Simulation of Acid-Strong Base Titrations for Indicators Choice
A frequent problem in a chemistry laboratory is the titration of an acid by a padronized base in order to estimate the concentration of the acid in a given sample. If one follows the titration by a visual method, an appropriate indicator has to be previously chosen to detect the end point of the neutralization through a sudden change of its color. This is common practice, in alternative to the use of a pH meter, and does not imply the errors that at first sight may be suggested due the involved subjective aspect of detecting a color change.
The present simulation is just an example of how one can assist the experimental work with the help of a computer.
Model
Let's take the volume VA (in cm3) of an aqueous solution of a monoprotic acid HA (acetic acid, for example) of molar concentration CA. Then, the number of moles (NA) of the acid in VA is: NA=VA*CA/1000.
Let's drop over the acid a certain number of moles (NB), of a strong monofunctional base (sodium hydroxide, for example), following the procedure by the titration coordinate, f(i)=NB/NA.
Let's change f(i) from 0 to 2 with increments of 0.05, resulting in a titration with 41 steps ( i =0, 1, 2,..., 40). Therefore, step 20 corresponds to the equivalence point.
From NB and the molar concentration of the base (CB), the total volume of the base (VB) at the end of each step is: VB=1000*NB/CB, so the total volume of the mixture (VT) is: VT=VA+VB. It follows that the total concentrations of acid and base in the mixture at the end of each titration step, supposing that have not yet reacted, are, respectively: AT=1000*NA/VT and BT=1000*NB/VT.
As the titration has 41 steps, we should work out a titration curve with 41 pH values, stored in the array pH(i), in function of f(i).
Before the equivalence point (0⋜ f(i) <1) the titration process obeys the equation:
[H3O+]3 + (Ka+BT) * [H3O+]2 + (KA*BT - Ka*AT - Kw)*[H3O+] - Ka*Kw = 0 (BEP)
where [H3O+] is the hydronium ion concentration, Ka the acid ionization constant and Kw the water ionic product. AT and BT were defined above. Of course, the only unknown is [H3O+].
Resolving this equation with the different values of AT and BT, the values of pH=- log [H3O+] are determined for the titration process before the equivalence point.
At equivalence point and afterwards (f(i) ⋝ 1):
a) when f(i)=1, NA moles of salt are formed; this is the equivalence point.
b) when f(i)>1, the NA moles of salt, and the NB-NA moles of base in excess have to be taken into account.
The concentrations of salt, and of the base in excess, are respectively: ST=1000*NA/VT and BE=1000*(NB-NA)/VT. The salt and the strong base are totally ionized. The salt, however, undergoes hydrolysis, except in the titrations of strong acids by strong bases; this is why the pH, at the equivalence point, is generally different from 7. The titration process for f(i) ⋝ 1 obeys the equation:
[H3O+]3 + (BE+ST+Ka) * [H3O+]2 - (KW-BE *Ka)*[H3O+] - Ka*Kw = 0 (EPAEP)
Resolving this equation with the values of ST and BE, the pH's are determined for the titration process at, and after the equivalence point.
A few computational detais
The equations are numerically solved by the method of successive bisections.
Once the pH at the equivalence point is determined, the appropriate indicator is chosen from a table included in the code. Both are displayed at the bottom of the plotting panel. The respective color change of the indicator is also displayed at the panel top.
The default variable values are for acetic acid (Ka=1.85E-5), with CA=0.10M, VA=50 cm3 and CB=0.10M.
The respective fields, however, can be edited. Try, for example, Ka=1E9 for a strong acid or/and change the values of the other variables. To this end, please Reset the simulation and actualize each new value by pressing the Return/Enter key.
The program has been tested in a wide range of Ka's: from 10- 10 (for very weak acids like hydrocyanic acid and phenol) to 109 (for very strong acids like hydrochloric and sulphuric acids). Nonetheless, if any inconsistency is found, please let us know.
- Incidentally, has the value of VA any influence on the titration results? Why?
- As the model is intended for strong bases, sodium hydroxide (NaOH) was chosen. Changing the name to another strong base, KOH for example, would it alter the results? Why?
- In textbooks, at least, the pH of a given solution is generally assumed as being between o and 14. Can it not be less than 0, or greater than 14? Why?
Finally, a suggestion: the code can be generalized to comprise weak bases and polifunctional acids and bases.
Author: Fernando M.S. Silva Fernandes
University of Lisboa, Portugal
Email: fsilva@fc.ul.pt