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How to Interpret Titration Curves
• find the equivalence point
– it is the steepest part of the curve where the pHrises the fastest
– the equivalence point can be used to determinethe equivalent weight (molar mass) of the acid
• find the mid point
– located in the center of the buffer region
– geometrically halfway between the equivalencepoint 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
How to Interpret Titration Curves
• things to do first
– 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
– 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
• there are two methods of analysis that will be
shown
– geometric method
• requires a ruler, a pencil, and the titration graph
– 1st derivative method
• 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
• pick your method (either will work)
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0 10 20 30 40 50
p H
Net Titrant Volume Added (mL)
Weak Acid Titration Curve
equivalence
point
mid point
A Typical Titration Curve
Weak Acid Titration Curve
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Buret Volume (mL)
p H
equivalence point
Find the Equivalence Point
(Geometric method)
1) using a ruler,
draw lines that
follow the flat,
more horizontal
part of the curve
2) draw a line that
follows the flat,
more vertical part
of the curve
Weak Acid Titration Curve
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Buret Volume (mL)
p H
equivalence point
Find the Equivalence Point
(Geometric method)
3) using a ruler,
measure the distance
between the top
intersection and the
bottom intersection
4) the geometric
center of this line
segment is the
equivalence point
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Weak Acid Titration Curve
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0 10 20 30 40 50
Buret Volume (mL)
p H
equivalence
point
Find the Equivalence Point
(Geometric method)
5) draw a verticalline from the
equivalence point
to the x-axis
6) where the line
crosses the x-axis is
the volume at the
equivalence point
(28.7 mL in this case)
Weak Acid Titration Curv e
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0 10 20 30 40 50
Buret Volume (mL)
p H
mid point
Find the Mid Point (Geometric
method)
1) if there is a steep rise in the pH
at the beginning of the graph,
draw a line that follows the steep
part of the curve
Weak Acid Titration Curve
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0 10 20 30 40 50
Buret Volume (mL)
p H
equivalence
point
Find the Mid Point (Geometric
method)
2) using a ruler, measure the
distance between the far left and
right intersections
3) the geometric center
between these points is
the mid pointmid point
Weak Acid Titration Curv e
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0 10 20 30 40 50
Buret Volume (mL)
p H
equivalence
point
Find the Mid Point (Geometric
method)
4) draw a horizontal line from the
mid point to the y-axis
5) where the line crosses
the y-axis is the pH at
the equivalence point
(pH = 7.2 in this case)
mid point
How to Interpret Titration Curves
• find the equivalence 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 significantfigures
• 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
How to Interpret Titration Curves
• find the mid point
– mid pt = 7.2 = pKa of the acid
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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.• mid point
– make a new graph and reverse the axes for the pH curve
• 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
• 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)
• or just the reciprocal of the equiv. pt. derivative
Weak Acid Titration Curv e
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Buret Volume (mL)
p H
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1 s t D e r i v a t i v e ( m L - 1 )
pH
1st deriv.
Find the Equivalence Point
(derivative method)
1) identify volume
value at the peak
1) identify volume
value at the peak
(28.5 mL in this case)
Weak Acid Titration Curve
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pH
B u r e t V o l u m e ( m L )
0
5
10
15
20
25
30
35
40
1 s t D e r i v a t i v e ( m L )mL
1st deriv.
Find the Mid Point (derivative
method)
1) identify pH value at the peak
(pH = 7.3 in this case)