Download H/ t = W/m

Determination of the Heat of Combustion
of Cysteine and Cystine
Submitted by:
Sigmund Kulessa
Alyson Lease
Amit Mehta
Sarah Tao
April 29, 1998
Abstract:
The primary objective of this experiment was to calculate and compare the heats
of combustion of cysteine and cystine using the Parr Instrument Model 1341 Oxygen
Bomb Calorimeter. The calculated heat of combustion value for cysteine was found to be
4140.90 + 23.50 cal/g, and the heat of combustion for cystine was found to be 3852.14 +
69.97 cal/g. The experimental integration of Labview software and a thermocouple, was
used as an alternative method for recording temperature data. The combustion values with
this method varied by 1.14% from the values found using the Parr thermometer, and the
thermocouple was proven statistically to be a viable alternative for gathering combustion
data.
1
Background:
Calorimetry is the science of measuring heat based on the change in temperature
that occurs during the energy exchange between a reaction system and its environment.
This exchange in energy can be measured using a thermally insulated container known as
a calorimeter. The calorimeter and its contents are considered the environment while the
reaction system refers to the chemical or physical process that occurs within the confines
of the container(2).
Standard heats of combustion are precisely defined thermodynamic quantities
which are measured at STP (1 atm, 298 K). In this process, the entire compound is
burned in a pure oxygen environment, and any carbon, hydrogen, and nitrogen atoms are
assumed to be converted to CO2 (g), H2O (l) , and N2 (g). (The presence of sulfur creates
additional reactions that will be discussed.) In the bomb calorimeter, the reactants are
converted to products by the following general process.
C(T1)
+
R(T1) 
C(T2)
+
P(T2)
Where C represents the calorimeter, R is the reactants (O2 and the experimental
compound), T1 and T2 are the initial and final temperatures, and P signifies the products
(CO2, H2O, N2).
During this experiment we used a non-adiabatic Parr Bomb Calorimeter to
determine the heat of combustion of cyteine and cystine. The specific reaction that
occurs during the combustion of cystine is:
C6H12N2O4S2 (c) + 10O2 (g)

6CO2 (g) + N2 (g) + 2(H2SO4(2.7H2O)) (l) – 1.4H2O(l)
The reaction for cysteine (C3H4NO2S(c)) is similar to cystine, but because cystine
is its dimer, half the products of this reaction are created. However, it is important to
note that the bond structure of cystine is not exactly the same as its monomer, cysteine.
Although the chemical structure of the two compounds is identical, an additional
disulfide bond forms between two monomers in the creation of the dimer. Because of
this, the heat of combustion generated by cystine was predicted to be close to twice the
combustion of cysteine, however, not exact.
In both reactions carbon reacts with oxygen to form CO2, and hydrogen reacts
with oxygen to form H2O. Nitrogen ultimately forms nitrates in this combustion reaction.
Since the nitrates can not exist by themselves, nitrate must combine with water vapor to
form nitric acid, hence giving the overall reaction: 2N2 + 5O2 + 2H2O = 4HNO3.
Cysteine and cystine both contain approximately 26.7% sulfur. The presence of
this element in our experimental compounds creates secondary reactions that ultimately
affect the overall heat of combustion. Sulfur, a versatile element, can act as either an
oxidizing or a reducing agent. In the reaction of cystine sulfur acts as a reducing agent
towards more electronegative compounds such as oxygen (to form SO2), but also acts as
an oxidizing agent towards less electronegative elements like hydrogen or carbon (for
example H2 + S = H2 S). In combustion reactions H2S reacts with more oxygen to form
pure sulfur (H2 S + O2 = 2H2 O + 2S). Thus eventually all sulfur will form sulfur dioxide
2
(S + O2 = SO2), and in less concentration, sulfur trioxide (2S + 3O2 = 2SO3). Sulfur
dioxide or trioxide then combine with water vapor to form sulfuric acid:
SO3 (g) + H2 O (l) = H2 SO4 (l)
2SO2 (g) + 2H2O (l) + O2 (g) = 2H2 SO4 (l)
Therefore the heat of formation of sulfuric acid must be accounted for in the total
combustion of sulfur containing compounds.
The value of the heat of combustion was found by the following formula:
Equation 1.
