Posted by Rio on Wednesday, March 31, 2010 at 4:14pm.
Rather than go through each "problem" point by point, we would do a lot of back-tracking, and I think that would be even more confusing. I can see what your troubles are so let me just start from the beginning.
1. Yes, at the beginning, the pH = pKa because the concns of base and acid are the same.
2. Apparently you are ok until you add the 5 mL of 0.1 M HCl. So let me begin there. To make things a little simpler typing, I will call CH3COOH just HAc and the acetate ion, CH3COO^-, will be Ac^-. When HCl is added, the Ac^- grabs it (that's why it's a buffer--the Ac^- ties up what would have been free H^+) and makes HAc of it. Also I would like to work in millimoles so I don't have to type all those zero's. I think from your post that you're a pretty good student and can handle that. Instead of M x L = moles, we have mL x M = millimoles and mmoles/mL = M.
What did we have to start:
HAc = 25 mL x 0.1 M = 2.5 mmoles.
Ac^- = 20 mL x 0.1 M = 2.0 mmoles.
Now we add 5 mL x 0.1 M HCl.
Ac^- + H^+ ==> HAc
5 mL x 0.1 M = 0.5 mmoles. From your ICE chart, I think it is better to work in moles (millimoles).
So Ac^- is decreased by 0.5 and HAc is increased by 0.5.
After equilibrium is established,
new HAc = 2.5 + 0.5 = 3.0 mmoles.
new Ac^- = 2.0 - 0.5 = 1.5 mmoles.
new pH = pKa + log (base/acid).
You can substitute as well as I can but I get new pH of 4.44 if I didn't goof but you need to confirm that and let me know if I goofed.
Should you use concn or moles? I use moles (millimoles) to do the ICE chart because that's so much easier. TECHNICALLY, for substitution in the H-H equation, you should use concn BECAUSE the Henderson-Hasselbalch equation is pH = pKa + log [(base)/(acid)] and that is concn units in molarity. HOWEVER, the astute will notice that the volume is ALWAYS (and that's ALWAYS ALWAYS) the same since the acid, the salt, and the HCl all go into the same container. I always counted off if the student used moles and not concn BUT I always showed them that since the volume is always the same, there is no need to go through all the trouble to divide moles by liters to obtain molarity. We just write 1.5/V for concn Ac^- and 3/V = concn HAc because the V will cancel anyway and we can use any number we choose. The net effect is that we can use moles. I must admit that when the students aren't looking, I use millimoles, don't change to molarity by dividing by mL. It just makes for things a lot faster. After re-reading your post, I see I've addressed everything, I think, except the pH of 4.65. I don't know how you obtained that. If any of the above is confusing, post again with your questions. I THINK the 4.65 you calculated probably is the 4.44 I calculated above. It's a little strange to see buffers with more HAc than Ac^- at the beginning unless we want to add NaOH but I don't believe I have transposed those values. I hope this helps. I love these problems.
Oh ok thanks! I understand what I did wrong. I used the concentrations calculated from part A as my starting concentrations.
Isn't it impossible to use concentrations in part b though? Since HAc and Ac^- both start a 0.1 M and you are adding 0.1M HCl? Wouldn't that then make [] of HAc 2.0M and Ac^- 0M?
So what if the buffer in part A was made and then went to equilibrium. And then after a while HCl was added? Would that change the final pH since the initial mol of HAc and Ac^- would be different in this case right? What volume would you have to multiply the concentrations by to get the # of mol in this case?
So you're saying that in Intial change and Equlibrium states, the volume you multiply or divide by to get the #mol or concentration is the same?? But why is that since in the change part you add a certain # of mol and that obviously means a larger volume. Some questions I see are like that and that just confuses me. Thanks for all your help. Sorry if I'm making a simple question much more complicated than it really needs to be.
Oh ok thanks! I understand what I did wrong. I used the concentrations calculated from part A as my starting concentrations.
That's right. Part A is the starting point.
Isn't it impossible to use concentrations in part b though? Since HAc and Ac^- both start a 0.1 M and you are adding 0.1M HCl? Wouldn't that then make [] of HAc 2.0M and Ac^- 0M?
If you are asking if you can subtract 0.1 M from 0.1 M, no but you already know that. When you have 20 mL of 0.1 M Ac^- and you add 5 mL of 0.1 M HCl, it isn't realistic to think you can subtract 0.1 M - 0.1 M and make sense of it. You can't because you added DIFFERENT VOLUMES of the same concn and its obvious that the different volumes represent different amounts. You had 2.0 mmoles of Ac^-, you took away 0.5 mmole with HCl, which leaves you with 1.5 mmoles Ac^- and it is in 25 mL so the concn is 1.5 mmoles/25 mL = 0.06 M (later I use another example with a different volume which isn't 0.06 M so don't get those confused.
So what if the buffer in part A was made and then went to equilibrium.
I think you are making it much more complicated that it needs to be. I can guarantee you that when the HAc and Ac^- are mixed and stirred that the system is at equilibrium before you take the stirring rod out of the solution. Even before you can wink your eye. :-)
And then after a while HCl was added? Would that change the final pH since the initial mol of HAc and Ac^- would be different in this case right? What volume would you have to multiply the concentrations by to get the # of mol in this case?
The HAc and the Ac^- are not going to change concn unless you add more of one or the other OR if you add something else that reacts with one of them, such as the HCl. You have so many millimoles of each there (determined by mL x M) and that's in concrete. Those moles aren't going anywhere.
So you're saying that in Intial change and Equlibrium states, the volume you multiply or divide by to get the #mol or concentration is the same?? But why is that since in the change part you add a certain # of mol and that obviously means a larger volume. Some questions I see are like that and that just confuses me. Thanks for all your help. Sorry if I'm making a simple question much more complicated than it really needs to be.
I think you misunderstood me. I never said that the volumes didn't change. I said that the volume was the same for all parts of the solution. For example, we had 20 mL of 0.1 M Ac^- = 2.0 mmoles. We had 25 mL x 0.1 M HAc = 2.5 mmoles. When we added the 5 mL of 0.1 M HCl (yes the volume just changed by 5.0 mL), now we have a TOTAL volume of 20 + 25 + 5 = 50 mL.
We have 1.5 mmols Ac^-, we have 3.0 mmols HAc and we have a total volume of 50 mL. So the (Ac^-) = 1.5/50 = 0.030 M and (HAc) = 3.0/50 = 0.06 and the 5 mL of 0.1 M HCl is diluted instantly to 0.5 mmol/50 = 0.01 M. Note that the moles HCl did not change but the concn did. That's why I like to work in moles. 5 mL x 0.1 M = 0.5 moles. That's what reacts, not the concns.
Don't feel that you are a bother. This is important and it is important that you understand it, thoroughly. So don't hesitate to post again if needed.