HEATS OF COMBUSTION

Theory

Experimental

Procedure

Calculations

Discussion

Apparatus

References

THEORY

In this experiment a bomb calorimeter is employed to determine the heat of combustion of naphthalene, C10H8. The heat of combustion, Hc for naphthalene is determined at constant temperature and pressure:

C10H8(s) + 12 O2(g) 10 CO2(g) + 4 H2O(l)                                                           (1)

In this experiment, the problem is to experimentally determine the enthalpy change, H, and the energy change, U, accompanying an isothermal change in the state of a system, when a chemical reaction occurs.

A(T0) + B(T0) C(T0) + D(T0)                                                                                (2)

In practice we do not actually carry out the reaction isothermally. This is not necessary becauseH and U are state functions, independent of the path. In calorimetry, it is often most convenient to use a path composed of two steps:

Step I. A change in state is carried out adiabatically in the calorimeter vessel to yield the desired products generally at another temperature:

A(T0) + B(T0) + S(T0) C(T1) + D(T1) + S(T1)                                                       (3)

where S represents those parts of the system (e.g., inside wall of the calorimeter vessel, stirrer, thermometer, water) that are always at the same temperature as the reactants or products because of the experimental arrangement. These parts, plus the reactants or products, constitute the system under discussion.

Step II. The products of Step I are brought to the initial temperature, T0, by adding heat to (or taking heat from) the system:

C(T1) + D(T1) + S(T1) C(T0) + D(T0) + S(T0)                                                       (4)

As we shall see, it is often unnecessary to actually carry out this step.

By adding equations (3) and (4) we obtain equation (2). Accordingly, H or U for the change in state (2), is the sum of the values of these quantities for the two separate steps:

H = HI + HII                                                                                               (5)

U = UI + UII                                                                                               (6)

The first law of thermodynamics states that:

U = q - w                                                                                                               (7)

The only work to be considered for the gases in the calorimeter is pressure-volume work. The calorimeter, however, is a constant volume device, so:

w = pdV = 0                                                                                                            (8)

Since Step I in the combustion is adiabatic:

UI = qv = 0                                                                                                             (9)

similarly, if step I is carried out at constant pressure:

HI = qp = 0                                                                                                             (10)

The heat, q, for Step II can either be measured or calculated. It can be measured directly by carrying out Step II (or its inverse) by adding a measurable quantity of heat or electrical energy to the system. Alternatively, it can be calculated from the temperature change, (T1 - T0), resulting from adiabatic Step I, if the heat capacity of the product system is known. Thus, if both steps are carried out at constant pressure,

H = HII                                                                                                             (11)

or if both are carried out at constant volume,

U = UII                                                                                                             (12)

In the current experiment, you want to determine U. Because U is one part of the cyclic process shown below, it is simply given by UII, as discussed above.

Whether the process is carried out at constant pressure or at constant volume is a matter of convenience. Experiments like determining heats of ionic reaction and heats of solution are most conveniently carried out at constant pressure (open to the atmosphere). Determination of heats of combustion are most conveniently carried out at constant volume in a bomb. We can easily calculate H, if U has been measured by a constant-volume process (or U, if H has been measured by a constant-pressure process) by using the equation:

H = U + (pV)                                                                                             (13)

When all reactants and products are in condensed phases, the (pV) term is negligible in comparison to H or U, and the difference between these two quantities is unimportant. When gases are involved, as in the case of combustion reactions, the (pV) term is likely to be significant in magnitude, though still small, in comparison with H or U. Since it is small, we can employ the ideal gas law and rewrite equation (13) in the form:

H = U + RT ngas                                                                                         (14)

where ngas is the change in the number of moles of gas in the system.

We must now concern ourselves with procedures for determining H or U for Step II. It is often unnecessary to actually carry out this step. If we know or can determine the heat capacity of the system, the temperature change (T1 - To) resulting from Step I provides all the additional information that is needed:

HII = ToT1 Cp(C + D + S) dT                                                                                (15)

UII = ToT1 Cv(C + D + S) dT                                                                               (16)

The heat capacities ordinarily vary only slightly over the small temperature ranges involved. Accordingly we can write:

HII = Cp(C + D + S)(T0 - T1)                                                                                  (17)

UII = Cv(C + D + S)(T0 - T1)                                                                                  (18)

where Cp and Cv are average values over the temperature range which are constants (to a good approximation).

