16.2 Captain Kirk, of the Starship Enterprise, has been told by his superiors th

Question

16.2 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 is the pH of solution A described below, followed by the pH of solution C. (For example: If the pH of solution A s 3.47 and that of solution C is 8.15, the combination is 3-47-8-15.) The chemist must determine the combination using only the information below. (All solutions are at 25 °C.) Solution A is 50.0 mL of a 0.100 M solution of a monoprotic acid HX. Solution B is a 0.0500 M solution of the salt NaX. It has the a pH of 10.02. Solution C is made by adding 15.0 mL of 0.250 M KOH to solution A. What is the combination of the safe?

Explanation / Answer

Solution B,

pH = 10.02

pOH = 14 - 10.02 = 3.98

pOH = -log[OH-]

[OH-] = 1.05 x 10^-4 M

Kb = (1.05 x 10^-4)^2/(0.05 - 1.05 x 10^-4) = 2.20 x 10^-7

Ka = 1 x 10^-14/2.20 x 10^-7 = 4.54 x 10^-8

Solution A,

4.54 x 10^-8 = x^2/0.1

x = [H+] = 6.74 x 10^-5 M

pH = -log[H+] = 4.17

Solution C,

X- formed = 0.250 M x 15 ml = 3.75 mmol

HX remained = 0.1 M x 50 ml - 3.75 = 1.25 mmol

pKa = -log[Ka] = 7.34

pH = -pKa + log(base/acid)

     = 7.34 + log(3.75/1.25)

     = 7.82

So,

combination of safe is,

4-17-10-02-7-82

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