How to Interpret Titration Curves
How to Interpret Titration Curves
• find the equivalence point
• things to do first
– it is the steepest part of the curve where the pH
rises the fastest
– the equivalence point can be used to determine
the equivalent weight (molar mass) of the acid
– graph your data as seen in the next slide
– make sure you turn on the major and minor tick
marks on both axes
• right click on the axis, choose Format Axis…, change
Major/Minor Tick Mark settings
• find the mid point
– located in the center of the buffer region
– geometrically halfway between the equivalence
point and the beginning of the titration
– sometimes it is a little more complicated than this
- see the example
– the midpoint determines the pKa of the acid
– Is there enough precision in the tick marks?
• you should have at least 1 mL or smaller for the minor
tick mark on the x-axis
• you should have at least 0.2 pH units or smaller for the
minor tick mark on the y-axis
• Format Axis…, change Major/Minor Units
Two Different Methods
A Typical Titration Curve
• there are two methods of analysis that will be
shown
Weak Acid Titration Curve
– geometric method
12
• requires a ruler, a pencil, and the titration graph
mid point
10
– 1st derivative method
equivalence
point
8
pH
• requires a spreadsheet and some formula entries
• gives you cool graphs with the 1st derivative pointing
to the equivalence and mid points
• scores you brownie points with the instructors
6
4
2
0
• pick your method (either will work)
10
20
30
40
50
Net Titrant Volume Added (mL)
Find the Equivalence Point
(Geometric method)
Weak Acid Titration Curve
3) using a ruler, Weak Acid Titration Curve
measure the distance
12
between
the top
intersection
and the
10
bottom intersection
equivalence
point
8
6
pH
pH
1) using a ruler,
draw lines that
12
follow
the flat,
more
10horizontal
part of the curve
Find the Equivalence Point
(Geometric method)
2) draw a line that
follows the flat,
more vertical part
of the curve
4
2
0
10
20
30
Buret Volume (mL)
40
50
8
6
equivalence
point
4) the geometric
center of this line
segment is the
equivalence point
4
2
0
10
20
30
40
50
Buret Volume (mL)
1
Find the Equivalence Point
(Geometric method)
Find the Mid Point (Geometric
method)
Weak Acid Titration Curve
Weak
Acid
Curve
1) if there is a steep
rise in
the Titration
pH
at the beginning of the graph,
12
draw a line that follows the steep
part
10 of the curve
equivalence
point
8
6) where the line
crosses the x-axis is
the volume at the
equivalence point
6
4
2
0
10
20
30
pH
pH
5) draw a vertical
12
line from the
10 equivalence point
to the x-axis
8
6
4
mid point
2
(28.7 mL
in this case)
40
50
0
10
Buret Volume (mL)
Find the Mid Point (Geometric
method)
10
mid point
2
pH
pH
4
equivalence
point
8
5) where the line crosses
the y-axis is the pH at
the equivalence point
6
4
mid point
(pH = 7.2 in this case)
2
0
10
20
30
50
12
3) the geometric center
between these points is
the mid point
6
40
Weak
Titration Curve
4) draw a horizontal
line Acid
from the
mid point to the y-axis
equivalence
point
8
30
Find the Mid Point (Geometric
method)
Weak Acid
2) using a ruler, measure
the Titration Curve
distance between the far left and
12
right intersections
10
20
Buret Volume (mL)
40
50
Buret Volume (mL)
0
10
20
30
40
50
Buret Volume (mL)
How to Interpret Titration Curves
How to Interpret Titration Curves
• find the equivalence point
• find the mid point
–
–
–
–
make sure you subtract the initial buret volume!
in this case, the initial buret volume was 1.07 mL
true equiv. pt. = 28.7 mL - 1.07 mL = 27.63 mL
the 3 is the indicate the limit of the significant
figures
– mid pt = 7.2 = pKa of the acid
• calculate the equivalent weight (molar mass)
– equiv. wt. = (acid mass)/[(NaOH conc)(equiv. pt.)]
– equiv. wt. = (430.2 mg)/[(0.1139 M)(27.63mL)]
– equiv. wt. = 136.699 = 137 g/mol
2
Find the Equivalence Point
(derivative method)
For you Excel Aficionados
• equivalence point
– use the first derivative  d pH / d Vol
– plot volume as x and 1st derivative as y in a 2nd series on graph
– the spike in the graph points to the equiv. pt.
Weak Acid Titration Curve
6
1)1)identify
identify
volume
volume
10
value
value
atatthethe
peak
peak
– make a new graph and reverse the axes for the pH curve
pH
• x axis = pH values; y-axis = Vol values
– use the first derivative  d Vol / d pH
– plot pH as x and 1st derivative as y in a 2nd series on graph
– the spike in the graph points to the mid point
pH
5
1st deriv.
4
8
(28.5
mL in this case)
3
6
2
4
• use extra columns in the spreadsheet to make these calcs
– equiv. pt. deriv. (d pH / d Vol) = (pH2 - pH1)/(Vol2 - Vol1)
– midpoint deriv. (d Vol / d pH) = (Vol2 - Vol1)/ (pH2 - pH1)
1
2
1st Derivative (mL -1)
7
12
• mid point
0
0
10
20
30
40
50
Buret Volume (mL)
• or just the reciprocal of the equiv. pt. derivative
Find the Mid Point (derivative
method)
Weak Acid Titration Curve
45
40 =
(pH
35
30
25
20
15
10
5
0
2
40
7.3 in this case)
mL
35
1st deriv.
30
1st Derivative (mL)
Buret Volume (mL)
50
1)
identify pH value at the peak
25
20
15
10
5
0
4
6
8
10
12
pH
3