Hey there,
The way you did this question isn't the right way in my opinion. You might get a close answer, but through wrong math. Here's my thought process
1. Amines are weak bases. HCL is a strong acid. I am titrating a weak base by a strong acid.
2. I know I need to use something like the HH. But HH is for titrating a weak acid by strong base. I'll use similar steps to derive the counterpart equation for titrating a weak base by a strong acid. Skipping my derivation steps, eq is:
pOH = pKb + log ([HA]/[A-])*
3. Solve the eq. HA is the FINAL amount of conjugate acid and A- is FINAL amount of remaining base after complete reaction.
4. I have the pOH. pH = 14 - pOH
I get 10.638, which is slightly more exact but the numbers were probably rounded during the math in BR.
What you actually did was that you put
pH = pKa (of the BASE, not acid) + log (WeakBase/Strong Acid)
The pKa given is the pKa of the amine (RNH2) to be deprotonated to an amine anion (RNH-). What you want is the pK, with K being the equilibrium constant of amine (RNH2) going to aminium (RNH3+). Basically, you made an inappropriate substitution.
You put the concentration or the mole of WEAK BASE when you needed conjugate acid of weak base on the numerator on the ratio.
You put the concentration or the mole of STRONG ACID when you needed Weak Base on the denominator on the ratio.
My bottom line is that you might want to review titration and buffer and try some derivations to understand the concept better. If you're a math person, you should be well off after couple hours!
*The A- stands for base and HA for conjugate acid. Just as a conceptual double check, K = P/R. I'm making c. acid from base. So K=P/R, which is acid/base. So it makes sense (although during derivation there's actually 2 reciprocalization which cancels out so it's not directly this.
