Titration of Trimethylamine with HCl (g)

[plexus0208]

1. The problem statement, all variables and given/known data
Trimethylamine has a Kb of 6.3 x 10-5. How many liters of HCl gas, measured at 1.20 bar and 298 K, must be added to 250.0 mL of 0.500 M trimethylamine to give a pH of 10.30?

2. Relevant equations

3. The attempt at a solution
I don't know where to start because I don't know how the gaseous HCl affects the pH.

[Borek]

It is gaseous just to make you think it is a difficult question. Just solve for number of moles of HCl that have to be added to get given pH, then it is simple pV=nRT.

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[plexus0208]

How do I set up the expression for Ka for this reaction?

Is Ka = [(CH3)3N][H3O+] / [(CH3)3NH]?

Since Kb = 6.3*10^-5, I found Ka by dividing Kw by Kb, and that turned out to be 1.6*10^-10
Also, since pH = 10.3, [H3O+] = 5*10^-11

I'm not sure what to do from that point on...

I tried to set an equation up:
Ka = (x)(5*10^-11 + x) / (0.500 - x)
But this can't be right...

Am I supposed to use the equation pH = pKa + log [A-]/[HA]?

[symbolipoint]

The form of your equation looks reasonable, but you might be much more comfortable using the Kb value and any other corresponding changes.

[Borek]

Am I supposed to use the equation pH = pKa + log [A-]/[HA]?

That sounds like the simplest approach, although part under the log would take

\frac {[B]} {[BH^+]}

form. But that's just a minor detail.

--
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pH calculator (http://www.chembuddy.com/?left=BATE&right=pH-calculator), stoichiometry calculator (http://www.chembuddy.com/?left=EBAS&right=equation-balancing-stoichiometry)