Gross _ Heat _ Of _ Combustion __( H g ) _ 
tW  e1  e2  e3
m
The variables involved in the above formula include the following:
a = time of firing
b = time(to nearest 0.1 min.) when the temperature reaches 60 per cent of the total rise.
c = time at beginning of period (after the temperature rise) in which the rate of
temperature change has become constant.
ta = temperature at time of firing, corrected for thermometer scale error.
tb = temperature at time c, corrected for thermometer scale error.
r1 = rate (temperature units per minute) at which temperature was rising during the 5-min.
period after time c. If the temperature was falling instead of rising after time c, r2 is
negative and the quantity – r2(c-b) becomes positive and must be added when computing
t he corrected temperature rise.
c1 = milliliters of standard alkali solution used in the acid titration.
c2 = percentage of sulfur in the sample.
c3 = centimeters of fuse wire consumed in firing.
W = energy equivalent of the calorimeter, determined under standardization.
m = mass of sample in grams.
t = tc – ta –r1(b-a) – r2(c-b) (corrected temperature) (Equation 2)
e1 = correction in calories for heat of formation of nitric acid (HNO3). = c1 if 0.0709N
alkali was used for the titration.
e2 = correction in calories for heat of formation of sulfuric acid (H2SO4) = 13.7*c2*m
e3 = correction in calories for heat of combustion of fuse wire = (2.3)(c3) when using Parr
45C10 nickel chromium fuse wire.
As stated, the combustion of cysteine and cystine are greatly influenced by secondary
reactions. As a result, the sulfur and nitrogen present in the oxygen bomb combine with
water vapor to form sulfuric and nitric acid. The correction factors given in the Parr
Instrument Manual take into account both secondary reactions by allocating correction
factors that are based on the difference between the heats of formation for nitric and
sulfuric acid (assuming that a 0.17N sulfuric acid solution was created). Hence e1 and e2
take into consideration the fact that 1 mole of nitric acid will react for every 2 moles of
sulfuric. Likewise, the additional energy generated in burning of the nickel chromium
fuse wire is accounted for in e3.
3
In this experiment we tested the feasibility of using an integrated thermocouple
with Labview software to increase the accuracy of the temperature recording procedure.
Human interaction with the calorimeter following firing requires periodic reading of the
water temperature. By automating temperature recording we hoped to reduce this
interaction, therefore eliminate virtually all human error that could result from reading
temperature.
A thermocouple consists of a junction of two dissimilar metals and an appropriate
two wire extension lead. A thermocouple operates on the basis of the junction producing
a small voltage which increases with temperature. It does so on a reasonably stable and
repeatable basis. A thermocouple has a very fast temperature response, but compared to
other thermoelements, for example RTD’s and thermistors, it lacks stability in the signal.
To compensate, a 16th order virtual low-pass Butterworth filter is used to filter out any
unwanted noise. A Butterworth filter is a filter whose pass-band and stop-band are both
smooth on the frequency response plot, but the slope of the cutoff is not very steep. This
is where LabView sparkles; LabView allows us to construct a virtual 16th order filter with
the very low cutoff frequency of 0.12 Hz at the click of a button. It would be
prohibitively complicated and arduous to physically wire this circuit, particularly for our
purposes.
4
Apparatus and Materials:
1. Parr Instrument Model 1341 Oxygen Bomb Calorimeter, including stirrer, precision
thermometer, and associated components
2. Parr Instrument Model 1108 Oxygen Combustion Bomb
3. High Pressure oxygen cylinder, equipped with Model 1825 filling connection for bomb
4. Parr Model 2901 Ignition Unit
5. Parr Pellet Press
6. Associated components for test, including sample cups, ignition wire (Parr 45C10 nickel
alloy fuse wire), stands for bomb head and calorimeter cover, thermometer magnifier.
