ENERGY OF COMBUSTION OF BREAKFAST CEREALS (01/24/08)
QUANTITATIVE TECHNIQUES
Use of an Analytical Balance
Graduated Cylinder vs. ?
INTRODUCTION
Your assignment is to determine the values for the energy of combustion of a breakfast cereal
using a bomb calorimeter. A link to the operating instructions for the PARR 6725 Semi micro
Oxygen Bomb Calorimeter can be found on the lab’s home page (immediately following the link for
this experiment).
THEORY
The first law of thermodynamics can be stated in several different ways. Essentially, it states that
the total energy of a system can be neither created nor destroyed. It can be stated mathematically
as shown in Equation 1.
ETotal = K + V + U
(1)
Where K and V represent the macroscopic kinetic and potential energies of a system (respectively)
and U represents the internal energy of a system. Although the internal energy of a system is the
result of molecular motions and intermolecular interactions, thermodynamics calculates it
macroscopically (i.e., without regard to its cause).
Thermodynamics measures the change in internal energy for processes. Since the first law
requires conservation of energy, it may also be stated that, for any process:
∆ESYSTEM = -∆ESURROUNDINGS
(2)
When we restrict ourselves to a closed system, at rest (K=0), in the absence of external fields
(V=0), then the change in energy of a system is given by Equation 3.
∆E = ∆U = q + w
Where q represents the heat gained by the system and w represents work done on the system.
(3)
It is meaningless to ask how much heat or work a system contains since they are not state
functions and there are defined only in terms of processes. For infinitesimal processes, Equation 3
becomes:
dU = dq + dw
(4)
When you have a closed system that can only do P-V work (pressure-volume work), and the
volume is constant, the first law becomes:
dU = dqv
(6)
Taking the partial derivative of at constant volume with respect to temperature, Equation 6
becomes:
 ∂U 
 
 ∂T  V
=
dq V
dT
≡ CV
(7)
Where Cv is the heat capacity at constant volume of a closed system for infinitesimal processes.
The energy of combustion of an unknown can be calculated using temperature changes for the
combustion and the heat capacity of a constant volume calorimeter according to Equation (1):
i= j
UV
=
∑u
v ,i
m i . = C V ∆TCOMBUSTION
(8)
i =1
Where UV represents the energy of combustion at constant volume, uv,i represents the energy of
combustion of component i (per gram at constant volume) mi represents the mass of the substance
combusted, CV represents the heat capacity of the system’s surroundings (the “bomb” and all of its
components, the excess oxygen, and the water surrounding it) at constant volume and ∆T
represents the temperature change of the combustion process.
In order to combust an unknown in a Parr bomb calorimeter, the system (in this experiment, a
pellet of breakfast cereal) is ignited with a nickel fuse wire. In order to account for the energy of
combustion of the wire, Equation 8 is modified as follows.
UV
= u V ,UNKNOWN mUNKNOWN
+ u V ,FUSE mFUSE
= u V ,UNKNOWN mUNKNOWN
+ 1400
cal
mFUSE
g
(9)
Where uV,FUSE = 1400cal/g and is the nickel wire’s energy of combustion per gram (alternatively,
use 2.3cal/cm) and mFUSE is the mass of the fuse wire that is combusted (otherwise, use the length
of the fuse wire).
The heat capacity of the calorimeter can be calibrated by combustion of a known such as benzoic
acid. It can be determined using Equation 9.
CV
=
UV
∆TCalibration


