What molar ratio of HPO4 2- to H2PO4 - in solution would produce a pH of 7.0? Phosphoric acid (H3PO4), a triprotonic acid, has pKa values: 2.14, 6.86, and 12.4. Only one of the pKa values is relevant here. how do i know which pka value to use.. please explain
To determine the relevant pKa value for calculating the molar ratio of HPO4 2- to H2PO4 - in solution, we need to consider the pH at which the solution is requested to be 7.0.
Since the first pKa value (2.14) is significantly lower than 7.0, it is safe to assume that the first proton is almost completely dissociated at pH 7.0. This means that H3PO4 is mainly in the form of H2PO4 -.
Therefore, the relevant pKa value for this calculation is the second pKa value (6.86).
To further explain, the three pKa values represent the acid dissociation constants for the three successive ionizations of H3PO4:
H3PO4 ⇌ H+ + H2PO4 - (pKa1 = 2.14)
H2PO4 - ⇌ H+ + HPO4 2- (pKa2 = 6.86)
HPO4 2- ⇌ H+ + PO4 3- (pKa3 = 12.4)
At pH 7.0, we assume that the first proton is fully dissociated, leaving only H2PO4 - and HPO4 2- in significant amounts. Therefore, we only consider the equilibrium between H2PO4 - and HPO4 2-.
Now, we can use the Henderson-Hasselbalch equation:
pH = pKa + log([A-]/[HA])
where [A-] represents the concentration of the conjugate base (HPO4 2-) and [HA] represents the concentration of the acid (H2PO4 -).
Rearranging the equation to solve for the concentration ratio [A-]/[HA]:
[A-]/[HA] = 10^(pH - pKa)
Substituting the given values (pH = 7.0 and pKa = 6.86):
[A-]/[HA] = 10^(7.0 - 6.86) = 1.99
Therefore, the molar ratio of HPO4 2- to H2PO4 - in solution that would produce a pH of 7.0 is approximately 1.99:1.
To determine which pKa value to use for calculating the molar ratio of HPO4 2- to H2PO4 - in solution, we need to consider the pH value at which our solution is targeted.
In this case, we want a pH of 7.0, which is between the pKa values of 6.86 and 12.4. Since the pH is closer to 6.86, we will consider the dissociation of H3PO4 at pKa = 6.86.
The dissociation reaction of H3PO4 in water can be represented as follows:
H3PO4 ⇌ H+ + H2PO4 -
At the pKa value of 6.86, we can assume that half of the H3PO4 has dissociated into H+ ions and H2PO4 - ions. Therefore, the molar ratio of HPO4 2- to H2PO4 - is 1:1.
It's important to note that pKa values represent the acidity of a compound and the pKa closest to the desired pH is generally the most relevant to consider. In this case, pKa = 6.86 is the closest to the pH of 7.0, so we use this value to determine the molar ratio.