An indirect method of determining the heat capacity is to carry out a different reaction for which the heat of reaction is known, in the same calorimeter under the same conditions. This method depends on the fact that in most calorimetric measurements for chemical reactions the heat capacity contributions of the actual product species (C and D) are very small, and often negligible, in comparison with the contribution from the parts of the system denoted by the symbol S. In a bomb calorimeter experiment the reactants or products amount to one or two grams, while the rest of the system may be equivalent to about 2500 g of water. Thus we may rewrite equations (17) and (18) as:

HII = C(S)(T0 - T1)                                                                                                 (19)

UII = C(S)(T0 - T1)                                                                                                 (20)

for constant pressure and constant volume processes, respectively. In equations (19) and (20) we have omitted any subscript from the heat capacity since only solids and liquids with volumes essentially independent of pressure are involved. The value of C(S) can be calculated from the heat of a known reaction and the temperature change, (T'1 - T'0), produced by it, as follows:

C(S) = -Hknown/(T'1 - T'0)               constant pressure                                             (21)

C(S) = -Uknown/(T'1 - T'0)               constant volume                                              (22)

This method is used in this experiment for the heat of combustion of naphthalene.

Let us now consider Step I, the adiabatic step, and the measurement of the temperature difference, (T1 - T0), which is the fundamental measurement of calorimetry. It is an idealization to assume that Step I is truly adiabatic, since no thermal insulation is perfect. Some heat will leak into or out of the system during the time required for the change in state to occur and for the thermometer to come into equilibrium with the product system.

In addition, we usually have a stirrer present in the calorimeter to aid in mixing the reactants or to hasten thermal equilibration. The mechanical work done on the system by the stirrer constantly increases the energy of the system. During the time required for the change in state and thermal equilibration to occur, the amount of energy introduced can be significant.

We may assume that the rate of gain or loss of energy by the system resulting from stirrer work or heat leak is reasonably constant with time at any given temperature. We may therefore assume that the temperature is a linear function of time before the reaction is initiated and after the reaction is completed. Thus we can estimate the temperatures, T0 and T1, at the instant that the reaction is initiated by plotting the experimentally determined temperatures against time. This plot must extend over a long period of time, so that there are linear portions of the curve both before and after the reaction is initiated. This data can be extrapolated over the linear portions of the data to the time of the initiation of the reaction, as shown in Figure 1.

Figure 1. a) Schematic plot of temperature T versus time t showing the extrapolation for obtaining T0 and T1. b) Plot with interrupted temperature axis and greatly expanded temperature scale. Such a plot will allow one to more accurately determine the temperatures T0 and T1.

EXPERIMENTAL

The commercial bomb calorimeter is a self-contained instrument used to determine the heats of combustion of certain fuels and pure organic substances. Figure 2 shows a cross-sectional view of a plain jacket oxygen-bomb calorimeter. Figure 3 shows a photograph of the calorimeter components. The combustion bomb, made of a corrosion-resistant metal, holds the sample to be studied. The sample in pellet form is placed in the calorimeter cup and in contact with the fuse wire. After the sample and fuse wire have been properly placed in the bomb, the bomb is sealed, and charged with oxygen from a commercial gas cylinder to the prescribed pressure. The assembled bomb is placed in the bucket containing the specified quantity of water, as shown in Figure 2. The temperature rise associated with the combustion is read from a thermometer whose bulb is immersed in the water. A stirrer is used to equilibrate the water temperature. The bucket is surrounded by an insulating air space, which minimizes the heat leakage to the surroundings.



Figure 2. Schematic diagram of the bomb calorimeter system.

Figure 3. Photograph of the bomb calorimeter system.

In using the calorimeter, it is first necessary to determine the heat capacity of the calorimeter system. This is the number of joules required to raise the temperature of the entire calorimeter system by 1oC. This is determined by combustion of a material having a known heat of combustion. Benzoic acid is commonly used for this purpose, as it will be in this experiment. The temperature rise due to the combustion of the known substance is noted, and the calculated number of joules of heat, allow one to calculate the heat capacity of the calorimeter system. This is then used in the determination of the heat of combustion of other substances.

