Hi Aishawarya,
The Henderson Hasselbalch Equation is usually written
1) pH = pKa + log[A]/[HA].
Using the log rule logA/B = -logB/A, they have rewritten this as follows in the question:
2) pH = pKa - log[HA]/[A]
However, because it gives you all the known factors, you could use either 1) or 2) to solve this question.
Identifying the information given by the question:
pKa = 3.13
[HA] = [citric acid] = 5*10^-3 M
[A] = [citrate] = 5*10^-1 M
Plugging these values into the equation 1):
pH = 3.13 + log(5*10^-1M)/(5*10^-3M)
pH = 3.13 + log(10^2)
pH = 3.13 + 2
pH = 5.13, giving D as the correct answer.
What I like to do next is check to make sure I got the HA/A or A/HA part right.
In the question stated, the concentration of A is higher than the concentration of HA. This indicates that we should have a more basic solution, and as a result, our answer makes sense.
Please let me know if this clears things up.
Thanks!
Katt