1. UNIT IV
Titration Curves

2. FINDING THE PH OF MIXTURES OF ACIDS AND BASES
Mixing an acid and a base produces a solution which can be acidic, basic, or neutral depending on the relative amounts of reactants.
NOTE: In acid base reactions, if one or both of the reactants are “strong” then the reaction will go to completion.
Only when both reactants are “weak”, will you get an equilibrium situation.
Titrations always require reactions which go to completion (single arrow), so acid/base titrations will always have either a strong acid, a strong base, or both.

3. FINDING THE PH OF MIXTURES OF ACIDS AND BASES
Example If 3 moles of NaOH are mixed with 1 mole of HCl, what will happen? NaOH + HCl  H2O + NaCl

4. FINDING THE PH OF MIXTURES OF ACIDS AND BASES
Example mL of 0.100M NaOH is mixed with mL of M HCl. Find the pH of the final (resulting) mixture. Balanced equation: Initial moles of NaOH: Initial moles of HCl:

5. FINDING THE PH OF MIXTURES OF ACIDS AND BASES
Excess moles: [H3O+] = [HCl] in the final mixture: pH = Note: Moles of acid or base may be determined from solids samples as well using molar mass.

6. FINDING THE PH OF MIXTURES OF ACIDS AND BASES
Example mL of M NaOH is mixed with mL of M HCl. Calculate the pH of the resulting solution.

7. FINDING THE PH OF MIXTURES OF ACIDS AND BASES
Think of a diprotic acid as releasing 2 protons (H+’s) to the base.
(NOTE: even though we learned that diprotic acids like H2SO4, donate only 1 proton completely, that was to WATER, not to a STRONG BASE. A STRONG BASE will take both the protons from H2SO4!)
Dissociate bases to find out the number of OH- ions they provide.

8. FINDING THE PH OF MIXTURES OF ACIDS AND BASES
Example mL of M H2SO4 is mixed with mL of M NaOH. Calculate the pH of the resulting solution. Balanced equation: Dissociations:

9. FINDING THE PH OF MIXTURES OF ACIDS AND BASES
Initial moles of NaOH:
Initial moles of HCl:
Excess moles:
[H3O+]=
pH =
Hebden Textbook page 143 Questions #58-68

10. TITRATION CURVES
Titration Curves: a plot of pH as a function of volume of added titrant.

11. STRONG ACID – STRONG BASE TITRATION CURVES
We can calculate the pH of the mixture in the beaker throughout the titration. First, we separate the process into 3 stages:
INITIAL POINT: Acid before any base is added
EQUIVALENCE POINT: Equivalence (Stoichiometric) Point
FINAL POINT: Base in excess

12. STRONG ACID – STRONG BASE TITRATION CURVES
1. INITIAL POINT The beaker contains mL of M HCl. Calculate the pH.

13. STRONG ACID – STRONG BASE TITRATION CURVES
2. EQUIVALENCE POINT M NaOH is added to mL of M HCl. Find the volume of base added and calculate the pH.

14. STRONG ACID – STRONG BASE TITRATION CURVES
THE SALT FORMED FROM A SA-SB TITRATION IS ALWAYS NEUTRAL.
Since there is no SA, no SB, and just H2O and a NEUTRAL salt, the pH of the solution formed will be 7.00.
At the Equivalence (Stoichiometric)Point of
a SA—SB Titration, the pH is always = 7.00

15. STRONG ACID – STRONG BASE TITRATION CURVES
3. FINAL POINT mL of M NaOH is added to mL of M HCl. Find the pH of the resulting solution.

16. STRONG ACID – STRONG BASE TITRATION CURVES

17. WEAK ACID – STRONG BASE TITRATION CURVES
Again, this type of titration has the 3 stages:
INITIAL POINT: Acid before any base is added
EQUIVALENCE POINT: Equivalence (Stoichiometric) Point
FINAL POINT: Base in excess

18. WEAK ACID – STRONG BASE TITRATION CURVES
1. INITIAL POINT Find the pH of mL of 0.10 M CH3COOH before any base is added to it.

