1. Suppose that you have 0.500 L of each of the following solutions, and an unlimited supply of water.

(Note: C9H7NHBr is a salt containing the ions C9H7NH+ and Br− and C9H7N is quinoline, an organic
base with pKb = 6.24 at 298 K. If you like, you may represent C9H7NH+ as HB+ and C9H7N as B.)
Data
0.113 mol L−1 C9H7NHBr (aq)
0.104 mol L−1 HBr(aq)
0.122 mol L−1 NaOH(aq)
(a) Provide simple instructions for preparing 1.00 L of a solution having pH = 7.00 at 298 K.
Your instructions should include the volumes of the solutions required.
(b) What is the buffer capacity of the resulting solution? (The buffer capacity is the
number of moles of NaOH that must be added to 1.0 L of solution to raise the pH by one unit.)

To prepare a solution with a pH of 7.00 at 298K using the given solutions, follow these steps:

(a) Instructions for preparing 1.00 L of pH = 7.00 solution:
1. Start by determining the quantities of the solutions needed based on their concentrations and their contribution to the final pH.
2. The pH of 7.00 indicates a neutral solution, so we need to prepare a solution that can neutralize both acidic and basic components.
3. Since the HBr solution is acidic, we will use it to neutralize the basic component.
4. Calculate the moles of HB+ ions from the C9H7NHBr solution required to react with the moles of OH- ions from the NaOH solution to achieve a neutral pH.
- The balanced equation for this neutralization reaction is: HB+(aq) + OH-(aq) → B(aq) + H2O(l)
- From the equation, we can see that the moles of HB+ and OH- should be equal for a neutral pH.
5. Use the molarities and volumes to calculate the required volume from each solution using the following formula:
- Volume (L) = (moles required) / (molarity)
6. In this case, since the C9H7NHBr solution has a concentration of 0.113 mol L-1 and the NaOH solution has a concentration of 0.122 mol L-1, calculate the moles needed for the reaction:
- Moles of HB+ = Moles of OH- = (0.122 mol L-1) * (1.00 L) = 0.122 moles
7. Determine the volumes required from each solution:
- Volume of C9H7NHBr solution = (0.122 moles) / (0.113 mol L-1) = 1.081 L
- Volume of NaOH solution = (0.122 moles) / (0.122 mol L-1) = 1.000 L
8. Finally, to make a total volume of 1.00 L, add water to the solutions. Mix the appropriate volumes of the C9H7NHBr solution and the NaOH solution, and then add water until the final volume reaches 1.00 L.

(b) Calculating the buffer capacity:
1. The buffer capacity is a measure of the ability of the buffer solution to resist changes in pH.
2. It is defined as the number of moles of NaOH that must be added to 1.0 L of solution to raise the pH by one unit.
3. In this case, since we prepared a pH = 7.00 buffer solution, we can calculate the buffer capacity by determining the number of moles of NaOH required to raise the pH to 8.00.
4. The pH scale is logarithmic, so a change of one unit in pH represents a ten-fold difference in acidity/basicity.
5. Calculate the moles of NaOH required to raise the pH by one unit:
- Moles of NaOH = (moles NaOH) / (ΔpH)
- In this case, ΔpH = 8.00 - 7.00 = 1.00
- Moles of NaOH = 0.122 moles / 1.00 = 0.122 moles
6. Therefore, the buffer capacity of the resulting solution is 0.122 moles of NaOH that must be added to 1.0 L of solution to raise the pH by one unit.