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)
(1a) 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. (1b) 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 1.00 L solution with a pH of 7.00 at 298 K, follow these steps:
1a) Simple instructions for preparing the solution:
Step 1: Determine the desired acid-base ratio for the buffer system. In this case, you need to prepare a solution with a pH of 7.00, which is close to neutral. Therefore, the acid and base concentrations should be roughly equal.
Step 2: Calculate the volume of the 0.113 M C9H7NHBr(aq) solution required. Since we have an unlimited supply of water, we can dilute this solution to obtain the desired concentration. Use the equation:
C1V1 = C2V2
Where:
C1 is the initial concentration of the solution (0.113 mol L-1)
V1 is the initial volume of the solution (to be calculated)
C2 is the desired concentration of the solution (0.500 mol L-1)
V2 is the final volume of the solution (1.00 L)
Rearrange the equation to solve for V1:
V1 = (C2V2) / C1
Substituting the given values:
V1 = (0.500 mol L-1 * 1.00 L) / 0.113 mol L-1
= 4.425 L
So, measure 4.425 L of the 0.113 M C9H7NHBr(aq) solution.
Step 3: Calculate the volume of the 0.104 M HBr(aq) solution required. We need an equal amount of acid to form the buffer system. Repeat the same calculation as in Step 2, using the given concentrations and final volume:
V1 (HBr) = (0.500 mol L-1 * 1.00 L) / 0.104 mol L-1
= 4.808 L
So, measure 4.808 L of the 0.104 M HBr(aq) solution.
Step 4: Combine the calculated volumes (rounded to the appropriate number of significant figures), i.e.,
- 4.43 L of 0.113 M C9H7NHBr(aq)
- 4.81 L of 0.104 M HBr(aq)
- Fill the remaining volume with water up to 1.00 L
1b) To calculate the buffer capacity of the resulting solution, you need to determine the number of moles of NaOH required to raise the pH by one unit.
The buffer capacity can be calculated using the equation:
Buffer Capacity = ΔnHCl / ΔpH
Where:
ΔnHCl = the change in the amount of HCl (moles)
ΔpH = the change in pH
In this case, we will consider the addition of NaOH that will react with HB+ to form water and B.
Since adding NaOH will cause an increase in OH- concentration, we need to neutralize this OH- by HB+ from the solution. Thus, ΔnHCl will be equal to moles of NaOH added, and ΔpH will be 1 (unit increase in pH).
Therefore, the buffer capacity is equal to the number of moles of NaOH added to 1.0 L of the solution.
Hope this helps!