Example Problem


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.


  1. HNO3 + H2O --> NO3¯ + H30+ (this reaction occurs when mol HNO3 > mol KOH)
  2. KOH + H2O --> K+ + OH¯ (this reaction occurs when mol HNO3 < mol KOH)
  3. KOH + HNO3 --> KNO3 + H2O (this is the titration reaction)

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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