What is the volume of a solution of 0.5 M NaOH that must be added to adjust the pH
from 4 to 9 in 20 mL of a 100 mM solution of phosphoric acid?
Its been about 4 years since I've done this stuff. All I know is the pKa of phosphoric acid is 2.15 and I'm assuming In need to use the Henderson-Hassleback equation.
To determine the volume of the 0.5 M NaOH solution needed to adjust the pH of the phosphoric acid solution from 4 to 9, you can use the Henderson-Hasselbalch equation:
pH = pKa + log([A-]/[HA])
Here, [A-] and [HA] represent the concentrations of the deprotonated (base) and protonated (acid) forms of phosphoric acid, respectively. Since phosphoric acid is a triprotic acid, it can lose three protons to form three different anions: H2PO4-, HPO42-, and PO43-. Each of these anions has its own equilibrium constant (pKa1, pKa2, and pKa3), but in general, the logarithm of the concentration ratio simplifies to:
pH = pKa + log([A-]/[HA])
In this scenario, the initial pH is 4, and we want to adjust it to 9. We can calculate the initial concentration of [A-] using the pH:
[A-] = 10^(pH - pKa) * [HA]
Given that the pKa of phosphoric acid is 2.15, we have:
[A-] = 10^(9 - 2.15) * [HA]
[A-] = 10^6.85 * [HA]
Since the solution contains 20 mL of the 100 mM (0.1 M) phosphoric acid solution, we can calculate the initial concentration of [HA]:
[HA] = 0.1 M
Now, we can calculate the initial concentration of [A-]:
[A-] = (10^6.85) * (0.1 M)
[A-] = 1.95 M
The final concentration of [A-] will be the same as the initial concentration, and the final concentration of [HA] after adding NaOH will be zero (since NaOH is a strong base that will deprotonate all available [HA]).
To determine the volume of the 0.5 M NaOH solution needed to adjust the pH, we can use the equation:
[A-]final * Vfinal = [A-]initial * Vinitial
Substituting the values we have:
(1.95 M) * Vfinal = (1.95 M) * (20 mL)
Vfinal = (1.95 M * 20 mL) / (1.95 M)
Vfinal = 20 mL
Therefore, you would need to add 20 mL of the 0.5 M NaOH solution to adjust the pH of the phosphoric acid solution from 4 to 9.