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Problem: 180 mL of 0.300 M HNO3 are slowly titrated with 0.900 M KOH. What is the pH of the solution when 0, 3, 10, 25, 40, 58, 60, 64,75, 90, and 100 mL of KOH have been added? | |
Solution: Confucius says that we have a strong-strong titration.Why? Check the list, braniac. In case you were curious (and youdon't have to be), the following reactions occur in this problem. | |
You don't have to worry about rxn. #3, because it doesn't change the [H+] or [OH¯] in the solution. | |
Moving right along, you can start plugging away now. First,though, you probably want to get organized. | |
Probably the best way to attack this bear is to set up a neato chart. I don't know, maybe a chart like this one (check it out now, an explanation follows): |
ml (Base added) | Total V (mL and L) | MAVA (mols acid) | MBVB (mols base) |
|---|---|---|---|
| 0 | 180 mL 0.180 L | (0.300)(0.180) = 0.0540 | 0 |
| 3 | 183 mL 0.183 L | 0.0540 - 0.0027 = 0.0513 | (0.9)(0.003) = 0.0027 |
| 10 | 190 mL 0.190 L | 0.0540 - 0.009 = 0.0450 | (0.9)(0.010) = 0.009 |
| 25 | 205 mL 0.205 L | 0.0540 - 0.0225 = 0.0315 | (0.9)(0.025) = 0.0225 |
| 40 | 220 mL 0.220 L | 0.0540 - 0.0360 = 0.0180 | (0.9)(0.040) = 0.0360 |
| 58 | 238 mL 0.238 L | 0.0540 - 0. 0522 = 0.0018 | (0.9)(0.058) = 0522 |
| 60 | 240 mL 00.240 L | 0.0540 - 0. 0540 = 0 | (0.9)(0.060) = 0.0540 (The equivalence point!!!) |
| 64 | 244 mL 0.244 L | 0 | (0.9)(0.064) = 0.0576 0.0576 - 0.0540 = 0.0036 |
| 75 | 255 mL 0.255 L | 0 | (0.9)(0.075) = 0.0675 0.0675 - 0.0540 = 0.0135 |
| 90 | 270 mL 0.270 L | 0 | (0.9)(0.090) = 0.081 0.081 - 0.0540 = 0.027 |
| 100 | 280 mL 0.280 L | 0 | (0.9)(0.10) = 0.09 0.09 - 0.0540 = 0.036 |
That was a roller coaster ride of fun, wasn't it? In case you're lost (doubt it), a chart like this is key for staying organized. It keeps track of how many moles of acid you have as you titrate with base (you might care because strong acids/bases dissociate completely--so concentrated strong acid = [H30+] and concentrated strong base = [OH¯] ). | |
Anyway, if you take another look at the chart, up until the equivalence point (when mols acid = mols base) the MAVA column lists how many moles of H30+ are left in solution after the acid reacts with the base (rxns. 1 & 3 are happening). After the equivalence point, all the acid has been used up and the base is by its lonely self. Now the MBVB column tells you how much OH¯ is in solution (because rxns. 2 & 3 are happening). Got that? Now, you lucky stud, you can find pH values. Watch and learn. |
ml (Base added) | [H3O+] | [OH¯] | pH = -log ([H+]) = 14 + log ([OH¯]) |
|---|---|---|---|
| 0 | 0.300 | ----- | -log(0.300) = 0.523 |
| 3 | 0.0153/0.183 = 0.280 | ----- | -log(0.280) = 0.553 |
| 10 | 0.045/0.190 = 0.237 | ----- | -log(0.237) = 0.625 |
| 25 | 0.0315/0.205 = 0.157 | ----- | -log(0.157) = 0.804 |
| 40 | 0.0180/0.220 = 0.0818 | ----- | -log(0.0818) = 1.09 |
| 58 | 0.0018/0.238 = 0.00756 | ----- | -log(0.00756) = 2.12 |
| 60 | ----- | ----- | 7 |
| 64 | ----- | 0.0036/0.244 = 0.0148 | 14 + log(0.0148) = 12.2 |
| 75 | ----- | 0.0135/0.255 = 0.016 | 14 + log(0.0529) = 12.7 |
| 90 | ----- | 0.0270/0.270 = 0.100 | 14 + log(0.100) = 13.0 |
| 100 | ----- | 0.0360/0.280 = 0.129 | 14 + log(0.129) = 13.1 |
| So there you have it. That wasn't so bad, was it? All right, then, since you probably think you're pretty smart now, why don't you move on to Weak/Strong Titrations? |
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