Solving for the Safe Combination: pH of Solutions A & C

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SUMMARY

The combination to the safe containing the dilithium crystals is determined by calculating the pH of solutions A and C. Solution A is a 0.100 M solution of the weak monoprotic acid HX, while solution C is formed by adding 15.0 mL of 0.225 M KOH to solution A. The pH of solution A is calculated to be approximately 2.87, and after the addition of KOH, the pH of solution C is found to be around 10.15. Therefore, the final combination is 2-87-10-15.

PREREQUISITES
  • Understanding of weak acid dissociation and pH calculations
  • Knowledge of titration concepts involving strong bases
  • Familiarity with monoprotic acids and their properties
  • Basic skills in performing molarity and volume calculations
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  • Study the Henderson-Hasselbalch equation for buffer solutions
  • Learn about titration curves for weak acids with strong bases
  • Explore the concept of pKa and its relation to pH
  • Investigate the properties of weak acids and their salts in solution
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Chemistry students, educators, and professionals involved in acid-base chemistry, particularly those focusing on pH calculations and titration methods.

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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.
 
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