The dibasic compound B (pKb1 = 4.00, pKb2 = 8.00) was titrated with 1.00 M HCl. The initial solution of B was 0.100 M and had a volume of 100.0 mL. Find the pH at the following volumes of acid added and make a graph of pH versus Va; Va=0, 1, 5, 9, 10, 11, 15, 19, 20, and 22mL.

Answer 1

To calculate the pH at each volume of acid added (Va), we will use the Henderson-Hasselbalch equation:

pH = pKa + log ([base] / [acid])

For a given volume of acid added, we will first determine the moles and concentrations of each species present, and then use the equation above to determine the pH. Since we are adding HCl, we will use the pKa values, which are the negative logarithms of the base dissociation constants, Kb:

pKa = -log(Kb)

Since we have two pKb values (pKb1=4.00 and pKb2=8.00), we will also have two pKa values:

pKa1 = -log(10^(-4.00)) = 4.00
pKa2 = -log(10^(-8.00)) = 8.00

Here are the steps for each volume of acid added:

Va = 0 mL ("before titration"):
- No acid has been added yet, so only the dibasic compound B is present.
- The concentration of B is given as 0.100 M.
- Because B is a dibasic compound, it will be associated with two conjunct species: HB+ and H2B^2+.
- We will consider that B will react only once at this point (to form HB+), so we calculate the concentrations using the pKa1 value:

pH = 4.00 + log ([B] / [HB+])

0.100 M B and 0 mL of 1.00 M HCl are mixed, which means that no reaction occurs.
Therefore, the pH at Va=0 mL is:

pH = 4.00 + log (0.100 / 0) ≈ 4.00

Va = 1 mL:
- 1.00 mL of 1.00 M HCl is added, which means 0.001 moles of HCl are added.
- B will react with HCl to form HB+:

B + HCl → HB+ + Cl-

- From the stoichiometric ratio, 0.001 moles of B will react with 0.001 moles of HCl to form 0.001 moles of HB+.
- The total volume will now be 101 mL, and so our new concentrations will be as follows:

[B] = (0.100 - 0.001) moles / 101 mL ≈ 0.0009802 M
[HB+] = 0.001 moles / 101 mL ≈ 0.000009902 M

Now we can calculate the pH using the pKa1 value:

pH = 4.00 + log (0.0009802 / 0.000009902) ≈ 5.63

_va = 5 mL:
- 5.00 mL of 1.00 M HCl is added, which means 0.005 moles of HCl are added.
As Va increases, it is necessary to follow a similar procedure to find the concentration of all species (B, HB+, and H2B^2+) at every volume of HCl added.

You can follow the same procedure to calculate the pH for the other given volumes of acid added (Va = 9, 10, 11, 15, 19, 20, and 22 mL). Then, we will have the pH values at each volume.

Finally, to create a graph, you can use any graphing software or even graph paper. Plot the pH values on the y-axis and the volume of acid added (Va) on the x-axis. Your graph will give you a visual representation of the pH changes during the titration of the dibasic compound B with 1.00 M HCl.