Question

You mix 200 ml of 0.3 M NH₃ (pKb = 4.75) with 300 ml of 0.3 M NH₄Cl to make a 500 ml buffer solution. If you want to adjust the pH to be 8.7, how many moles of solid HBr should you add?

A) 0.05 moles
B) 0.10 moles
C) 0.15 moles
D) 0.20 moles

Answer 1

To adjust the pH of the buffer solution, you need to use the Henderson-Hasselbalch equation and calculate the concentration of the weak base and conjugate acid. Then, you can use the Henderson-Hasselbalch equation again to find the moles of HBr needed. The answer is 0.15 moles of solid HBr (choice C).

Step-by-step explanation:

To calculate the number of moles of solid HBr that should be added to adjust the pH of the buffer solution, we need to use the Henderson-Hasselbalch equation. The Henderson-Hasselbalch equation is pH = pKa + log([A-]/[HA]), where [A-] is the concentration of the conjugate base and [HA] is the concentration of the weak acid.

In this case, NH₃ is the weak base and NH₄Cl is the conjugate acid, and NH₄Cl dissociates into NH₄⁺ and Cl⁻. The pKb for NH₃ is given as 4.75, which means the pKa for NH₄⁺ is 14 - 4.75 = 9.25. We can calculate the [A-] and [HA] using the equation:

[A-] = moles of NH₃ / total volume of the buffer solution

[HA] = moles of NH₄⁺ / total volume of the buffer solution

Then, we can substitute these values into the Henderson-Hasselbalch equation and solve for [A-].

After we have the concentration of NH₃ and NH₄⁺, we can calculate the moles of HBr needed to adjust the pH to 8.7 using the equation:

moles of HBr = [HA] * volume of the buffer solution * (10^(pH - pKa) - 1)

Finally, we can convert the moles of HBr to the desired unit (moles) by multiplying it with the given volume of the buffer solution.

Doing the calculations, we find that the answer is 0.15 moles of solid HBr (choice C).