Overview

The primary purpose of the calorimetry simulation is to provide students a realistic environment where they can explore and better understand the concepts in chemical thermodynamics using fundamental calorimetric methods. In Virtual ChemLab: Calorimetry, experiments are performed in a framework consistent with the other Virtual ChemLab simulations; that is, students are 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 calorimetry simulation is to allow students to measure the heat effects of various chemical and physical processes using equipment that can be found in most instructional laboratories and some equipment that would be less readily available. From these measurements, students will be able to measure heats of combustion, heats of solution, heats of fusion, heat capacity, boiling point elevation, and freezing point depression. These results can then be used to validate Hess's law; demonstrate the interplay between enthalpy, entropy, and Gibb's free energy; calculate heats of formation from heats of combustion; and study the effects of dissolved solutes on the boiling point and freezing point.


Three calorimeters are provided in the simulation. The first is a bomb or combustion calorimeter that is a stainless steel container consisting of the "bomb", the bomb head, and a screw cap. A small cup that holds the sample rests on the bomb head. An ignition wire, roughly 4 cm long, is placed between the two posts and feeds down near the sample. The bomb is assembled by placing the bomb head in the bomb and then sealing the bomb with the screw cap. The assembled bomb is then placed in a bucket of water with approximately 2 L of water, and the bomb is pressurized with approximately 30 atm of O2. The heat of combustion of the sample is measured by igniting the sample and then measuring the resulting temperature change. Because of the large mass of the bomb and water, it will take at least five minutes before a steady state is achieved. 


The other two calorimeters are a dewar and a Styrofoam coffee cup. Both of these are insulating vessels that operate equivalently by reducing the flow of heat into and out of the calorimeter. The dewar is a double-walled glass vessel with an insulating vacuum in between. The dewar has superior insulating characteristics over the coffee cup but is relatively expensive. Consequently, most instructional laboratories use a coffee cup for the calorimetric experiments instead. The calorimetric experiments performed with the dewar and coffee cup operate in a similar manner. The dewar or coffee cup contains water or a solution and then heat is given off by the system (exothermic) or added to the system (endothermic) by a chemical or physical process such as a reaction, dissolving a salt, adding ice, or dropping in a hot piece of metal. The resulting temperature change, as measured by the thermometer, can be used to quantify the heat produced or consumed in the process.


The calculation of the heat produced or consumed by a process, including a combustion reaction in the bomb calorimeter, is based on the equation C=Q/ΔT where Q is the heat produced or consumed, ΔT is the temperature changed measured by the thermometer, and C is the heat capacity of the entire system. If C is known, then the heat can be calculated by rearranging the equation to Q=CΔT. Measuring ΔT is rather straightforward, however, the trick is knowing the heat capacity of the system. The heat capacity of the system includes the sample being measured (for example, the reaction solution, the water plus the metal, the water and the salt, the water and the ice, the organic compound) plus the calorimeter (the dewar; coffee cup; or the bomb, water, and bucket). To a first order approximation for the dewar and coffee cup, the heat capacity of the system can be taken as the heat capacity of the solution neglecting the contribution of the dewar or coffee cup. For the coffee cup, this is not necessarily a poor assumption since the coffee cup has so little mass, but the dewar makes a non-trivial contribution. A further approximation can be made that the heat capacity of any solution in the calorimeter can be approximated by the heat capacity of water. These assumptions cannot be applied to the bomb calorimeter since the combined mass of the bomb and bucket is several kilograms.


The heat capacity of the system (sample plus calorimeter) can be determined using an electrical calibration. For the dewar and coffee cup, an electrical heater has been provided where the heater can be turned on and off, the current going through the heater and the voltage across the heater can be measured, and the time the heater is on can be measured with a stopwatch. From this, the heat, Q, dissipated by the heater can be calculated using Q = power x time = V · i x t where V is the voltage across the heater while the heater is on, i is the current going through the heater (in amps), and t is the length of time the heater was on. With Q and the resulting temperature rise, ΔT, caused by the electrical heating, the heat capacity, C, can be calculated using the equation C=Q/ΔT.


Unfortunately for the bomb calorimeter, the heat capacity of the entire calorimetric system cannot be determined with an electrical heater. Instead, the calorimeter is calibrated by measuring the heat of combustion of a standard (such as benzoic acid), which produces a known heat per mole of sample. From this, the heat capacity of the calorimetric system can be calculated using the same method as described above. For calibration purposes, use ΔH° = 3226.9 kJ/mol or ΔH = 3228 ± 2 kJ/mole for the heat of combustion for benzoic acid where ΔH° is the standard state value and ΔH is the value under the actual conditions in the calorimeter or, in other words, the value that would be measured in the experiment. The 2 kJ/mole uncertainty in ΔH is caused by changes in the correction from the standard state for differing amounts of sample and O2 in the bomb during the combustion.


The calorimetry 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 experiments and observe the sign of the heating event and its magnitude relative to other processes. Students can also perform careful quantitative measurements where they can accurately determine the heats of combustion, solution, reaction, or fusion of a large collection of materials. All of these experiments are performed within the context of gaining a fundamental understanding of chemical thermodynamics.


Simulation Principles and Features

The important principles and features forming the foundation of the calorimetry simulation are listed below.

  1. The calorimeters used in the simulation are modeled after and have heat flow characteristics that are quite close to an actual dewar, coffee cup, and bomb calorimeter. Sophisticated heat flow equations have been used to model these characteristics; however, one limitation to the heat flow equations used in the simulation prevents multiple heating events from occurring simultaneously. For example, if a solid reagent is added to the solution, the second reagent for a reaction cannot be added until the dissolution process (or the heating) has finished. In a similar manner, while the electrical heater is on, reagents and water cannot be added to the calorimeter.
  2. The thermometer is assumed to have an infinitely fast response time or, in other words, the thermometer is in perfect equilibrium with the solution in the calorimeter.
  3. For the dewar and coffee cup, a stirrer has been provided to increase the rate that a process reaches equilibrium. If the stirrer is turned off, equilibrium times will be increased substantially. The user does not have control over the stirrer for the bomb calorimeter.
  4. The heat capacity of the solutions is calculated using the partial molar heat capacities for the various constituents of the solution. The simulation does not assume the solution has the heat capacity of water.
  5. The simulation assumes that the heat capacity of the solution is temperature independent.
  6. Keep in mind that the enthalpy for a particular process recorded in the literature or in textbook tables are for the standard state. In the simulation, the heats that are produced for a given process are not standard state heats since they do not occur in the standard state. In order to get results from the simulation to agree with textbook values, the standard state corrections must be applied.
  7. The barometric pressure in the laboratory will change from day to day but will remain constant for a given day. The boiling point of a solution will be affected by the current barometric pressure as well as the presence of any dissolved solutes. The freezing point will also be affected by the presence of dissolved solutes.
  8. Many of the calorimetric processes modeled in the simulation do not reach equilibrium for several minutes. An Acceleration button has been provided that will accelerate time in the laboratory by a factor of five in order to minimize any unnecessary waiting.
  9. When solids are dissolved in 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.
  10. The volume of liquids delivered by the graduated cylinders will not be the exact volumes as labeled on the graduated cylinder. Instead, the volumes delivered will have inaccuracies and randomness typical of actual graduated cylinders.
  11. 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.
  12. 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 thermometers. 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.