Calorimetry


Calorimetry is the quantitative measurement of the heat required or evolved during a chemical process. A Calorimeter is an instrument for measuring the heat of a reaction during a well defined process. The following diagram depicts a constant volume or 'bomb' calorimeter:

You may see a much simpler, but less accurate calorimeter in the laboratory, which, by its construction, is necessarily constant pressure:

Constant volume calorimetry measures the Internal Energy change between Reactants and Products, but constant pressure calorimetery measures directly the Enthalpy change during the reaction.  These two heats are slightly different when gases are evolved or consumed during the transformation. (Gases evolved expand if at constant pressure and thus do Work in the surroundings. This energy must come from somewhere...)

Both constant volume and constant pressure instruments use the fact that the heat evolved from the reaction changes the temperature of a working substance (usually a water bath) with a known heat capacity. Thus a measurement of the temperature rise in the surroundings (calorimeter body) allows a determination of the heat crossing the boundary between the system (where the reaction takes place) and the surroundings (where the temperature change is measured). For technical reasons, it is usually more accurate to measure constant volume heat flow (Internal Energy changes) and thus 'bomb' calorimeters are used almost exclusively for important measurements.

We usually assume that the heat capacity of a given substance is roughly constant (independent of temperature) over a small changes in temperature. (If we need to be more accurate, we can correct for this assumption, but we won't do that in this course). Every substance has a heat capacity, and the values of this property vary greatly with that substance. There are a couple of things that we can say universally about this property:


Comments on Heat Capacity...

Here is a list of some Heat Capacities

Note: The molar heat capacities of most metals around room temperature are all around 25 J/K.g. This is because the capacity to accomodate energy depends on the number of metal atoms. Non-metals are a little more complicated :(
Example Calorimeter Calculations:

A constant pressure calorimeter where the water bath has a mass of 150 grams.  1.00 g of diamond is burned to produce CO2 and Water.  If the water bath in the Calorimeter is initially at 22 oC, what is the final temperature of the Calorimeter?

First, let's write a balanced chemical reaction for the combustion
C (diamond) + O2 (gas) = CO2 (gas)

Next, the molar heat of reaction comes from the Heats of  Formation of the products minus the reactants.

DHrxn = -393.5 kJ/mol - (1.88 kJ/mol + 0) = -395.4 kJ/mol

The actual heat released by 1.00g /12.011 g/mol = 8.326 x 10-2 mol of diamond is

Q = (-395.4 kJ/mol) (8.326 x 10-2 mol) = -3.292 x 104 J

The temperature rise is the heat provided to the water (-Q) divided by the mass times the specific heat of water

DT = 3.292 x 104 J/ ((150. g)(4.184 J/K.g) = 52.5 K

The final temperature of the water bath is then

Tfinal = 22 + 52.5 = 74.5 oC
 

If 0.500 gram of another substance, H2CO, is burned in the same Calorimeter, and the temperature of the bath in the calorimeter (150 g H20) changes from 24.0 to 39.2 oC, what is the molar heat of formation of the H2CO?

Again, lets see what kind of reaction we should have in the reactor

H2CO (gas) + O2 (gas) = CO2 (gas) + H2O (l)
So the Heat of that reaction for 0.500 g / 30.03 g/mol = 1.665 x 10-2 mol of formaldehyde raised the temperature of 150. g of water by 15.2 K.  That means the heat released by that amount of reaction liberated:

-Q = (150 g)(4.184 J/g.K)(15.2 K) = 9.540 kJ

of heat.  One mole of reaction would liberate

-Q = 9.540 kJ/(1.665 x 10-2 mol) = 572.9 kJ/mole

which is the heat of combustion, DHcomb, of formaldehyde.

The heat of formation of formaldehyde, DHform{formaldehyde}, is related to the heat of combustion as:

DHcomb = DHform{water (l)} + DHform{CO2 (gas)} - DHform{formaldehyde}

So
-572.9 kJ/mol = -285.8 kJ/mol + -393.5 kJ/mol - DHform{formaldehyde}

or
DHform{formaldehyde} = -106.4 kJ/mol

This number is a little low, according to the The National Institute of Standards and Technology (NIST), which can be searched on the web at http://webbook.nist.gov/chemistry/

A Note on Calorimetry Questions: Sometimes the Heat Capcity of the Calorimeter is 'broken up' into that of the 'bath' (a pure substance) and that of the metal reaction vessel (which is usually much smaller). If both are given then add them up and use the total for the Heat Capacity of the calorimeter in your calculations. If the heat capacity of the 'empty' calorimeter is not explicitly given, ignore it and only use the heat capacity of the 'bath'.
In high accuracy work, sometimes the energy input of the igniter or even the stirrer is accounted. We will not worry about such minor contributions.
In practice, the entire calorimeter system can be calibrated with the combustion of any substance whose heat of formation is accurately known. The combustion of Benzoic acid is a famous calibrant for typical bomb calorimeters.


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