1. How to Interpret Titration Curves
find the equivalence point
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
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

2. 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

3. A Typical Titration Curve
mid point
equivalence point

4. Find the Equivalence Point (Geometric method)
1) using a ruler, draw a tangent line that follows the flat, more horizontal part of the curve
equivalence point
2) draw a line that follows the flat, more vertical part of the curve

5. Find the Equivalence Point (Geometric method)
3) using a ruler, measure the distance between the top intersection and the bottom intersection
equivalence point
4) the geometric center of this line segment is the equivalence point

6. Find the Equivalence Point (Geometric method)
5) draw a vertical line from the equivalence point to the x-axis
equivalence point
6) where the line crosses the x-axis is the volume at the equivalence point
(28.7 mL in this case)

7. 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
mid point

8. Find the Mid Point (Geometric method)
2) using a ruler, measure the distance between the far left and right intersections
equivalence point
3) the geometric center between these points is the mid point
mid point

9. Find the Mid Point (Geometric method)
4) draw a horizontal line from the mid point to the y-axis
equivalence point
5) where the line crosses the y-axis is the pH at the midpoint
(pH = 7.2 in this case)
mid point

10. How to Interpret Titration Curves
find the mid point (half point equivalence)
This is the point when the acid is half neutralized.
mid pt = 7.2 = Ka of the acid

11. 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

12. Find the Equivalence Point (derivative method)
1) identify volume value at the peak
(28.5 mL in this case)
1) identify volume value at the peak

13. Find the Mid Point (derivative method)
1) identify pH value at the peak
(pH = 7.3 in this case)