7. Thermocouple unit, LabView
8. Beakers, electronic stirring rod, hot plate
9. Burette, 0.0709 N sodium carbonate solution, 0.709 sodium carbonate solution, methyl
red indicator, 300ml beaker, stirring rod, stirring plate
10. Mettler BD6000 electronic balance
11. Mettler PB303 electronic balance
12. Tap water (2000mL/trial) and distilled water
13. Benzoic Acid, Cysteine, Cystine, Sulfur (rhombic)
Procedure:
During the first week of experimentation, on April 2, the standardization
procedure for the Parr calorimeter was performed, as well as a calibration of the
thermocouple. Initially, the calorimeter was assembled as described in the Parr Operating
Instructions to standardize and find its heat capacity. Three standardization trials were
run using calorific grade benzoic acid as a reference material. The samples (between 0.9
and 1.25 grams) were prepared using the Parr Pellet Press, also described in the Parr
Instructions. The bomb calorimeter was then charged as described in Instruction Sheet
No. 205M. We attempted to adjust the temperature of the water by varying the amount of
composing hot and cold water and were unable to attain a set degree for the initial
temperature. However the starting temperature for each trial was within one degree
Celsius. The calorimeter bucket was filled with the water and the bomb carefully set in
the calorimeter. The jacket (with thermometer) was then placed on the cover and the
stirrer was allowed to run for five minutes. During this time the temperature was
recorded at one-minute intervals for the remainder of the experiment. At the sixth minute
the bomb was fired in the method described in the Parr Operating Instructions.
Following the last temperature reading the gas pressure was released and the interior
surfaces of the bomb were washed with distilled water. The unburned fuse wire was
measured to determine the fuse wire correction. The bomb washings were titrated, using
0.0709N sodium carbonate and methyl red as an indicator, to account for the acid and
sulfur correction. We found the energy equivalent of our Parr calorimeter to be 2463.35
cal/C.
In order to calibrate the thermocouple, an apparatus consisting of a hot plate, a
beaker of water, an electric stirring rod, and a mercury thermometer was set up. Utilizing
the fact that the Parr company already calibrated the mercury thermometer and provided
5
error charts, this thermometer was used to calibrate the thermocouple (subsequently, the
same thermometer was used during the experiment). Both the thermometer and
thermocouple were placed in the beaker of water. The hot plate was used to slowly raise
the temperature as the stirring rod allowed the water to maintain a uniform temperature.
The Virtual Bench software was used to read voltage, while the mercury thermometer
was used to read temperature. These values were used to create a calibration curve in
order to determine the relationship between voltage and temperature (0C). The time delay
constant of the thermocouple was found by placing the thermocouple in three consecutive
beakers of water that varied in temperature. It was held in the first beaker for 20 seconds
then removed for 20 seconds before being placed in the next beaker. LabView was used
to record voltage as a function of time. This data was used to compute the period of the
voltage change. The time delay constant, defined as 63% of total response time, was
found to be 3.593 seconds for an 11.7 0C rise.
A thermocouple unit was used in conjunction with a GPIB analog to digital
converter and LabView software. The thermocouple was taped to the thermometer in
order to collect temperature readings during combustion. There was a small time delay
when starting the Lab View program (or VI) and a longer period (about 12 seconds) for
the temperature readings to come to equilibrium when the VI was first started. Since we
were comparing the thermometer and thermocouple data, both the stopwatch and
LabView had to be synchronized. To overcome the delay problems, a push-button switch
connected between ground and input was used to put a spike in the data, designating the
initial point for the trial. At first a 1 point per second sampling rate was used in an
attempt to control the number of points in the data file, but the curve was not smooth
enough. 20 points per second was found to work much better.
By the second week, April 9, the thermocouple had been successfully calibrated,
and the heat of combustion of cysteine was ready to be determined. The amount of
cysteine available was only sufficient to run two trials with an approximate sample size
of 0.9 grams. The bomb and calorimeter were prepared corresponding with the directions
in the Parr Instruction Manual. The firing procedure, as described in the standardization
procedure and Parr manual, was followed. Before titrating, we were able to calculate the
expected amount of 0.0709 sodium carbonate needed to neutralize the cysteine
combustion bomb washings to be approximately 207 mL. The amount of unburned fuse
wire and titration results were used to determine heat correction factors. This procedure
was applied to both trials of cysteine and our first trial of cystine.
During the third week, April 16, the same preparation and firing procedure was
used for the combustion of three additional trials of cystine. However during the titration
procedure, the amount of solution used was reduced by using a 0.709N sodium carbonate
solution. Before calculating the heat of combustion, this value was multiplied by ten in
order to determine the appropriate acid and sulfur correction. All other correction factors
were made corresponding to the Parr manual.
During this week, two trials were run combusting a mixture of cystine and added
sulfur. In order to double the mass percent of sulfur in the sample from 26% to 53%, we
calculated that the mass ratio of cystine to sulfur needed was 0.75g to 0.2g. These
amounts were measured for both samples. The cystine and sulfur were combined and
mixed as thoroughly possible and pelleted using the pellet press. Some mass may have
been lost during the pelleting process, however we assumed the mass percent of sulfur to
6
remain approximately 53%. During these trials, all other preparation and firing
procedures remained the same. The bomb washings from these trials were titrated with
0.709 sodium carbonate as well in order to reduce the amount of solution used. The heat
of combustion correction factors were determined as previously mentioned. From our
data, we were able to calculate and compare the heat of combustion values of cysteine,
cystine, and cystine with additional sulfur.
