Equivalence Volumes

1
Equivalence Volumes

• by Robert Lachcik

2
Equivalence Point

• The equivalence point is when the amount of
  titrant is equal to the amount of analyte being
  titrated
• In our experiments, we mostly performed acid-base
  titrations
• There are many ways to find the equivalence point
• Indicators
• Derivative Graphs
• Gran Plot

3
Indicators

• Indicators are used in titrations when
  determining the equivalence point
• The first lasting appearance of the color change
  is the sign that the equivalence point has been
  achieved
• In many of the experiments performed we titrated
  unknown solutions using indicators to find the
  equivalence point

• Common indicators used
• - Phenolphtalein
• - Methyl Red
• - Bromothymol blue
• - Bromocresol green
• - Methyl orange
• - Erythrosine

4
Indicators

• Phenolphthalein was used in carbonate /
  bicarbonate lab as well as others
• The solution ranged from purple when basic and
  colorless when acidic
• When titrating a basic solution with an acid,
  the colorless endpoint was very easily identified

• But not all indicators give such a clear
  indication of the end point as phenolphthalein

5
Indicators

• This problem didnt necessarily lead to poor
  precision for a single experimenter, but poor
  precision among a large group using the same
  indicator

• The methyl red indicator was used in the
  statistics lab
• In a solution of pH 6.2 is yellow and of pH 4.4
  is red
• The equivalence point in the statistics lab
  determining the exact molarity of the 0.1 M HCl
  was the disappearance of orange
• The problem here was that the equivalence point
  was not as obvious as say the colorless endpoint
  of phenolphthalein

6
A Titration with a pH Electrode

• Using a pH electrode during a acid base
  titration, the pH of the solution can be recorded
  at different amounts of titrant added.
• From this information, a graph can be plotted of
  pH versus volume of titrant to approximate the
  equivalence point

7
A Titration with a pH Electrode
31 mL
An equivalence volume can be determined in this
graph by looking at the point in the line with
the greatest slope. In this graph, the
equivalence point can be approximated around 31
mL of titrant. This approximation can be
improved using a second derivative graph.
8
Second Derivative

• The equivalence point can be determined in the
  second derivative graph by observing where the
  line crosses the x-axis with the largest slope
• In this second derivative graph, the data is
  ideal for finding the equivalence point
• The graph passes through the x-axis once with
  its largest slope at one point, 7.30 mL

7.30 mL

• The problem with this image and using this
  technique is that our data is rarely this ideal

9
Second Derivative

• The equivalence point in this graph is very
  difficult to determine since the graph crosses
  the x-axis three times
• The derivative graph is not as accurate near the
  equivalence point
• Also, buffering is minimal
• The three equivalence points are 30.71, 30.75
  and 30.83 mL

30.71, 30.75 and 30.83 mL

• These are problems in determining the
  equivalence point using the second derivative
• Because of this, the second derivative can give
  a bad approximation
• This problem is fixed with the Gran Plot

10
The Gran Plot

• The Gran Plot is made by plotting the volume of
  titrant versus the volume of titrant times 10-pH
• The span of the graph in the gran plot lab was
  from nine tenths of the approximated equivalence
  volume to the approximated equivalence volume

30.79 mL

• Using the same data used in the second
  derivative graph, the gran plot corrects the
  problems the second derivative encountered
• The graph appears as a linear line and the
  equivalence volume is determined by where the
  line crosses the x-axis.
• The equivalence volume in this graph is 30.79 mL

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Indicators, Second Derivative and the Gran Plot

• Using indicators to find endpoints is sometimes
  difficult to use, since some color changes can
  sometimes be very difficult to identify
  consistently
• The derivative graphs are not as accurate near
  the endpoint
• Ideally the second derivative graph would only
  have only one x-intercept
• However, our experimental data is rarely ideal.
  For example, my second derivative has a few
  x-intercepts which can cause problems in
  determining exact equivalence volumes
• The Gran Plot solves this problem because the
  graph is linear and only has one x-intercept
• Using the Gran Plot the equivalence volume can
  be determined without any doubt

12
Question

• Why is the gran plot used to determine the
  equivalence point rather than the second
  derivative graph?
• The equivalence point in the second derivative
  can sometimes be ambiguous. The derivative
  graphs are not as accurate near the equivalence
  point, but the gran plot will always show one
  definitive equivalence point. Also, buffering is
  minimal using the derivative graphs.