As a technician in a large pharmaceutical research firm, you need to produce 100.mL of 1.00 M a phosphate buffer solution of pH = 7.45. The pKa of H2PO4− is 7.21. You have 2.00 L of 1.00 M KH2PO4 solution and 1.50 L of 1.00 M K2HPO4 solution, as well as a carboy of pure distilled H2O. How much 1.00 M KH2PO4 will you need to make this solution?

Question

As a technician in a large pharmaceutical research firm, you need to produce 100.mL of 1.00 M a phosphate buffer solution of pH = 7.45. The pKa of H2PO4− is 7.21. You have 2.00 L of 1.00 M KH2PO4 solution and 1.50 L of 1.00 M K2HPO4 solution, as well as a carboy of pure distilled H2O. How much 1.00 M KH2PO4 will you need to make this solution?

Answer 1

Use the Henderson-Hasselbalch equation and the total buffer (both equations) and solve simultaneously.

7.45 = 7.21 + log (base/acid)
I get base/acid = estimated 1.8 but you need to do it more accurately.
And base + acid = 1M
Solve simultaneously. I obtained approximately 0.36M for acid and 0.64M for base. Again, you need to refine those numbers.
You want 100 mL (0.100L x 0.36M = 0.036 mols acid). Similarly you need 0.064 mols base.
Since M = mols/L and rearrange to
L = mols/M = 0.036/1 = 0.036 L or 36 mL of the acid and similarly 64 mL of the base.

Answer 2

To calculate the amount of 1.00 M KH2PO4 solution needed to make a 100 mL 1.00 M phosphate buffer solution of pH = 7.45, we can follow these steps:

Step 1: Determine the desired concentrations of [KH2PO4] and [K2HPO4]
Since the desired phosphate buffer solution has a pH = 7.45, we need to calculate the ratio of [KH2PO4] to [K2HPO4] using the Henderson-Hasselbalch equation:

pH = pKa + log([A-]/[HA])

Given:
pH = 7.45
pKa = 7.21

We can rearrange the equation as follows:

[KAH2PO4] / [K2HPO4] = 10^(pH - pKa) = 10^(7.45 - 7.21) = 1.5949

This means that the ratio of [KH2PO4] to [K2HPO4] in the buffer solution should be 1.5949.

Step 2: Calculate the moles of KH2PO4 required
Since we know the final volume and concentration of KH2PO4, we can calculate the number of moles using the equation:

moles = concentration × volume

moles of KH2PO4 = 1.00 M × 100 mL = 0.100 mol

Step 3: Calculate the moles of K2HPO4 required
Using the ratio determined in Step 1, we can calculate the moles of K2HPO4 needed:

moles of K2HPO4 = (0.100 mol) / 1.5949 = 0.0628 mol

Step 4: Determine the volumes of KH2PO4 and K2HPO4 solution required
To determine the volumes of the KH2PO4 and K2HPO4 solutions needed, we can use the molarity equation:

Molarity = moles / volume

For KH2PO4:
1.00 M = 0.100 mol / volume
volume of KH2PO4 = (0.100 mol) / (1.00 M) = 0.100 L = 100 mL

For K2HPO4:
1.00 M = 0.0628 mol / volume
volume of K2HPO4 = (0.0628 mol) / (1.00 M) = 0.0628 L = 62.8 mL

Thus, you will need 100 mL of 1.00 M KH2PO4 solution to make the desired phosphate buffer solution.