7
Results
From our trials, the average heat of combustion of cystine was found to be
3852.14 + 69.97 cal/g, while the average heat of combustion of cysteine was found to be
4140.90 + 23.50 cal/g.
Table 1: The following table summarizes the results of the experiment for the heats of
combustion.
Heat of Combustion Data
Thermometer
Thermocouple
Literature
Heat of Comb., cal/g Heat of Comb., cal/g Value
Trial
1
4124.283
4075.343
2
4157.522
4080.714
Mean
4140.90
4078.03 4473.42 + 0.5 *
St. Dev.
23.50
3.80
3
3941.256
3940.773
4
3773.767
3703.596
5
3830.269
3801.955
6
3863.258
3816.122
Mean
3852.14
3815.61 4225.14 + 0.9 **
St. Dev.
69.97
97.30
* literature value of the heat of combustion for cysteine, expressed in calories per gram
** literature value of the heat of combustion for cystine, expressed in calories per gram
Trials 1 and 2 are for the combustion of cysteine, while trials 3 through 6 are for the
combustion of cystine, the dimer of cysteine. As the chemical bonding in cystine is not
quite the same as cysteine, the mean heat of combustion for the two compounds, though
given in calories per gram, will inherently be slightly different. The values found through
the use of the mercury thermometer are given in the first column, whereas the values
found through the use of the thermocouple are given in the second column. The heats of
combustion were calculated by the formula described in the BE210 Laboratory Manual,
as summarized in the background. (see Equation 1)
In Table 2, we compared the value for the heat of combustion of cystine for each
of our trials to the three values listed in the NIST Chemistry WebBook. Literature Value
1 was derived by Becker and Roth in 1934, while Literature Value 2 was derived by
Huffman and Ellis in 1935, and Literature Value 3 was derived by Cox and Pilcher in
1970. The table also includes the mean percent deviation of experimental values as well
as the standard deviation. The values seen in Tables 2 and 3 are percentages; for
instance, in the first column, the mean with error correction is (7.71 + 1.67) %.
8
Table 2: Percent Deviation of Heat of Combustion Values from Literature Values for
Cystine (combustion values are in cal/g)
Lit. Value 1 Lit. Value 2 Lit. Value 3
4178.53
4207.24
4225.14
With error correction
Trial 1
3941.2563
Trial 2
3773.7674
Trial 3
3830.2692
Trial 4
3863.2583
mean
standard dev.
Without error correction
Trial 1
4168.4164
Trial 2
4153.4173
Trial 3
4186.3641
Trial 4
4215.4774
mean
standard dev.
5.68
9.69
8.33
7.55
6.32
10.30
8.96
8.18
6.72
10.68
9.35
8.56
7.81
1.67
8.44
1.66
8.83
1.66
0.24
0.60
-0.19
-0.88
0.92
1.28
0.50
-0.20
1.34
1.70
0.92
0.23
-0.06
0.64
0.63
0.63
1.05
0.63
In Table 3, we compared our actual values for the heat of combustion of cysteine to three
of the literature values in NIST Chemistry WebBook These three literature values were
derived by the same scientists noted above and chosen to correspond with the scientific
procedure used to determine the literature values for cystine. Included in the Table 3 is
the mean percent deviation and the standard deviation when comparing the values.
Table 3: Percent Deviation of Heat of Combustion Values from Literature Values for
Cysteine
Lit. Value 1 Lit. Value 2 Lit. Value 3
4396.67
4436.28
4473.42
With error correction
Trial 1
4124.2830
Trial 2
4157.5225
mean
standard dev.
Without error correction
Trial 1
4377.6440
Trial 2
4301.2601
mean
standard dev.
9
6.20
5.44
7.03
6.28
7.80
7.06
5.82
0.53
6.66
0.53
7.43
0.53
0.43
2.17
1.32
3.04
2.14
3.85
1.30
1.23
2.18
1.22
2.99
1.21
Figure 1: Temperature-Time Plot for the third cystine combustion trial. The line
indicates the linear increase in temperature in the bomb calorimeter, which
includes the point at which the temperature is at 60% of its total rise.
