Overview
The primary purpose of the titration simulation is to provide students a realistic environment where they can explore and better understand acid-base chemistry and electrochemistry using fundamental titrimetric methods. In Virtual ChemLab: Titrations., experiments are performed in a framework consistent with the other Virtual ChemLab simulations; that is, the student is put into a virtual environment where they are free to choose their reagents and equipment, build a conceptual experiment of their own design, and then experience the resulting consequences. The focus in the titration simulation is to allow students to perform these titrations on knowns and unknowns, monitor the titrations using a variety of methods, and interpret their results in terms of the acid-base chemistry and electrochemistry learned in the classroom.
Before the advent and widespread availability of instrumental techniques, quantitative determinations of unknown concentrations of acids, bases, and metals relied extensively on titrimetric methods. While modern instrumental methods have supplanted many titrations for specific analytes, a titration is still the method of choice for many quantitative determinations, particularly for acids and bases. Therefore, it is still important that students understand and experience the concepts and parameters that govern a titration experiment. These parameters would include (a) selecting the correct reagent for the analyte, (b) accurately delivering known volumes of titrant and analyte, (c) accurate mass weighings, and (d) determining the equivalence point for the titration.
The titration simulation allows a range of classroom and laboratory applications depending on the level of the class and the subject being taught. For example, students can perform simple, qualitative titrations and observe the results graphically as the titration proceeds, they can perform simple quantitative experiments on knowns and unknowns without applying corrections or calibrations, or they can perform experiments involving detailed glassware calibrations and buoyancy corrections in order to achieve accuracies less than 0.1%. All of these titrations are performed within the context of gaining a fundamental understanding of acid-base chemistry and electrochemistry.
Simulation Principles and Features
The important principles and features forming the foundation of the titration simulation are listed below.
- The pH of the solutions created in the simulation is calculated by solving the appropriate mass balance, charge balance, and equilibrium equations for the hydrogen ion concentration. These calculations also include the activity coefficients in the equilibrium expressions as calculated using the extended Debye-Huckle law. The activity coefficients can be turned on and off in order to study the effect of inert ions on the pH of the solution.
The electrical potential of the electrochemical solutions titrated in the simulation are calculated using the Nernst equation and also include activity coefficients. These potentials are calculated assuming the electrodes are Pt and a Standard Calomel Electrode (SCE). Since the half-cell reactions used in the Nernst equation depend on the pH of the solution in addition to the concentrations of the oxidant and reductant, the pH of the solution is defined as part of the oxidant solutions available in the stockroom.
The conductivity of the solutions is calculated using equations and data found in the physical chemistry text books by Mortimer (2nd edition), Raff (1st edition), and Atkins and de Paula (7th edition). The units for conductivity are Siemens/cm.
When solids are diluted with water and when solutions are mixed, the resulting solution volumes are calculated using the first-order, partial molar volumes for each ionic and nonionic species in the solution. Using these first-order, partial molar volumes will generally produce total volumes that are accurate to within 0.1% to 0.3% of the actual volume. Suitable estimates of partial molar volumes were made for species not found in the literature.
The acid-base indicators used in this simulation and the pH dependence of the color changes are shown on a chart hanging on the wall in the laboratory. In the simulation, indicators change color at specific pH values as shown on the indicator chart. There are no partial color changes near the equivalence point. It is also assumed in the simulation that indicators add no volume to the solution.
When beakers are placed on the stir plate, a stirring bar is placed in the beaker to enable stirring of the solution during the titration. However, the stirrer motor is not automatically turned on. If stirring is not on during the titration, then the pH/voltage, conductivity, and indicator color changes will occur with a significant time delay to mimic the slow mixing of titrant and analyte solutions without stirring. When stirring is on, there will still be a delayed response but only on the order of a second.
Actual volumetric burets and pipets do not deliver volumes that correspond exactly to the scale etched on the barrel. These volumetric errors are simulated in the laboratory by assigning appropriate error functions to each piece of precision glassware available in the laboratory. These glassware errors are unique to each student but remain constant over time. Consequently, for precise work, the glassware errors can be calibrated by delivering indicated volumes of water and weighing the water on the analytical balance. Note that the error function for the burets is not a constant; consequently, several calibrations at different volumes will need to be performed.
Items that are weighed on a balance in air are buoyed up by the air causing the observed mass, as displayed by the balance, to be different than the true mass. This buoyancy correction is small but does make a statistically significant contribution when accuracies approaching 0.1% are needed. The mass readings displayed on the analytical balance in the simulation are observed masses and have been reverse corrected from the true mass. The details involved in making buoyancy corrections can be lengthy, but the equation that is commonly used to make the corrections is as follows:
where mtrue is the true mass, mobs is the observed mass, ρair is the density of air, ρweights is the density of the weights (typically 8.0 g·cm-3) and ρsample is the density of the sample. The density of air can be calculated using a variety of methods, but each requires knowledge of the temperature and barometric pressure. The temperature and current barometric pressure for the day is given on the LED display located on the wall. Note that the barometric pressure will change from day to day in the virtual laboratory but will remain constant for the entire day.The accuracy and point-to-point noise are two sources of error that are intrinsic to each piece of glassware, the analytical balance, and to the pH/voltage and conductivity meters. Appropriately sized errors of each kind are applied in the simulation to each piece of equipment in order to provide an opportunity for realistic error analysis. In addition, the virtual auto-reading function of the volumetric buret can be turned off to force a visual determination of the volume delivered by the buret.