Online Chemistry Labs | Experimental Cooling Curves

When an object that is hotter than its surroundings cools, the rate of cooling follows Newton's Law of Cooling. This law states that the rate of heat transfer from an object to the surroundings is, to the first order, directly proportional to the temperature difference between the object and the surroundings. If the surroundings are large enough to maintain a constant temperature in spite of the heat transfer, then the cooling rate decreases exponentially with time, as does the temperature of the object.

In the case of the virtual freezing point calorimeter used in our freezing point depression experiment, the large mass of the calorimeter, which remains at ambient temperature, is a heat sink during sample cooling. The relatively small sample thus loses heat according to the equation:

heat loss    =    k (Tsample - Tcalorimeter)

The proportionality constant, k, is related to the heat transfer coefficient between the sample and the calorimeter as well as the heat capacity of the sample. In a virtual instrument we can adjust the value of k however we wish, but generally choose a k value to replicate a reasonable lab experience, albeit somewhat  accelerated so that a 2-3 minute data collection time is sufficient to return the sample close to ambient temperature.

The integrated form of the heat loss equation gives sample temperature as a function of time:

Tamb (ambient temperature) is adjustable in our experiment, and defaults in our virtual laboratory room to ≈ 22°C. Tstart is the simple dwell temperature of the virtual heating element used to heat and melt the sample.

The above considerations provide an ideal case, but do not closely resemble actual data collected in the lab. We know this because we've seen students perform these experiments hundreds or even thousands of times! To generate realistic results for more meaningful analysis, we need to consider some additional factors.

Supercooling occurs when samples do not rapidly freeze (relative to the cooling rate) upon reaching their equilibrium freezing point. This phenomenon is quite common in experiments of this type, and is usually observed in our students' real lab data. It's most likely that nucleation sites are not abundant in small, clean samples and containers of the sort used in lab experiments. Our virtual experiment controls the amount of supercooling with an adjustable parameter that adds this feature into the cooling curve. The observed supercooling "dip" can be more pronounced with higher sample cooling rates.

The length of the nearly horizontal section of the cooling curve, where the sample is freezing, is of course directly related to the sample mass. Larger samples will produce longer horizontal sections. Our virtual instrument calculates and scales this section length to conform to this relation. However, close inspection generally reveals that this section is not actually horizontal in real experiments; it usually has a slight downward slope. This results from the gradual drop in freezing point due to the presence of minor contaminants (we are not referring here to the unknown solute which produces the calculated freezing point depression). As the solution freezes, these other impurities can concentrate in the melt, causing the solution's freezing point to gradually drop, thus giving a slight downward slope. Our virtual data slopes are adjustable to reflect different impurity levels.

The virtual calorimeter has an "Analyze" button. When clicked, the virtual instrument software (actually our Silverlight code) extrapolates the horizontal section of the cooling curve (avoiding the supercooling region), back to its intersection with the maximum loss tangent to the initial cooling exponential decrease. The temperature at this intersection defines the freezing point of the sample, and is reported on the monitor.

Finally, generating the heating curves is a relative snap. There is no exponential character because our virtual heater, just like many real heaters, is designed to provide a linear temperature rise until the set dwell temperature is reached. The heater dwell temperature is adjustable.

We recommend the references below for further detail and some typical cooling curves from real lab experiments:

D. P. Shoemaker, C. W. Garland, and J. W. Nibler, Experiments in Physical Chemistry, 6th ed., exp. 10, p. 185, McGraw-Hill, New York (1996).

J. B. Ott and J. P. Goates, "Temperature Measurement with Application to Phase Equilibria Studies," in B. W. Rossiter and R. C. Baetzold (eds.), Physical Methods of Chemistry, 2d ed., Vol. VI. Chap. 7, Wiley-Interscience, New York (1992).