To find the Ka for the acid, we can use the Henderson-Hasselbalch equation and the given pH value. Using the Henderson-Hasselbalch equation again, we can calculate the concentration of [A-] required to achieve a specific pH. By substituting the known values and solving the equations, we can determine the Ka for the acid and the concentration of [A-] needed for a pH of 4.6.
To find the Ka for the acid, we can start by using the pH value and the Henderson-Hasselbalch equation:
pH = pKa + log([A-]/[HA])
In this equation, pKa represents the negative logarithm of the acid dissociation constant (Ka). [A-] and [HA] represent the concentrations of the conjugate base and the acid, respectively.
Given that the pH is 2.4, we can rearrange the equation to solve for pKa:
pKa = pH - log([A-]/[HA])
Substituting the values, we have:
pKa = 2.4 - log([A-]/[HA])
Next, we need to calculate the concentration of [A-] required to achieve a pH of 4.6. We can rearrange the Henderson-Hasselbalch equation once again to solve for [A-]:
pH = pKa + log([A-]/[HA])
Substituting the values, we have:
4.6 = pKa + log([A-]/[HA])
To isolate [A-], we can rearrange the equation:
log([A-]/[HA]) = 4.6 - pKa
Next, we can calculate the antilog of both sides of the equation to solve for [A-]:
[A-]/[HA] = 10^(4.6 - pKa)
Finally, we can calculate the concentration of [A-] using the given values and the calculated pKa:
[A-] = [HA] * 10^(4.6 - pKa)