Temperature Rise Curve
27.8
Temperature (Celcius)
27.6
27.4
27.2
27
26.8
R2 = 0.9981
26.6
26.4
26.2
26
25.8
0
2
4
6
8
10
12
14
Time (M in)
The first four points show the temperature in the water in the bomb calorimeter, prior to
ignition. Following ignition, which occurred at the end of the 5th minute, the temperature
rose steadily, reaching 60 % of its total rise in 1.5 minutes. This time was found by
estimating the point at which the temperature had reached the 60 % mark, and then
calculating the time at this point by the slope of the line for the rise (see Figure 1). This
was possible to do since the temperature-time relationship was approximately linear
through the 7th minute, as seen by the R2 value, which was 0.9981. After the rapid rise
period, which lasted until about the 11th minute, the temperature reached a maximum, and
then dropped off slightly. The error bars display an error of + 0.005 C, which is the
precision of the thermometer used.
Figure 2: Thermocouple calibration of voltage versus temperature.
Thermocouple Calibration
3.5
y = -0.0448x + 4.6404
R2 = 0.9999
Voltage (V)
3.45
3.4
3.35
3.3
3.25
25
26
27
28
29
Temperature (Celcius)
10
30
31
The equation of the trendline relates temperature in Celsius and voltage by the
relationship Voltage = (-0.0448)*(Temperature, oC) + 4.6404. The range of the
temperatures used for the calibration is based on the average temperatures over which the
combustion reactions for cysteine and cystine occur (assuming the initial temperature is
about room temperature).
Thermocouple vs. Thermometer
Table 4: Comparison of results for the thermocouple and the thermometer over the
cysteine and cystine combustion trials.
Thermometer vs. Thermocouple
Trial
1
2
3
4
5
6
Thermometer
Thermocouple
% difference
Heat of Comb., cal/g
Heat of Comb., cal/g
(in heat of comb.)
4124.283
4157.522
3941.256
3773.767
3830.269
3863.258
4075.343
4080.714
3940.773
3703.596
3801.955
3816.122
Mean
St. Dev.
1.19
1.85
0.01
1.86
0.74
1.22
1.14
0.70
Combustion data was gathered using both the thermometer and the thermocouple for each
trial. The average percentage difference in the results between the two methods was 1.14
+ 0.70.
Error Analysis
Several sources of error in the thermometer and thermocouple were accounted for
mathematically.
T-test Analysis
Table 5: The following is a portion of the t-test performed between each trial.
Thermometer
Trial 3 vs. 4
Mean
Variance
t Stat
t Crit. 1-tail
Thermocouple
Trial 3 vs. 4
Trial 3 vs. 5
Variable 1 Variable 2
25.4920
26.8317
0.0729
0.0622
-68.8342
2.9200
Mean
Variance
t Stat
t Crit. 1-tail
Variable 1 Variable 2
25.4920
26.3960
0.0729
0.0861
-66.5835
2.9200
11
Mean
Variance
t Stat
t Crit. 1-tail
Variable 1 Variable 2
25.6637
26.7872
0.0550
0.0659
-75.5000
2.9200
A test of significance, the t-test, was implemented in the analysis of the trials. The t-test
is helpful in determining whether the difference between two values is statistically
significant, or just due to random error. In the comparison of all the trials, the t-stat was
always less than the t-critical, indicating that there is no significant difference between
the means. However, in some trials, the t-stat was much less than the t-critical, while in
other trials the difference was much closer. Statistically, the greater difference between
these two values translates into a greater probability that there is no significant difference
between the means. The values shown in Table 3 are among the highest differences
between t-stat and t-critical. The t-test was used on the temperature data from the
experiments, since the rise in temperature corresponds directly with the value of the heat
of combustion of the compound. Thermometer data was not compared with
thermocouple data using the t-test, instead, the test of analysis of variance was used.
Analysis of Variance
In order to test the consistency of the two methods, the analysis of variance test was
implemented. The test allows one to calculate a ratio and compare it to statistical tables;
if the ratio is greater than the corresponding table value, then something other than just
sampling error is leading to the differences between two groups. The following data and
calculations were used to calculate the “analysis of variance” ratio. The two “groups”
compared were the thermometer data and thermocouple data.
Table 6: Data from trials necessary to performing calculations for analysis of variance.