19. WEAK ACID – STRONG BASE TITRATION CURVES
We see that for a WEAK ACID – STRONG BASE titration, the pH before the base is added is higher (ex. 2.87) than it was for a SA-SB titration (where the pH before the base is added is 1.00).
For the same concentration, the weaker the acid, the HIGHER the pH will start out!

20. WEAK ACID – STRONG BASE TITRATION CURVES
A note about the BUFFER REGION: mL of M NaOH is added to mL of 0.10 M CH3COOH.

21. WEAK ACID – STRONG BASE TITRATION CURVES
What we are left with is a mixture of a weak acid (CH3COOH) and the salt of its conjugate base (NaCH3COO).
A mixture of a weak acid and a weak base (the salt of its conjugate base) is called a BUFFER SOLUTION.
As we will see later, a buffer solution is a solution which maintains the pH at a fairly constant value.
This causes the titration curve to decrease in slope during this stage. The area on the curve is called the “Buffer Region”.
(In Chem12, we will not need to be able to calculate the pH in a buffer solution.)

22. WEAK ACID – STRONG BASE TITRATION CURVES
2. EQUIVALENCE POINT M NaOH is added to mL of M CH3COOH.

23. WEAK ACID – STRONG BASE TITRATION CURVES
But, this time we must consider the salt (NaCH3COO) that is produced  because it is NOT neutral!
NaOH + CH3COOH  H2O + NaCH3COO
This salt that is produced (NaCH3COO) dissociates to form Na+ (spectator) and CH3COO- which undergoes base hydrolysis in water.

24. WEAK ACID – STRONG BASE TITRATION CURVES
We can now use the hydrolysis equation and an ICE table to calculate the [OH-] and then pOH and then pH:

25. WEAK ACID – STRONG BASE TITRATION CURVES
For a WEAK ACID – STRONG BASE Titration,
the pH at Equivalence Point is ALWAYS > 7
This is because, when a weak acid reacts with a strong base, you always produce the conjugate base of the weak acid, which is BASIC.

26. WEAK ACID – STRONG BASE TITRATION CURVES
3. FINAL POINT
Looking at the Balanced equation:
NaOH + CH3COOH  H2O + NaCH3COO
Once NaOH is in excess, you will have some STRONG BASE (NaOH) and some WEAK BASE (CH3COO-) in the resulting mixture.
The OH- contributed by the weak base ( CH3COO-)was significant when there was no other base present (EP), but once a strong base (NaOH) is present, the OH- contributed by the weak base is insignificant compared to that produced by the NaOH.
So, the titration curve past the EP for a WA/SB Titration is the same as it is for a SA/SB Titration (where NaOH is in excess).

27. WEAK ACID – STRONG BASE TITRATION CURVE

28. WEAK BASE – STRONG ACID TITRATION CURVE
An example of a WB/SA Titration could be done with the strong acid HCl and the weak base NH3.  
HCl + NH3  NH Cl-
The pH will start out high (base), but not too high (weak).

29. WEAK BASE – STRONG ACID TITRATION CURVE
When HCl is added but the NH3 is still in excess, we will have a mixture of NH3 (a weak base) and NH4+ (a weak acid) which is a buffer.
So again, we will have a buffer region as the pH goes down.

30. WEAK BASE – STRONG ACID TITRATION CURVE
At the equivalence point in this titration, all of the HCl and NH3 will be gone and only NH4+ (a weak acid) and Cl- (a neutral spectator) will remain.
Because there is a WEAK ACID (NH4+) present, the pH will be LESS THAN 7. (but not really low). 

31. WEAK BASE – STRONG ACID TITRATION CURVE

32. SUMMARY Reactants Salt Formed Is... pH at EP Strong Acid – Strong Base
Neutral (conjugate base of SA)
= 7.00
Weak Acid –
Strong Base
Basic (conjugate base of WA)
> 7.00
Strong Acid –
Weak Base
Acidic (conjugate acid of WB)
< 7.00

33. INDICATORS FOR TITRATIONS
Indicators can be used to tell you when you have reached the equivalence (stoichiometric) point in a titration.
However, different indicators must be used for different types of titrations.
Ideally, the pH at the transition point (pKa) of the indicator will be the same as the pH at the equivalence point of the titration.
pKa (indicator) = pH at EP of Titration

34. SELECTING A SUITABLE INDICATOR
STRONG ACID-STRONG BASE TITRATION:
The best indicators would be Bromthymol Blue (6.0 – 7.6), Phenol Red (6.6 – 8.0) or Neutral Red (6.8 – 8.0) as these all have pH =7 within their transition ranges.
However, looking at the graph, there is an almost vertical line from pH = 3 to pH = 11 on the graph.
(This means that VERY LITTLE volume change of base would give a huge change in pH. Any of the indicators from Bromcresol Green to Thymolphthalein would change colour in this pH range, so they would all work.)

