This is a question regarding buffer solutions of polyprotic acids. The reaction for this buffer is as follows:
H₂PO₄⁻ + H₂O → HPO₄²⁻ + H₃O⁺
We can use the henderson-hasselbach equation for this:
pH = pKa + log[A⁻]/[HA]
pH = 7.21 + log[HPO₄²⁻/H₂PO₄⁻]
The pKa for this equation is 7.21. We are also told that the ratio of acid to conjugate base is 1:1 as there are 0.5 moles of both monobasic phosphate and dibasic phosphate. Therefore, before the addition of any acid, the pH of the solution will be equal to the pKa, so pH = 7.21. Now we are asked to determine how much HCl can be added to change the pH drastically. A drastic change in pH would be a change in 1 pH unit. So we can determine the ratio of acid:conjugate base by changing the pH by 1.
6.21 = 7.21 + log[HPO₄²⁻/H₂PO₄⁻]
-1 = log[HPO₄²⁻/H₂PO₄⁻]
0.1 = [HPO₄²⁻/H₂PO₄⁻]
To determine how much acid can be added to cause this change, we can find the change in each amount of acid and conjugate base that would give this ratio.
0.1 = (0.5 - x)/(0.5 + x)
0.05 + 0.1x = 0.5 - x
1.1x = 0.45
x = 0.41 moles
The addition of 0.41 moles of HCl to this buffer solution will result in a change of pH of 1 unit which would qualify as a drastic change.