PROCEDURE

Handle the calorimetric apparatus with great care. There is a hazard of electrical shock or of a short circuit from the exposed terminals. It is necessary to keep the working space clean and dry. The bomb is expensive and should be handled with care. In particular, be very careful not to scratch or dent any of the closure surfaces. When the bomb is dismantled its various parts should be placed gently on a clean, paper towel. Always place the lid to the calorimeter apparatus on its stand when it is not in place on the apparatus. Be especially careful when moving the lid, not to break the long thermometer or to bend the stirring shaft. When the bomb head is not in the bomb, it should be carefully placed on the bomb head support stand. Check the condition of the bomb. The bomb must be clean and dry, with no bits of iron wire in the terminals. Make sure that the jacket is completely empty and that the inside of the calorimeter is dry.

Preparing the sample: Cut about a 10 cm length of the fuse wire, making sure that it is free of kinks or sharp bends. Accurately weigh the piece of fuse wire (use an analytical balance). Prepare pellets of the samples to be used. The pellets should be 0.8 ± 0.1 g for the benzoic acid (a prepressed pellet may be used if available) and 0.5 ± 0.1 g for naphthalene. Your lab instructor will show you how to use the pellet press. Weigh the pellet accurately. If the pellet is too large, shave it to the desired weight with a spatula. Reweigh the pellet, if necessary. Handle the pellet and wire very carefully after weighing.

Attaching the fuse wire: Use tweezers or forceps for handling the wire. The pellet should be sitting in the bottom of the pan. The fuse wire must only come into contact with the two electrode terminals and the pellet, not the pan or the walls of the bomb, as shown in Figure 4. Figure 5 shows a photograph of the bomb head with the points of attachment for the fuse wire.

Figure 4. Diagram showing the steps for attaching the fuse wire to the electrodes in the bomb.

Figure 5. Photograph of the bomb head, where fuse wires are to be attached.

Installing the bomb head: Take care not to disturb the sample when moving the bomb head from the support stand to the bomb cylinder. Slide the head into the cylinder and push it down as far as it will go. Set the screw cap on the cylinder and turn it down firmly by hand. Do not use a wrench. Hand tightening is sufficient to obtain a tight seal. Check for electrical continuity with an ohmmeter. The resistance between the two leads on the outside of the calorimeter should be quite low.

Filling the bomb with oxygen: Press the fitting on the end of the oxygen hose into the inlet valve socket and the tighten the knurled union nut finger tight. Line up the fittings carefully before tightening, since misaligning the threads may damage them. Close the control valve on the filling apparatus. Then slowly open or "crack" the oxygen cylinder valve not more than one quarter turn. Open the filling connection control valve slowly and watch the outlet pressure gauge. When the bomb pressure rises to the desired filling pressure of 18-20 atm, close the control valve. Release the pressure in the bomb by slowly opening the knurled vent valve on the bomb head. This is done to flush out the atmospheric nitrogen in the bomb. Close the vent valve and refill the bomb to the desired pressure. The bomb inlet check valve will automatically close when the oxygen supply is shut off, leaving the bomb pressurized to the highest indicated pressure. DO NOT VENT THE BOMB. Release the residual pressure in the connecting hose by pushing downward on the lever attached to the relief valve. The gauge pressure should now return to zero. Remove the oxygen filling connection. Again, check for electrical continuity.

Assembly of the calorimeter: Check the temperature range of the thermometer on the calorimeter apparatus that you will be using. Fill a 2000 ml volumetric flask with deionized water near the lower end of the temperature range of the thermometer. It may be necessary for you to add some ice to the water to cool it to the desired temperature range. Check the temperature of the water with a thermometer. Carefully pour the water from the volumetric flask into the pail. Avoid splashing. Allow the flask to fully drain.

Set the filled bucket in the calorimeter. Attach the bomb lifting handle to the two holes in the side of the screw cap on the bomb. Start lowering the bomb into the water. Before the head is submerged, push the ignition wires into the two terminal sockets on the bomb head. Lower the bomb into the water with its feet spanning the raised area on the bottom of the bucket. Handle the bomb carefully during this process so that the sample and fuse wire will not be disturbed. Remove the lifting handle and shake any drops of water back into the bucket. Check the bomb for gas leaks by looking for gas bubbles around the screw cap. An occasional bubble (one every 5 or 10 seconds) is inconsequential. Again check for electrical continuity. Set the cover on the calorimeter with the cover locating pin inserted into the hole in the jacket rim. Turn the stirrer by hand to be sure that it rotates freely, then attach the drive belt and start the motor. Connect the "10 cm fuse" terminals on the ignition unit to the leads on the calorimeter jacket.

