Spreadsheet #16:  Titration of a Weak Acid with a Strong Base - Using a Derivative to Determine the Endpoint

[Back to Group 1 Assignments] [Back to Chem3020 home]

When pH data are collected for the titration of a weak monoprotic acid with a strong base, pKa=pH at half-way to equivalence.  Determination of the endpoint is based upon the rapid change in pH as the final amount of weak acid is consumed.  A derivative is an easy way to find the endpoint in the midst of such rapid pH  changes.  Spreadsheets are particularly useful in mathematically calculating derivatives.  A derivative is simply the change in value for one parameter divided by the change in another.  For example, the change in pH is easily calculated by subtracting the pH value in one spreadsheet cell from the prior value.  The change in volume of base added may also be calculated by difference after each addition.  By dividing the change in pH by the change in volume, the value of the derivative is calculated at that point, d(pH) / dV.   The endpoint of an acid-base titration is where d(pH) / dV reaches a maximum.

Download the following data for the titration of acetic acid with sodium hydroxide.  Plot the volume of base added on the x-axis and the resulting pH on the y-axis.  Then, in a separate column(s), calculate the derivative for each point and plot the resulting data on the same graph.  (Click here to download data:16-dpHdV )

Spreadsheet # 16
Titration Curves for Weak Acid - Strong Base
Derivative Plot to Determine Endpoint and pKa
#	Vb	pH	Deriv/10	pKa =	.	.
1	0.004	2.890	.	Ka =	.	.
2	0.048	2.964	.	Endpoint =	.	mL
3	0.094	3.038	.
4	0.142	3.112	.
5	0.194	3.186	.
6	0.251	3.260	.
...	...	...	...
128	14.994	12.301	.
129	16.211	12.375	.
130	17.818	12.449	.
131	20.000	12.523	.

Programming Tips:

To visualize both sets of data on the same chart, you will have to divide each value in the derivative column by 10. This is often called “scaling” the data so it fits the chart better.

Alternatively, you do not have to scale the data mathematically. You can simply chart the second set of data utilizing a separate “secondary” axis. Excel will make it look neat and keep the value as it was originally calculated.

To utilize a “secondary axis,” chart the data, the select the data set on the chart with a right click. Select: Format Data Series > Axis Tab > Secondary Axis.