In: Chemistry
While carring out a research project you find that you need a 0.15 M solution of sodium phosphate buffer, at pH of 8.4. Unfortunately your technician has left already and you must make the solution yourself. On the shelf you find bottles labeled: NaH2PO4.2H2O Wt. 156.01, and Na2HPO4 Wt. 141.96. What weights of A and B in grams would you dissolve to make 1 liter of the required buffer?( The pKs for phosphoric acid are 2.0, 7.2 and 12.0).
Use the Hendderson Hasselbach equation:
pH = pKa + log [S]/[A]
Now if you need to make the buffer, this means that you need to sum both solutions, let's call the Buffer as "B" so:
[B] = [NaH2PO4] + [Na2HPO4]
As you need to make a buffer of 8.4, you need to use the value of pKa closer to that one, in this case, the second one according to the following reaction of phosphoric acid:
H2PO4- -----------> HPO42- + H+ pKa2 = 7.4
So the HH equation would be: pH = pKa + log [HPO42-] / [H2PO4-]
8.4 = 7.2 + log [HPO42-] / [H2PO4-]
8.4 - 7.2 = log [HPO42-] / [H2PO4-]
101.2 = [HPO42-] / [H2PO4-]
[HPO42-] / [H2PO4-] = 15.85
[HPO42-] = 15.85[H2PO4-]
0.15 = [NaH2PO4] + [Na2HPO4]
0.15 = 15.85[H2PO4-] + [H2PO4-]
0.15 / 16.85 = [H2PO4-]
[H2PO4-] = 0.0089
[HPO42-] = 15.85 * 0.0089 = 0.1411 M
mass HPO42- = 0.1411 mol/L * 1 L * 141.96 g/mol = 20.0306 g
mass H2PO4- = 0.0089 * 1 * 156.01 = 1.3885 g
Hope this helps