What is the concentration of ammonium chloride in a buffer solution of pH=9 with .1M ammonia?

Question

The answer is .18, but I have no idea how I got it. Can someone help?

Answer 1

Sure! Well this problem can be solved using the Henderson-Hasselbalch equation:

pH = pKa + log ([proton acceptor]/[proton donor])

The pKa for ammonia is 9.25.
Ammonium is the proton donor, and ammonia the proton acceptor.
We must rearrange the equation to obtain [NH4+]:

pH - pKa = log ([NH3]/[NH4+])

10^(pH - pKa) = [NH3]/[NH4+]

[NH4+] = [NH3]/10^(pH - pKa)

then

[NH4+] = 0.1 M/10^(9 - 9.25) = 0.18 M

ready!

Answer 2

This is sort of a "backwards" problem, in that you know one component and the pH, but not the other. The NH3 - NH4+ base reaction equation
[NH4+][OH-]/[NH3] = Kb, where Kb=
1.8x10-5
In a buffer solution, the concs of the two components >> [OH-]. If SMALL concs. of OH- are introduced, the NH4+ reacts with it to form molecular NH3, rather than having the OH- added set the pH of the solution. The situation is similar if SMALL conc. of H+ are added. If pH=9, pOH=5 and
[OH-]=10-5. So we have
[ [NH4+] 10-5 ]/0.1 = 1.8x10-5, which gives the answer above.