35. SELECTING A SUITABLE INDICATOR
WEAK ACID-STRONG BASE TITRATION:
For a WA-SB Titration Curve, the vertical section is shorter than that of a SA-SB curve.
This means that you have a more narrow range of suitable indicators. For this particular titration, any indicator which has pH = 9 (8 - 10) within its transition range is suitable.
List all indicators suitable for a WA-SB Titration:

36. SELECTING A SUITABLE INDICATOR
WEAK BASE-STRONG ACID TITRATION:
For a WB-SA Titration Curve, the vertical section is shorter than that of a SA-SB curve.
For this particular titration, any indicator which has pH = 5 (4 - 6) within its transition range is suitable.
List all indicators suitable for a WB-SA Titration:

37. CALCULATIONS INVOLVING TITRATION CURVES
I. Draw a Titration Curve Using THREE Points Example 0.10 M HNO3 is added to 25.0 mL of 0.10 M NaOH. Draw the titration curve you would expect would result from the following titration. Get the shape and the important points (IP, EP, FP) as close as you can.

38. CALCULATIONS INVOLVING TITRATION CURVES
Name an indicator which would be suitable for this titration. _________________________
As you pass through the equivalence (stoichiometric) point in this titration, the colour of your indicator would change from _____________ to ____________ (to ____________)

39. CALCULATIONS INVOLVING TITRATION CURVES
II. Identify a Sample as Strong or Weak
If we have a strong base (ex. NaOH or KOH) in the burette (“Volume of base” is on “x” axis), we can tell by the shape and by the pH at the beginning (Volume of Base = 0) whether the acid is strong or weak (given the [acid]).

40. CALCULATIONS INVOLVING TITRATION CURVES
Example:
If we have a 0.10 M acid in the beaker and 0.10 M KOH in the burette and the titration curve looks like

41. CALCULATIONS INVOLVING TITRATION CURVES
Then we know that our acid must be a STRONG acid because the pH with no base added (Volume of Base = 0 ) is 1.0.
This means…
[H3O+] = antilog (-pH) = antilog (-1.0) = 0.1 M
So, since H3O+] = [acid] we can see that this is a Strong Acid.
Also the pH at EP = 7, which also signifies that we have a strong acid.
Note: You could also calculate the initial concentration of the acid in this example from the volume of base added at the equivalence point.

42. CALCULATIONS INVOLVING TITRATION CURVES
III. Calculate the Ka of a Weak Acid (or Kb of a Weak Base)
By using the pH at “Volume of Base = 0”, we can calculate the Ka for a weak acid we are titrating.
Look at the following example in which a 0.10 M weak acid is being titrated with 0.10 M NaOH.

43. CALCULATIONS INVOLVING TITRATION CURVES
Since pH = 2.5, [H3O+] = antilog (-2.5) = 3.16 x 10-3 M

44. CALCULATIONS INVOLVING TITRATION CURVES
Solve for Ka.

45. CALCULATIONS INVOLVING TITRATION CURVES
IV. Calculate the Concentration of Strong Base (or SA) Added
When titrating a 25.0 mL sample of 0.10 M HCl with a solution of NaOH, the following titration curve was obtained. Calculate the [NaOH] in the burette:
32 mL

46. CALCULATIONS INVOLVING TITRATION CURVES
We know that this is a SA-SB titration, so at the EP, pH = 7.
Also, the EP is always in the center of the “almost vertical” region.
We mark the EP and draw a straight line down to see where it hits the “Volume of Base” axis.
This will give us the Volume of NaOH needed to reach the equivalence point.

