1. Experiment 9: The Gran Plot - Calculations
Presented by Alfred Tadalan

2. Determining Ve Other than the Gran Plot:
Theoretical determination of Ve from standardized NaOH.
Given:
A sample of KHP was dissolved in 250 mL of water.
100.0 mL of this solution was titrated with standardized NaOH.
1:1 Molar ratio of KHP to NaOH.

3. Determining Ve (cont.) Other than the Gran Plot (cont.):
Colored Indicator (Phenolphthalein).
Ve = mL.
Plot of pH versus VNaOH.

4. Ve = mL

5. Determining Ve (cont.) Other than the Gran Plot (cont.):
Plot of VNaOH vs. 2nd Derivative.

6. Ve = mL

7. Detemination of Ve via Gran Plot
Why use Gran Plot?
Derivatives are less accurate near the end point.
Buffering is minimal.
Electrode response is sluggish.

8. Detemination of Ve via Gran Plot (cont.)
The Gran Plot is a graph of VNaOH vs. VNaOH10-pH
The Gran plot utilizes the data points between Ve and 0.9Ve.
Ve = mL.
0.9Ve = mL.

11. Detemination of Ve via Gran Plot (cont.)
Because of the inaccuracies near the end point, only the linear portion of the Gran Plot is interpolated to determine Ve.
The equation of the line is determined by the Least-Squares Equations.
Where:
m = Slope
b = y-intercept
x = VNaOH
y = VNaOH10-pH

12. Detemination of Ve via Gran Plot (cont.)
Equation of the Linear portion of the Gran Plot:
y = (-8.004(10-6))x (10-4)
VNaOH10-pH= (-8.004(10-6))(VNaOH) (10-4)
Ve is the VNaOH at the x-intercept of the Gran Plot.
0 = (-8.004(10-6))(Ve) (10-4)
Ve =25.27 mL

13. Determining Ka
The slope of the Gran plot is related is a function of Ka and the activity coefficients.
And to determine the activity coefficients the ionic strength must be
0.95V = (0.95)(25.27) = mL.
Also at data points correlating to,
0.33V = (0.33)(25.27) = 8.34 mL.  8.08mL, pH = 4.78
0.67V = (0.67)(25.27) = mL  17.00mL, pH = 5.40

14. Determining Ionic Strength
The concentration of each ion in solution is calculated.

15. Determining Ionic Strength (cont.)
Using the ionic strength, Table 8-1 can be referenced to determine the activity coefficients for HP- and P2-

16. Determining Activity Coefficients
Assuming a linear interpolation between the listed values for Activity Coefficients.
Also assumes that the Ion size for HP- is similar to P2- (600 pm).
The listed values are shown:
Ionic Strength [M]
Activity Coef. For HP-
Activity Coef. For P2-
0.0500
0.8350
0.4850
0.0677 ?
0.1000
0.8000
0.4050

17. Determining Activity Coefficients
Ka can now be calculated from the activity coefficients.
Literature values:
Ka = 3.90X10^-6
pKa = 5.41