Making the run: Begin the time and temperature readings while the water temperature slowly increases. Read the precision thermometer once every 30 seconds and record both the time and the temperature. Estimate the temperature to the third decimal place, if possible. You may use an electrical timer, the clock on the wall, or a watch. Ignite the bomb after the water temperature has becomes fairly constant for about five minutes. Continue time and temperature readings every 30 seconds until the run is over.

To ignite the bomb, press the button on the ignition unit to fire the charge. The passage of current through the fuse wire will ignite the pellet. The temperature will begin rising after a 15-20 second delay. Continue recording time and temperature readings at 30 second intervals. After a few minutes the water temperature should reach its maximum value. After this point the temperature of the water should again change at a slow, steady rate. Continue making time and temperature reading for about 5 minutes after the rate of temperature change has slowed. This data will provide a valid basis to extrapolate the time and temperature plot.

Opening the calorimeter: After the last temperature observation has been made, stop the stirrer motor, remove the belt and lift the cover from the calorimeter. Set the cover on its support stand. Using the bomb lifting handle, lift the bomb out of the bucket, remove the ignition leads and wipe the bomb with a clean dry towel. Open the knurled vent valve on the bomb slightly to release the residual gas pressure slowly before attempting to remove the cap. After all the pressure has been released, unscrew the cap, lift the head out of the cylinder and place it on its support stand. Remove and weigh any unburned fuse wire. Ignore any "globules" unless attempts to crush them reveal that they are fused metal rather than oxide. Subtract the weight of unburned wire from the initial wire weight to obtain the net weight of wire burned. Examine the interior of the bomb for soot, which would suggest incomplete combustion. If this should occur, the amount of oxygen present at the time of ignition was presumably insufficient to give complete combustion and the run should be discarded. Wipe dry all bomb parts.

The procedure described above is to be used to perform two runs with each the benzoic acid standard and naphthalene.

CALCULATIONS

For each run, plot temperature versus time using an expanded, interrupted temperature scale similar to that shown in Figure 1. Perform the necessary extrapolations to determine the temperature change for the combustion process. The heat capacity of the system, C(S), is found by determining the temperature rise, (T'1 - T'0), obtained in the combustion of a known weight of benzoic acid and the known weight of fuse wire, and by making use of equation (22). For calculating the energy change produced, the energies of combustion for benzoic acid and fuse wire given below can be used:

UBA = -26425 J g-1                                                                                                 (23)

UWire = -5858 J g-1                                                                                                  (24)

In this experiment U for the combustion of a weighed sample of naphthalene is determined from the rise in temperature, (T1 - T0), and the heat capacity, C(S), by use of equations (12) and (20). The value of U obtained includes the contribution for the combustion of the fuse wire. This must be subtracted to yield the contribution from the naphthalene alone. The molar energy change can be determined, and then the molar enthalpy change H can be determined by use of equation (14). Report the individual and average values of the heat capacity, C(S), and the molar enthalpy change, H, for the combustion of naphthalene.

DISCUSSION

Compare the value of H determined for naphthalene in this experiment with the literature value.

APPARATUS

Parr bomb calorimeter system including a bomb, pail, jacket, cover, stirring motor and precision thermometer. Support stands for the calorimeter cover and the bomb head. Ignition unit for the calorimeter, oxygen filling system, pellet press and fuse wire. 2000 ml volumetric flask, timer, and an ohmmeter. The chemicals required include an oxygen cylinder, benzoic acid and naphthalene.

REFERENCES

1. D. P. Shoemaker, C. W. Garland and J. W. Nibler, Experiments in Physical Chemistry, 6th ed., pp. 152-158, McGraw-Hill, New York, NY (1996).

2. R. J. Sime, Physical Chemistry: Methods, Techniques, and Experiments, pp. 420-431, Saunders, Philadelphia, PA (1990).

3. Instructions for the 1341 Plain Oxygen Bomb Calorimeter, Parr Instrument Co., Moline, IL (1960).

© 1999 Larry G. Anderson