Finding the Calorimeter Constant

The calorimeter constant is the net heat capacity of the bomb, the thermostat water, the bucket, and the thermometer.  It will vary from one apparatus to the next, because the precise mass of each component will vary slightly.  You need to know this value in order to calculate how much heat is generated by combustion of your sample.  In general, the relation between what you measure (change in temperature of the thermostat water) and the chemical change (the heat generated by combustion) is given by the simple equation:

q_obs = CDT

Here

• q_obs is the energy released by combustion in calories;
• C is the calorimeter constant in calories per °C;
• DT is the temperature change induced by the heat absorption, in °C. 

(We could certainly use SI units of Joules instead of calories, though organic thermochemistry has traditionally used the latter units.)

Measuring DT is somewhat involved.  The calorimeter is continually losing heat to the environment, and heat transfer from the inside of the bomb to the water is not instantaneous.  Therefore, we have to extrapolate the cooling curve before ignition (the five minutes of data collection at first) and the cooling curve after ignition to a "t₀" point.  This won't exactly be the ignition time; it is the time at which the average temperature is passed.  Take a look at the following data set.

First, find the most linear portion of the two cooling curves.  You will have to be judicious in your choice!  For example, if you do not use points late enough on the upper cooling curve, T_high will be too low and you will get inaccurate results.  Use a spreadsheet to perform linear regression for both cooling curves.

If r² is not greater than 0.97, you need to restrict the number of points used.

Next, you have to find the "t₀" point.  Find the high and low temperature that you actually measure, and take the average.  Next, expand the X-axis for the T vs. time data, and find the time at which the temperature passes this T_avg point.  You will probably have to interpolate your data; see below.  Remember, you would like as many significant figures as possible!

 

Use the slope and intercept of each cooling curve to find T_low and T_high for X = t₀.  The difference between these two temperatures is DT, the theoretical temperature that would be seen if heat transfer were instantaneous.  This is the value you use in the equation above.

To calculate q_obs, you must take into account heat generated by combustion of methyl salicylate, heat generated by combustion of the iron wire, and the error introduced by incomplete combustion (evidenced by formation of carbon soot).

For measurement of the calorimeter constant, the energy of combustion of methyl salicylate is 5902 ± 1 cal/g.  (No correction for PV work needs to be done.)  Multiply this by the mass of methyl salicylate you used to find DE_sample.

The change in the mass of the iron wire is used to calculate DE_iron.  Do not count the mass of any spherical nodules; these are iron oxide.  Use you spatula to knock these off the remaining wire.  The energy of combustion for iron is 1.400 ± 0.001 cal/mg.

Soot represents energy that was not produced.  By weighing the combustion capsule, you can determine how much was formed.  The energy that was not produced is 7.800 cal/mg soot.

After computing all three values, calculate q_obs = DE_sample + DE_iron - DE_soot.  Use this and DT to determine C, the calorimeter constant.

The TA will tell you whether your result is in the acceptable range of ± 1% of the accepted value.  The purpose is to verify your technique and your ability to correctly treat the data.

Q.  The calorimeter constant is used in all subsequent calculations.  What impact would it have if your value is off by 1% from the accepted value?

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