiller]

Ok I saw this question in another thread and it wasn't answered but said it had previously been answered I've been searching for a while now and can't find it

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 25EC.

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.

 

[chemisttree]

To find the pH of a solution of a weak acid you must know the pKa (or the Ka) which isn't given directly in this problem. You do know that a solution of NaX gives a pH of 10.02. From this you can calculate the Ka. Familiarize yourself with problems of that type before you try to tackle this one.