47. CALCULATIONS INVOLVING TITRATION CURVES
We see that the volume of NaOH needed to reach the equivalence point is approximately 32 mL.  
Given this and the information at the beginning of the question, calculate the [NaOH] in the burette:

48. CALCULATIONS INVOLVING TITRATION CURVES
Example:
The following titration curve results from titrating mL of a 0.10 M weak acid HA with a strong base KOH:
17 mL

49. CALCULATIONS INVOLVING TITRATION CURVES
a. Use this graph to estimate the Ka of the acid HA.
b. Use this graph to calculate the [KOH].

50. SELECTING SOLUTIONS FOR ACID-BASE TITRATIONS
If you are titrating an acid, make sure you use a base so that your titration reaction is a neutralization. It should have at least one STRONG reactant so it will go to completion.
Also, the concentration of your standard should be relatively close to the concentration of the solution you are titrating so that the volumes used are comparable. (So you don’t need “buckets” or “a fraction of a drop”).

51. ASSIGNMENT
1. A mL sample of H2SO4 was neutralized by mL of M NaOH solution. Determine the concentration of H2SO4.

52. ASSIGNMENT
2. A 35.0 mL sample of M NaOH was titrated with M unknown acid, HxA. It took mL of the acid to reach the equivalence point. Determine the proton number of the acid.

53. ASSIGNMENT
3. Hebden Textbook Page 167 Question #124

54. ASSIGNMENT
4. A mL sample of HBr was titrated with NaOH. A volume of mL of M NaOH was required to reach the equivalence point.
Determine the concentration of HBr.
Sketch the titration curve.
Name a good indicator to use.

55. ASSIGNMENT
5. A mL sample of sulfuric acid was titrated with NaOH. A volume of mL of M NaOH was required to reach the equivalence point.
Determine the concentration of sulfuric acid.
Sketch the titration curve.
Name a good indicator to use.

56. ASSIGNMENT
mL of acetic acid of unknown concentration was titrated with 0.10 M NaOH. The following data was obtained. Use EXCEL to plot the data with pH on the y-axis and volume of NaOH on the x-axis.
Calculate the concentration of acetic acid.
Calculate the Ka of acetic acid.

57. Volume of NaOH (mL) pH
0.00
2.87
5.00
4.14
10.00
4.57
15.00
4.92
20.00
5.35
22.00
5.61
24.00
6.12
24.50
6.43
24.80
6.84
24.90
7.14
24.95
7.44
24.99
8.14
25.00
8.72
25.01
9.30
25.05
25.10
10.30
25.20
10.60
25.50
11.00
26.00
11.29
28.00
11.75
30.00
11.96
40.00
12.36
50.00
12.52

58. ASSIGNMENT
7. A mL sample of hydrofluoric acid, HF, was titrated with mL of M KOH.
Determine the concentration of hydrofluoric acid.
Sketch the titration curve.
Is the pH at the equivalence point neutral, basic, or acidic? Explain your answer with equations. (Calculate pH at EP?!!)
List 2 indicators which would be good for this titration.

59. ASSIGNMENT
8. Draw the titration curve (IP, EP, FP) when mL of 1.00 M sodium hydroxide is added to mL of M acetic acid.

60. ASSIGNMENT 25.00 mL of weak base A-1 with an unknown concentration
9. Data:
25.00 mL of weak base A-1 with an unknown concentration
19.22 mL of M HCl was used to reach the equivalence point
initial pH =
Determine the concentration of A-1 .
Determine the Kb of A-1 from the data given.

61. ASSIGNMENT
10. What colour is a solution of chlorophenol red in 1.0 x 10-4 M HCl?

62. ASSIGNMENT
11. Determine the Ka of phenol red indicator.

63. ASSIGNMENT
12. The indicator Hin is clear in acids and pink in bases. What colour is the anion In-1?

64. ASSIGNMENT
g of the diprotic acid oxalic acid dihydrate ( g/mol) was used to make a mL solution mL of the oxalic acid solution was used to titrate an unknown NaOH solution. It took mL of NaOH solution to neutralize the oxalic acid solution. Determine the concentration of the NaOH.

65. ASSIGNMENT
14. Which indicator could be used in a titration of HF and KOH?
Bromcresol green?
Bromthymol blue?
Thymolphthalein?