Titration curve approximations
web page written and maintained by Mark Chapman
under direction of Robert J. Hamers
UW - Madison Dept. of Chemistry
Interactive Chemistry
Acid-Base Chemistry
web grant from DoIT Learning Technology and Distance Education
Contents
Monoprotic titration curve:
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A monoprotic titration curve has 4 regions:
- Before Base is Added -- weak acid
- Before the Equivalence Point -- buffer
- At the Equivalence Point -- weak base
- After the Equivalence Point -- excess strong base
The first region is simply a weak acid problem:
The weak acid equilibrium makes:
This simplifies to:
Which can be solved by the quadratic equation:
Approximation A
The next region, from the first addition of base to the equivalence point, can be solved
using the Henderson-Hasselbalch equation (the buffer equation):
Approximation B
The third region is at the equivalence point. This point acts just as if the solution
was a solution of only the conjugate base of the weak acid titrated, so the region can be
calculated as a weak base problem:
Approximation D
The final region for a monoprotic weak acid is after the equivalence point. For the rest
of the titration, the curve can be approximated as a curve for an excess of strong base:
Approximation E
Polyprotic titration curve:
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A polyprotic titration curve has 5 regions:
- Before Base is Added
- Before the first Equivalence Point and between Equivalence Points
- At middle Equivalence Points
- At the final Equivalence Point
- After the final Equivalence Point
Just like for a monoprotic weak acid, the first region is simply a weak acid problem:
The weak acid equilibrium makes:
This simplifies to:
Which can be solved by the quadratic equation:
Approximation A
The next region, from the first addition of base to the equivalence point, can be solved
using the Henderson-Hasselbalch equation (the buffer equation), as can any region later
on that falls inbetween two equilibrium points. These correspond to buffer zones:
Approximation B
The third region differs from anything found on a monoprotic titration curve. The region
exists at any equilibrium point that are not the final equilibrium point. The
corresponding approximation includes the pK of of the acid for the regions directly to the
left and right of the equilibrium point, and looks like this:
Approximation C
The fourth region is at the final equivalence point. This point acts just as if the
solution was made only of the conjugate base of the weak acid titrated, so the region can be
calculated as a weak base problem:
Approximation D
The final region falls after the final equivalence point. For the rest of the titration,
the curve can be approximated as a curve for an excess of strong base:
Approximation E
Complete solution using the systematic method:
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Approximations:
Approximation A:
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Approximation B:
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Approximation C:
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Approximation D:
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Approximation E:
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Summary:
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| Approximation A
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| Approximation B
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| Approximation C
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| Approximation D
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| Approximation E
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Exercises:
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Exercises with the Virtual Titrator
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