3. a) Calculate the pH of the buffer solution prepared by mixing 40.0 mL of 0.100 M H3PO4 and 60.0 mL of 0.100 M KH2PO4. Given the pKa of H3PO4 is 2.12.
Use the Henderson-Hasselbalch equation.
2.296
To calculate the pH of a buffer solution, we need to consider the Henderson-Hasselbalch equation, which is given by:
pH = pKa + log([base]/[acid])
In this case, the acid is H3PO4 and the base is KH2PO4. The pKa given for H3PO4 is 2.12.
Step 1: Calculate the concentration of the acid and base in the buffer solution.
To find the concentration of acid in the buffer solution, we can use the equation:
C1V1 = C2V2
where C1 is the initial concentration of the acid, V1 is the volume of the acid, C2 is the final concentration of the acid in the buffer solution, and V2 is the final volume of the buffer solution.
C1 = 0.100 M (concentration of H3PO4)
V1 = 40.0 mL (volume of H3PO4)
C2 = ?
V2 = 40.0 mL + 60.0 mL = 100.0 mL = 0.100 L (total volume of the buffer solution)
Using the formula, we can calculate the concentration of the acid in the buffer solution:
C2 = (C1 * V1) / V2
= (0.100 M * 40.0 mL) / 0.100 L
= 0.040 M
Similarly, we can find the concentration of the base in the buffer solution:
C1 = 0.100 M (concentration of KH2PO4)
V1 = 60.0 mL (volume of KH2PO4)
C2 = ?
V2 = 0.100 L (total volume of the buffer solution)
C2 = (C1 * V1) / V2
= (0.100 M * 60.0 mL) / 0.100 L
= 0.060 M
Step 2: Substitute the concentration values into the Henderson-Hasselbalch equation and calculate the pH.
pH = pKa + log([base]/[acid])
= 2.12 + log(0.060 M / 0.040 M)
Calculating the ratio of base to acid:
0.060 M / 0.040 M = 1.5
Taking the logarithm of the ratio:
log(1.5) ≈ 0.176
Substituting this value into the equation:
pH = 2.12 + 0.176
≈ 2.296
Therefore, the pH of the buffer solution is approximately 2.296.