UNIT IV
Titration Curves
FINDING THE PH OF
MIXTURES OF ACIDS AND BASES
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•
•
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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.
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
FINDING THE PH OF
MIXTURES OF ACIDS AND BASES
Example
10.00 mL of 0.100M NaOH is mixed with
25.00 mL of 0.100 M HCl. Find the pH of
the final (resulting) mixture.
Balanced equation:
Initial moles of NaOH:
Initial moles of HCl:
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.
FINDING THE PH OF
MIXTURES OF ACIDS AND BASES
Example
40.00 mL of 0.100 M NaOH is mixed with
25.00 mL of 0.100 M HCl. Calculate the
pH of the resulting solution.
FINDING THE PH OF
MIXTURES OF ACIDS AND BASES
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•
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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 OHions they provide.
FINDING THE PH OF
MIXTURES OF ACIDS AND BASES
Example
15.00 mL of 0.100 M H2SO4 is mixed with
12.50 mL of 0.200 M NaOH. Calculate the
pH of the resulting solution.
Balanced equation:
Dissociations:
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
TITRATION CURVES

Titration Curves: a plot of pH as a function of
volume of added titrant.
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:
1.
2.
3.
INITIAL POINT: Acid before any base is added
EQUIVALENCE POINT: Equivalence
(Stoichiometric) Point
FINAL POINT: Base in excess
STRONG ACID – STRONG BASE
TITRATION CURVES
1. INITIAL POINT
The beaker contains 25.00 mL of 0.100 M HCl.
Calculate the pH.
STRONG ACID – STRONG BASE
TITRATION CURVES
2. EQUIVALENCE POINT
0.100 M NaOH is added to 25.00 mL of 0.100 M
HCl. Find the volume of base added and
calculate the pH.
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
STRONG ACID – STRONG BASE
TITRATION CURVES
3. FINAL POINT
26.00 mL of 0.100 M NaOH is added to 25.00 mL of
0.100 M HCl. Find the pH of the resulting
solution.
STRONG ACID – STRONG BASE
TITRATION CURVES
WEAK ACID – STRONG BASE
TITRATION CURVES
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1.
2.
3.
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
WEAK ACID – STRONG BASE
TITRATION CURVES
1. INITIAL POINT
Find the pH of 25.00 mL of 0.10 M CH3COOH
before any base is added to it.
WEAK ACID – STRONG BASE
TITRATION CURVES
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
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!
WEAK ACID – STRONG BASE
TITRATION CURVES
A note about the BUFFER REGION:
10.00 mL of 0.100 M NaOH is added to 25.00 mL of
0.10 M CH3COOH.
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”.
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(In Chem12, we will not need to be able to calculate the pH
in a buffer solution.)
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WEAK ACID – STRONG BASE
TITRATION CURVES
2. EQUIVALENCE POINT
0.100 M NaOH is added to 25.00 mL of 0.100 M
CH3COOH.
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 CH3COOwhich undergoes base hydrolysis in water.
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:
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.
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 OHcontributed 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).
WEAK ACID – STRONG BASE
TITRATION CURVE
WEAK BASE – STRONG ACID
TITRATION CURVE
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
An example of a WB/SA Titration could be done
with the strong acid HCl and the weak base
NH3.
HCl + NH3  NH4+ + ClThe pH will start out high (base), but not too
high (weak).
WEAK BASE – STRONG ACID
TITRATION CURVE
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
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.
WEAK BASE – STRONG ACID
TITRATION CURVE
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
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).
WEAK BASE – STRONG ACID
TITRATION CURVE
SUMMARY
Reactants
Strong Acid –
Strong Base
Salt Formed Is...
Neutral (conjugate
base of SA)
pH at EP
= 7.00
Weak Acid –
Strong Base
Basic (conjugate
base of WA)
> 7.00
Strong Acid –
Weak Base
Acidic (conjugate
acid of WB)
< 7.00
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
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.)
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:
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:
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.
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 ____________)
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]).
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
CALCULATIONS INVOLVING
TITRATION CURVES
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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.
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.
CALCULATIONS INVOLVING
TITRATION CURVES
Since pH = 2.5, [H3O+] = antilog (-2.5)
= 3.16 x 10-3 M
CALCULATIONS INVOLVING
TITRATION CURVES
Solve for Ka.
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
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.

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:

CALCULATIONS INVOLVING
TITRATION CURVES
Example:
The following titration curve results from titrating
25.0 mL of a 0.10 M weak acid HA with a strong
base KOH:
17 mL
CALCULATIONS INVOLVING
TITRATION CURVES
a. Use this graph to estimate the Ka of the acid
HA.
b. Use this graph to calculate the [KOH].
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”).

ASSIGNMENT
1. A 25.00 mL sample of H2SO4 was neutralized by
67.82 mL of 0.125 M NaOH solution. Determine
the concentration of H2SO4.
ASSIGNMENT
2. A 35.0 mL sample of 0.500 M NaOH was titrated
with 0.350 M unknown acid, HxA. It took 49.4
mL of the acid to reach the equivalence point.
Determine the proton number of the acid.
ASSIGNMENT
3. Hebden Textbook Page 167 Question #124
ASSIGNMENT
4. A 15.00 mL sample of HBr was titrated with
NaOH. A volume of 34.87 mL of 0.1250 M NaOH
was required to reach the equivalence point.
a) Determine the concentration of HBr.
b) Sketch the titration curve.
c) Name a good indicator to use.
ASSIGNMENT
5. A 20.00 mL sample of sulfuric acid was titrated
with NaOH. A volume of 23.55 mL of 0.1500 M
NaOH was required to reach the equivalence
point.
a) Determine the concentration of sulfuric acid.
b) Sketch the titration curve.
c) Name a good indicator to use.
ASSIGNMENT
6. 25.00 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.
a) Calculate the concentration of acetic acid.
b)
Calculate the Ka of acetic acid.
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
10.00
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
ASSIGNMENT
7. A 15.00 mL sample of hydrofluoric acid, HF, was
titrated with 28.13 mL of 0.100 M KOH.
a) Determine the concentration of hydrofluoric acid.
b) Sketch the titration curve.
c) Is the pH at the equivalence point neutral, basic,
or acidic? Explain your answer with equations.
(Calculate pH at EP?!!)
d) List 2 indicators which would be good for this
titration.
ASSIGNMENT
8. Draw the titration curve (IP, EP, FP) when 40.0
mL of 1.00 M sodium hydroxide is added to 10.0
mL of 1.50 M acetic acid.
ASSIGNMENT
9. Data:
25.00 mL of weak base A-1 with an
unknown concentration
 19.22 mL of 0.113 M HCl was used to
reach the equivalence point
 initial pH = 11.855

a)
Determine the concentration of A-1 .
a)
Determine the Kb of A-1 from the data given.
ASSIGNMENT
10. What colour is a solution of chlorophenol red in
1.0 x 10-4 M HCl?
ASSIGNMENT
11. Determine the Ka of phenol red indicator.
ASSIGNMENT
12. The indicator Hin is clear in acids and pink in
bases. What colour is the anion In-1?
ASSIGNMENT
13. 3.000 g of the diprotic acid oxalic acid dihydrate
(126.07 g/mol) was used to make a 100.0 mL
solution. 20.00 mL of the oxalic acid solution was
used to titrate an unknown NaOH solution. It
took 48.21 mL of NaOH solution to neutralize the
oxalic acid solution. Determine the concentration
of the NaOH.
ASSIGNMENT
14. Which indicator could be used in a titration of
HF and KOH?
 Bromcresol green?
 Bromthymol blue?
 Thymolphthalein?