A buffer solution of pH=9.24 can be prepared by dissolving ammonia and ammonium chloride in water. How many moles of ammonium chloride must be added to 1.0 L of .50 M ammonia to prepare the buffer?
I would use the Henderson-Hasselbalch equation.
pH = pKa + log[(base)/(acid)]
To answer this question, we need to consider the Henderson-Hasselbalch equation, which relates the pH of a buffer solution to the ratio of the concentrations of the conjugate acid and base. In this case, ammonia (NH3) is the base and ammonium chloride (NH4Cl) is the conjugate acid.
The Henderson-Hasselbalch equation is:
pH = pKa + log([conjugate acid] / [base])
In this case, the base is ammonia (NH3) and the conjugate acid is ammonium chloride (NH4Cl). We are given the pH of the buffer solution, which is 9.24. The pKa of ammonium chloride is known to be 9.24. Therefore, we can substitute the given values into the Henderson-Hasselbalch equation:
9.24 = 9.24 + log([NH4Cl] / [NH3])
Simplifying the equation, we have:
0 = log([NH4Cl] / [NH3])
Since log(1) = 0, we know that [NH4Cl] / [NH3] must be equal to 1.
Now, let's calculate the number of moles of NH3 and NH4Cl in the solution:
Number of moles of NH3 = molarity × volume = 0.50 M × 1.0 L = 0.50 moles
Number of moles of NH4Cl = [NH4Cl] × volume = [NH3] × volume (since [NH4Cl] = [NH3]) = 0.50 moles
Since we need to add enough NH4Cl to form an equal concentration as NH3 in the buffer, we need to add an additional 0.50 moles of NH4Cl to the 1.0 L of 0.50 M NH3 solution to prepare the buffer.