pH = pKa + log([A-]/[HA])
where:
pH is the pH of the solution
pKa is the acid dissociation constant of the conjugate acid (trimethylammonium ion)
[A-] is the concentration of the base (trimethylamine)
[HA] is the concentration of the conjugate acid (trimethylammonium chloride)
Given that the concentration of trimethylamine ([A-]) is 0.04 M and the concentration of trimethylammonium chloride ([HA]) is 0.2 M, we can substitute these values into the Henderson-Hasselbalch equation:
pH = pKa + log([A-]/[HA])
pH = 9.8 + log(0.04/0.2)
pH = 9.8 - 0.7
pH = 9.1
Therefore, the approximate pH of the solution is 9.1, which is closest to option 1 (9.2).
