Question

Describe the preparation of 1L of a 0.1 M phosphate buffer at pH 8.0. The pKa for the buffer is 6.86

Answer 1

Solution:

The values given in the question are as follows.

Buffer pH = 8.0; pKa = 6.86; Required concentration = 0.1M; and Required volume = 1 L.

We know that the pKa's of phosphoric acid are 2.3, 7.21 and 12.35. Required pH is 8 and pKa is 6.86. This means, monosodium dihydrogen phosphate monohydrate [diprotic (H2PO4^-)] and disodium monohydrogen phosphate heptahydrate [monoprotic (HPO4^2-)] shall be used. Further, consider monosodium dihydrogen phosphate monohydrate as acid (HA) and disodium monohydrogen phosphate heptahydrate as conjugate base (A^-).

Step 1: Calculating [A^-] / [HA] ratio.

The [A^-] / [HA] ratio can be calculated using Handerson Hasselbach equation 1

pH = pKa + log([A^-] / [HA]) --------> 1

Substitute the values pf pH & pKa in equation 1.

8.0 = 6.86 + log([A^-] / [HA])

log([A^-] / [HA]) = 8.0 - 6.86 = 1.14

[A^-] / [HA] = antilog1.14

[A^- ] / [HA] = 13.804 ---------> 2

Step 2: Calculating required quantity of [A^-] & [HA].

Now we know the fold difference between these salts from equation 2. Required molarity of the solution is 0.1M,  and we can calculate the required amount.

[HA] + [A^-] = 0.1M    ---------> 3   

From equation 2,  [A^-] = 13.804 [HA]    ---------> 4

Substitute equation 4 in equation 3.

[HA] + 13.804 [HA] = 0.1M

(14.804) [HA] = 0.1M

[HA] = 0.00675M

Substitute [HA] value in equation 3.

0.00675M + [A^-] = 0.1M

[A^-] = 0.1M - 0.00675M = 0.09325M

Hence we need to dissolve 0.00675 mol of [HA] and 0.09325 mol of [A^-] in 1 L water. Molar mass of [HA] is 137.99 g / mol and  [A^-] is 268.07 g / mol.

Quantity required;

[HA] = (0.00675 mol / 1 L) x 137.99 g / mol = 0.9314 g / L

[A^-] = (0.09325 mol / 1L) x 268.07 g / mol = 24.997 g / L

Hence 0.9314g monosodium dihydrogen phosphate monohydrate and 24.997g disodium monohydrogen phosphate heptahydrate is required to prepare 1L of 0.1M phosphate buffer at pH 8.0

Step 3: Buffer preparation procedure.

1. Add about 800 mL of distilled water in a suitable container.

2. Add 0.9314g of NaH₂PO₄H₂O to the container.

3. Add 24.997g of Na₂HPO₄-7H₂O to the solution.

4. Check the pH using a pH meter and adjust the pH as necessary using phosphoric acid or sodium hydroxide solution.

4. Once you have reached the desired pH, add distilled water to bring the total volume of phosphoric acid buffer to 1 L.