Captain Kirk of the Starship Enterprise has been told by his superiors that only

Question

Captain Kirk of the Starship Enterprise has been told by his superiors that only a chemist can be trusted with the combination of a 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, also described below. (Example: If the ph of solution A were 3.47 and the pH of solution C were 8.15, the combination would be 3-47-8-15.) Determine the combination of the safe from the information below: Solution A: is a 0.150 M solution of a weak monoprotic acid HX. Solution B: is a 0.0500 M solution of NaX, the sodium salt of this acid. It has a pH of 10.55. Solution C: is made by adding 12.0 mL of 0.2500 M KOH to 50.0 mL of Solution A. What is the combination to the safe?

Explanation / Answer

Solution B,

pH = 10.55

pOH = 14 - pH = 3.45

pOH = -log[OH-]

[OH-] = 3.55 x 10^-4 M

X- + H2O <==> HX + OH-

Kb = [HX][OH-]/[X-]

[OH-] = [HX]

Kb = (3.55 x 10^-4)^2/(0.05 - 3.55 x 10^-4) = 2.54 x 10^-6

Ka = 1 x 10^-14/2.54 x 10^-6 = 3.94 x 10^-9

pKb = -log[Kb] = 5.59

pKa = 14 - pKb = 8.41

solution A : pH

HX + H2O <==> H3O+ + X-

Ka = [H3O+][X-]/[HA]

3.94 x 10^-9 = x^2/0.150

x = [H3O+] = 2.43 x 10^-5 M

pH = -log[H3O+] = 4.61

Solution C : pH

pH = pKa + log(X-/HX)

moles KOH added = 0.25 m x 12 ml = 3 mmol

pH = 8.41 + log[3 mmol/(0.15 M x 50 ml - 3 mmol)]

     = 8.23

so combination to the safe is : 4-61-8-23

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