Final answer:
To calculate the pH of the buffer solution, the Henderson-Hasselbalch equation is used along with the Ka value derived from the given Kb for NH₃. The pKa for NH₄+ is determined, and the concentrations of NH₃ and NH₄+ are plugged into the equation. The correct pH of the buffer solution is 9.43.
Step-by-step explanation:
To calculate the pH of a buffer solution containing 0.30M NH₃ and 0.20M NH₄+, we should use the Henderson-Hasselbalch equation, which relates pH, pKa, and the concentrations of a weak acid and its conjugate base:
pH = pKa + log([base] /[acid])
First, we need to find the pKa of NH₄+, which is the conjugate acid of NH₃. Given that the equilibrium constant Kb for NH₃ is 1.8×10−5, we can find the Ka for NH₄+ by using the ion product constant of water (Kw):
Ka = Kw / Kb, where Kw at 25°C is 1.0×10−14. Thus, Ka = 1.0×10−14 / 1.8×10−5 = 5.6×10−10. The pKa can then be found by taking the negative logarithm:
pKa = -log(Ka) = -log(5.6×10−10) = 9.25
Using the Henderson-Hasselbalch equation with the calculated pKa, the concentrations of NH₃ (base) and NH₄+ (acid), we get:
pH = 9.25 + log(0.30/0.20) = 9.25 + log(1.5)
To find log(1.5), we can use the given log value of 2.7 being 0.43:
log(1.5) = log(3/2) = log(3) - log(2)
Since log(2.7) is approximately 0.43 and log(3) is slightly greater than log(2.7), we can estimate log(3) to be slightly greater than 0.43. If log(2) is about 0.30, then log(1.5) will be close to 0.18. Therefore, pH = 9.25 + 0.18 = 9.43.
Therefore, the correct option is C. 9.43.