Final answer:
The pH of a 0.24 M diethylamine solution can be calculated using the Henderson-Hasselbalch equation. The approximate pH value is 3.42. The correct option is (b).
Step-by-step explanation:
The pH of a solution can be calculated using the concentration of the weak base and the equilibrium constant (Kb) for the base. In this case, the diethylamine solution has a concentration of 0.24 M and a Kb value of 8.6 x 10-4. Using the Henderson-Hasselbalch equation, we can calculate the pH:
pH = pKa + log([A-]/[HA])
The pKa can be calculated using the equation: pKa = -log(Ka), where Ka is the equilibrium constant for the conjugate acid.
Since diethylamine is a weak base, its conjugate acid is very weak. Therefore, we can approximate the pKa to be equal to the pKb (since pKa + pKb = 14).
Now, let's substitute the values into the equation:
pH = 14 - log(Kb) - log([A-]/[HA])
We can assume that the diethylamine is completely ionized, so [A-] will be equal to the initial concentration of the diethylamine (0.24 M). [HA] will be zero since it is the concentration of the conjugate acid, which we assume to be negligible.
pH = 14 - log(8.6 x 10-4) - log(0.24/0)
pH = 14 - log(8.6 x 10-4)
pH ≈ 3.42