1. 17.1 Calorimetry Calorimetry is the experimental science of measuring (metry) heat (calor) transfer under controlled conditions. Almost all thermodynamic data was developed from calorimetric measurements. There are a number of different types of calorimetry, but we will focus on adiabatic oxygen bomb calorimetry in which a combustion reaction is carried out in a constant volume “bomb” calorimeter in the presence of excess oxygen. The process is refered to as adiabatic since the experimental apparatus is designed to confine all of the heat transfer within an adiabatic “wall” surrounding the calorimeter. A sketch of a stainless steel bomb is shown below: sample cup & sample iron fuse wire 30 atm of O 2 (g)

2. 17.2 In practice the sample is carefully weighed into the sample cup, the iron fuse wire is also carefully weighed (since the heat generated by its combustion must be taken into account), and the calorimeter is assembled and pressurized with ~30 atm of O 2 (g). 30 atm O 2 (g) of is far more oxygen than is necessary to completely react with the sample. Why is an excess of oxygen used? The assembled bomb is then immersed in a silvered dewar containing 400.0 grams of water (to increase the heat capacity of the calorimeter and keep temperature excursions small). The silvered dewar and surrounded static air jacket combine to form an adiabatic wall within which all heat transfer is to be confined. Heat released in the combustion reaction is transfered to and warms the reaction products, the stainless steel bomb, and the surrounding water. The temperature increase in these components is measured by a precision thermometer immersed in the water jacket: silvered dewar water jacket thermometer stirrer static air jackets bomb

3. 17.3 The heat capacity of the calorimeter and its contents must first be determined, i.e., the calorimeter must be calibrated. Typically the heat capacity of the calorimeter is determined either by precision resistive heating of the calorimeter or by carrying out a reaction whose heat of combustion is known and recording the resulting temperature rise. We will illustrate the calibration procedure in the latter case: A 0.1000 gram sample of solid benzoic acid, C 6 H 5 COOH (s), is combusted in an adiabatic bomb calorimeter containing 400.0 grams of water that was initially at 25.000 o C. The final temperature of the calorimeter is 26.250 o C. The heat of combustion of benzoic acid is - 771.24 kcal/mole. In this example we will ignore the contribution to the heat from the burning of the iron wire. What is the heat capacity of the calorimeter? The balanced equation for the combustion of benzoic acid in the presence of excess oxygen is: C 6 H 5 COOH (s) + 15/2 O 2 (g) -----> 7 CO 2 (g) + 3 H 2 O (l) How do we know that the water is in the liquid and not the vapor state? The enthalpy change of -771.24 kcal/mole is for this reaction carried out at constant pressure, but the reaction was carried out at constant volume, so that we are really interested in the internal energy change,  E. Using the definition of enthalpy we have:  E =  (H - P V) =  H -  (P V) What assumptions allow us to then write?  E =  H - R T  n gases

4. 17.4 For this combustion  n gases is:  n gases = 7 - 15/2 = - 1/2 mole of gases / mole of C 6 H 5 COOH The internal energy change per mole of benzoic acid is thus:  E = (-771.24 kcal/mol) - (0.001987 kcal / mol K) (298.15 K) (-1/2 mol of gases/mol) = - 770.94 kcal/mole Though not obvious, the appropriate temperature to use in this calculation is the initial temperature. The heat therefore released when 0.1000 grams of benzoic acid is combusted is: q v = (0.1000 g) (1.0000 mole / 122.13 g) (-770.94 kcal/mole) = - 0.6312 kcal The heat capacity of the calorimeter is therefore: C cal = q cal /  T = - q v /  T = - (-631.2 cal) / (26.250 o C - 25.000 o C) = + 505.0 cal / o C Why do q cal and q v have opposite sign? The above calculation tells us that for every 505.0 calories of heat that are introduced into the calorimeter, its temperature will increase by 1 o C.

5. 17.5 Now that the heat capacity of the calorimeter is known it can be used to determine the heat of combusiton of other compounds. For example suppose that when 0.1100 grams of cyclopropane, C 3 H 6 (g), is combusted in 30 atm of oxygen, the calorimeter that we just calibrated is observed to increase in temperature from 25.000 o C to 27.580 o C. How much heat in calories is released as a result of combusting the 0.1100 grams of cyclopropane? What is the internal energy change for this combustion in kcal/mole? Write the balanced equation describing the combustion of cyclopropane in the presence of excess oxygen: What is  n gases for this reaction (remember cyclopropane is a gas)? Show that the enthalpy change for this combustion,  H comb  is 499.89 kcal/mole?

6. 17.6 This enthalpy of combustion at 298 K can now be used with the standard enthalpies of formation of carbon dioxide and liquid water at 298 K to calculate the standard enthalpy of formation of cyclopropane: C 3 H 6 (g) + 9/2 O 2 (g) -----> 3 CO 2 (g) + 3 H 2 O (l)  H o comb, 98 K = - 499.89 kcal/mole = (3 mols)  H o f, 298 K [CO 2 (g)] + (3 moles)  H o f, 298 K [H 2 O (l)] - (1 mole)  H o f, 298 K [C 3 H 6 (g)] - (9/2 moles)  H o f, 298 K [O 2 (g)] = (3 mols) (- 94.051 kcal/mole) + (3 mols) (- 68.315 kcal/mole) - (1 mole)  H o f, 298 K [C 3 H 6 (g)] - (9/2 moles) (0 kcal/mole) Solving for  H o f, 298 K [C 3 H 6 (g)] gives:  H o f, 298 K [C 3 H 6 (g)] = + 12.79 kcal/mole of C 3 H 6 (g) It is in this fashion that tables of standard enthalpies of formation were developed!

7. 17.7 A 20.000 gram chunk of Remalloy, an iron/molybdenum/cobalt alloy, initially at 100.0 o C is dropped into 150.0 grams of water initially at 25.00 o C in an insulated dewar that is open to the atmosphere. The final temperature of the water and Remalloy is 33.40 o C. The heat capacity of water at can be taken as 0.9981 cal / g o C. Assuming that all the heat transfer occurs between the Remalloy and the water, what is the heat capacity of the Remalloy in cal / g o C ?