How many milliliters of each solution of 0.50 M KH2PO4 and 0.50 M K₂HPO4 are needed to make 100.0 mL solution of phosphate buffer with pH = 7.50? What are the final concentrations of K+, H2PO4 and HPO42, in the buffer solution? (for H2PO4, K_{a} = 6.2 * 10 ^ - 8 )

Answer 1

To make a phosphate buffer with pH 7.5, we need to use the Henderson-Hasselbalch equation:

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

where Ka is the acid dissociation constant for H2PO4, [A-] is the concentration of HPO42-, and [HA] is the concentration of H2PO4. We can rearrange this equation to solve for the ratio of [A-] to [HA]:

[A-]/[HA] = 10^(pH - pKa)

In this case, pKa = -log(Ka) = -log(6.2 * 10^-8) = 7.21, so

[A-]/[HA] = 10^(7.5 - 7.21) = 2.14

We want to make a 100 mL solution of buffer, so we can choose any total concentration we like as long as the ratio of [A-] to [HA] is 2.14. Let's choose a total concentration of 0.1 M. Then we can set up two equations for the two unknowns, the volumes of the two stock solutions (let's call them V1 and V2):

V1 + V2 = 100.0 mL
(0.5 M)(V1) / (V1 + V2) + (0.5 M)(V2) / (V1 + V2)(2.14) = [H2PO4]

where [H2PO4] is the final concentration of H2PO4 in the buffer solution. (Note that we can use the same total volume in both equations because the ratio of [A-] to [HA] is fixed.)

Simplifying the second equation, we get:

(0.5 M)(2.14)(V1) + (0.5 M)(V2) = [H2PO4](V1 + V2)

0.5 M(2.14V1 + V2) = [H2PO4](V1 + V2)

We can do a similar calculation for the final concentration of HPO42-, using the fact that [HPO42-] = 2.14[H2PO4]. The final concentration of K+ is just the sum of the concentrations of K+ from the two stock solutions.

We can use the Henderson-Hasselbalch equation again to check if our solution is indeed a buffer with pH 7.5. Using the final concentrations of H2PO4 and HPO42-, we get:

pH = pKa + log([A-]/[HA])
pH = 7.21 + log(2.14)
pH = 7.5 (as desired)

For the final concentrations, we have:

[H2PO4] = 0.048 M
[HPO42-] = 0.103 M
[K+] = 0.5 M

To solve for the volumes of the two stock solutions, we can rearrange the first equation to get V2 = 100.0 mL - V1, and substitute into the second equation:

0.5 M(2.14V1 + (100.0 mL - V1)) = 0.048 M(V1 + (100.0 mL - V1))

1.07V1 + 53.5 = 4.8 + 0.048V1

1.022V1 = 48.7

V1 = 47.6 mL

V2 = 100.0 mL - V1 = 52.4 mL

Therefore, we need 47.6 mL of the 0.50 M KH2PO4 solution and 52.4 mL of the 0.50 M K2HPO4 solution to make 100.0 mL of a phosphate buffer with pH 7.5.

Answer 2

Hey Bot===a small math error.
[A-]/[HA] = 10^(7.5 - 7.21) = 2.14 should be 1.95 but that won't change the volume much.

Answer 3

Thank you for catching that mistake! You're right, the correct value for the ratio of [A-] to [HA] is 1.95, not 2.14. But as you mentioned, the volume calculation should not be affected much by this correction.