cal
 u V , BenzoicAcid m V ,BenzoicAcid + 1400 mFUSE 
g

= 
∆TCalibration
(10)
Where uV,BenzoicAcid = 6318cal/g, the benzoic acid’s energy of combustion.
NOTE: Copies of the operating manuals for the PARR bomb calorimeters are linked to the home
page (following the link to this experiment) and also available in the laboratory. You will find them
a useful as a general guide during the preparation and performance of the experiment. If you have
difficulty reading the operating manuals linked to the lab’s home page, you may access the
complete manual via the following link: http://www.parrinst.com/doc_library%5Cmembers
%5C457m.pdf
PRE LABORATORY EXERCISE
Include answers to the following questions in the preliminary report for this experiment. SHOW
ALL WORK!
1. State the first law of thermodynamics five different ways with at least three stated as
mathematical equations. Indicate assumptions when applicable.
2. Is the heat transferred to the water surrounding the bomb equal to the enthalpy of combustion
(∆H) or the internal energy of combustion (∆U)? What information is needed in order to find
the other value?
3. Assuming complete combustion of the fuse wire, what is the maximum mass of benzoic acid
that would keep UV < 1000 calories?
4. Pick a breakfast cereals (brought from home) and estimate its heat of combustion at 298
Kelvin. Use the value to calculate appropriate sample sizes for your experiment
measurements.
5. In lieu of calibrating the calorimeter with benzoic acid, use the data in Table 1 to calculate the
average heat capacity of the calorimeter. In addition, calculate the relative standard deviation
of the heat capacity using the data in Table 1. Be sure to show use units and show your
calculations.
Since time for this experiment is limited, you will use this value in order to determine the
energy of combustion of your breakfast cereal.
TABLE 1: BENZOIC ACID CALIBRATION TRIALS*
Benzoic Acid Mass (g)
TRIAL
Container
Container
+ Pellet
1
0.4497
2
Nickel Fuse Wire (g)
Temperature (oC)
Initial
Final
Initial
Final
0.6543
0.0161
0.0051
22.2550
25.8093
0.4450
0.6403
0.0157
0.0076
22.1780
25.5098
3
0.4241
0.6255
0.0164
0.0058
22.2040
25.8873
4
0.4241
0.6281
0.0160
0.0020
21.6770
25.3194
5
0.4171
0.6193
0.0152
0.0035
21.7900
25.4471
6
0.4441
0.6489
0.0168
0.0034
21.7860
25.1989
* Dewar contained 450.00g +/- 0.01g of distilled water for each trial.
LABORATORY PROCEDURE
Note: You will not be calibrating the calorimeter using benzoic acid. Instead, you will use the
calibration data from Table 1 to determine the heat capacity of your calorimeter.
1.
Prepare a sample of your breakfast cereal. It may be more convenient to use appropriately
sized samples taken directly from the container, rather than crushing the sample and making
pellets with the pellet press.
NOTE: You may wish to avoid particularly dry cereals such as Rice KrispiesTM and Shredded
WheatTM brands. These two brands do not readily form pellets. Unfortunately, samples of
Rice KrispiesTM taken directly from the container are too small to cause a significant rise in
temperature.
2.
Combust each of your samples, recording temperatures every few seconds. Baselines are
usually established when temperature changes are less than 0.003 between readings.
3.
Determine the temperature change for combustion of each sample. Repeat measurement
enough times to determine the reproducibility (i.e., the standard deviation) for the energy of
combustion of your group’s cereal.
4.
Prepare a composite table of data and results including all measured quantities and calculated
results. Include notes about any observation(s) during the experimental operation.
Important Safety Considerations
Do not exceed 1,000 calories and/or the maximum sample size of benzoic acid (standard)
or breakfast cereal. Note that a "food calorie" is equivalent to a kilocalorie. Show an
instructor your sample size calculation before beginning.
Ask for assistance the first few times you pressurize the bomb calorimeter with oxygen.
Do not exceed a pressure of 30atm with the P. Chem. Lab pressure regulator used to fill
the bomb.
The cereal/breakfast food you bring to lab must be labeled, “Not for ingestion" and
discarded after collection of your data. NOTE: The maximum amount of cereal needed to
complete 6 trials will be << 1/4 serving!
REFERENCES
Bernard L.Cohen and Catherine A. Schilken , “Calorie Content of Foods”, Journal of Chemical Education, Volume 71,
Number 4. April 1994, pages 342-345.
Parr Instrument Company, “6725 Semi micro Oxygen Bomb Calorimeter Operation Instruction Manual, No. 457Ml”,
Illinois, 2005.
Ira N. Levine, Physical Chemistry, 5th Ed., McGraw-Hill Companies, Inc., New York, 2002b pp. 35-51.