A 100.0 mL aliquot of 0.100 M weak base B (pKb=5.00) was titrated with 1.00 M HClO4. Find the pH at the following volumes of acid added Va= 0, 1, 5, 9, 9.9, 10, 10.1, and 12mL
To find the pH at various volumes of acid added, we can use the concept of acid-base titration and the Henderson-Hasselbalch equation.
1. Write the balanced chemical equation for the reaction between the weak base B and the strong acid HClO4:
B + HClO4 -> BH+ + ClO4-
2. Determine the initial moles of the weak base B in the 100.0 mL aliquot:
mol B = Molarity x Volume (L)
= 0.100 M x 0.100 L
= 0.0100 mol
3. Calculate the number of moles of HClO4 added at each volume:
mol HClO4 = Molarity x Volume (L)
4. Determine the moles of weak base B reacted at each volume:
mol B reacted = mol HClO4 added
5. Calculate the remaining moles of weak base B at each volume:
mol B remaining = Initial moles of B - moles of B reacted
6. Convert the remaining moles of B to concentration:
[B] = mol B remaining / Total volume (L)
7. Use the Henderson-Hasselbalch equation to calculate the pH:
pH = pKa + log ([B]/[BH+])
Now, let's go through each volume and calculate the pH.
1. Va = 0 mL (Before any acid is added):
- mol B reacted = 0 mol
- mol B remaining = 0.0100 mol
- [B] = 0.0100 mol / 0.100 L = 0.100 M
- pH = 5.00 + log (0.100/0.000) = 5.00 (since [BH+] = 0)
2. Va = 1 mL:
- mol HClO4 = 1.00 M x 0.001 L = 0.001 mol
- mol B reacted = 0.001 mol
- mol B remaining = 0.0100 mol - 0.001 mol = 0.0090 mol
- [B] = 0.0090 mol / 0.100 L = 0.090 M
- pH = 5.00 + log (0.090/0.001) = 6.95
3. Va = 5 mL (Note: This is just an illustrative step. You can calculate the pH at other volumes using the same approach):
- mol HClO4 = 1.00 M x 0.005 L = 0.005 mol
- mol B reacted = 0.005 mol
- mol B remaining = 0.0100 mol - 0.005 mol = 0.0050 mol
- [B] = 0.0050 mol / 0.100 L = 0.050 M
- pH = 5.00 + log (0.050/0.005) = 7.00
Repeat steps 2-7 for the remaining volumes of acid added (9 mL, 9.9 mL, 10 mL, 10.1 mL, and 12 mL) to obtain the respective pH values.
Note: The Henderson-Hasselbalch equation assumes that the volume of the weak base is much larger than the volume of the acid added. Make sure that this condition holds true, or you may need to employ more accurate methods such as the quadratic equation or a pH calculator.