to michaelamae1,
this is how I am thinking about the problem and I don't know if it's right so someone please correct me:
use Molarity x Volume = Molarity x Volume
That equals sign means something! Remember that Molarity units are Moles/L and Volume L. So basically we are saying that the moles of something is equal to the moles of something else.
Now, think about this: the moles of HCl you use during the titration is the same amount of moles of HCl you end up with at the end of the titration right? So one side of the equation should be the amount of moles of HCl during the titration:
(1 M)(x liters)
and the other side of the equation will be how many moles of HCl we have at the end of the titration:
(.01)(40 + x liters)
We got .01 by noting that we want a pH of 2.
pH = -log [H+]
2= - log [H+]
[H+] = 1 x 10-2 = .01
Also note that when we combine 20 ml of the base and 20 ml of the acid, we have 40 mL total and neutralize everything to pH=7. However, we want to get down to pH=2 so we need to add a bit more acid, that is why we have (40 + x)
Putting everything together:
(1 M)(x mL) = (.01)(40+ x mL)
x =.4
So 20 mL of acid gets us to neutral pH but if we add .4 extra (so 20.4 mL total), we get down to pH =2
Is my thinking correct??? Titrations are my weakness in genchem and I'd love to fully understand them