Let's begin this problem by examining what kind of solution we have.
And it tells us right here at the beginning that we have a buffer, so
let's underline that word.
And when we have a buffer, we know that the Henderson–Hasselbalch
equation is a good way to calculate the pH of a buffer.
So let's write the Henderson–Hasselbalch equation,
pH = pka + log [B]/[A].
Now you can also use instead of concentrations,
you can put moles of base over moles of acid.
And this problem, one way is about as easy as the other.
We are trying to calculate the PH so we need to know the PKA.
Well the PKA is the negative log of the KA value but
I don't have the KA value, I have the KB of ammonia.
To get the KA we will take KW divided by
KB which is 1.76 times 10 to -5.
Okay, then plus the log of the concentration of the base
over the concentration of the acid.
NH3, nitrogen with three things attached, that's my base.