For cystine trials, no additional sulfur
# of observations mean
variance
thermometer (Group A)
4 3874.849 4953.175
thermocouple (Group B)
4 3838.108 9578.478
The following formulas are used to calculate the “analysis of variance” ratio.
Grand Mean = Y
= [(# observationsA)*(Group meanA) + (# observationsB)*(Group meanB)]
(total observations)
= 3856.48
_
-
_
-
Numerator of Ratio =  [(YA – Y) + (YB – Y)2]
(k-1)
= 1349.96
2
Denominator of Ratio =  (Yij – Yi)2/(total observations –2)
= 7265.83
where k = (number of groups)
YA = mean of Group A
Yi = mean of Group A or B
12
Yij = heat of combustion of the jth trial in Group I
Analysis of Variance Ratio = 0.1858
Thus the variance between the groups can be attributed to sampling error and not to
anything fundamental to the methods themselves. See discussion for further
interpretation of the analysis of variance test.
Estimation of Systematic Uncertainty Interval (for trials using the thermometer)
Hg = (tW – e1 – e2 – e3)
m
H/t = W/m
H/m = -(tW – e1 –e2 –e3)/m2
H/W = t/m
t = 1.58 C
m = 0.941 g
W = 2463.35 cal/C
e1 = 292.15
e2 = 3.440
e3 = 15.64
t = 0.005 C
m = 0.0005 g
W = 16.40 cal/C [standard deviation from standardization]
H/t = 2617.8
H/m = -4044.0
H/W = 1.68
H = [((H/t)(t))2 + ((H/m)(m))2 + ((H/W)(W))2]1/2
= 30.57 cal/g
the error in the heat of combustion when using the thermometer is 30.57 cal/g. The
method of estimation of systematic uncertainty interval allows one to quantify the
uncertainty due to systematic sources of error in an experiment. This is different from
random sources of error, which can be analyzed through standard statistical techniques
such as the mean and variance of a set of data. The following is the error in the heat of
combustion when using the thermocouple.
13
Estimation of Systematic Uncertainty Interval (for trials using the thermocouple)
Hg = (tW – e1 – e2 – e3)
m
H/t = W/m
H/m = -(tW – e1 –e2 –e3)/m2
H/W = t/m
t = 1.58 C
m = 0.941 g
W = 2463.35 cal/C
e1 = 292.15
e2 = 3.440
e3 = 15.64
t = 0.02 C
m = 0.0005 g
W = 16.40 cal/C [standard deviation from standardization]
H/t = 2617.8
H/m = -4044.0
H/W = 1.68
H = [((H/t)(t))2 + ((H/m)(m))2 + ((H/W)(W))2]1/2
= 59.20 cal/g
the error in the heat of combustion when using the thermocouple is 59.20 cal/g.
Results of the variation of the percentage of sulfur in the sample
As another validation for our results, we used trials 8 and 9, which contained
cystine + sulfur, to calculate the heat of formation of sulfuric acid. The general theory
behind these calculations was that the heat of combustion of cystine with additional
sulfur, should be equivalent to the heat of combustion of cystine portion plus the heat of
formation of sulfuric acid, or:
Htotal (cystine+sulfur) = (mass of cystine) * Hcomb (cystine) + (mass of sulfur) * Hf (H2SO4)
The heat of combustion of cystine + sulfur (Htotal) is the average heat of combustion
generated from trials 8 and 9 (thermometer-3497.525 cal/g, thermocouple-3486.63 cal/g),
and the heat of combustion of cystine (Hcomb (cystine)) is the average combustion value
calculated in the cystine combustion trials (thermometer-3852.14 cal/g, thermocouple3815.61 cal/g). Using this method we calculated the heat of formation of sulfuric acid in
calories per gram and compared it to the CRC Handbook value. The heat formation of
14
sulfuric acid calculated from this method as seen in Table 5 in comparison with the
literature value was found to be accurate to approximately 8.86%.
Table 7: Comparison of Heat of Formation of Sulfuric Acid.
Avg. Heat of Comb.
Hf H2SO4 (calories)
Hf H2SO4 (KJ/mol)
Percent Deviation
(Lit. Val. = 814 kJ/mol)
Thermometer Thermocouple
3497.5253
3486.6309
437.0902
426.8495
896.6535
875.6455
10.15
7.57
Least Significant Bit
The least significant bit (LSB) is the inherent error in any analog to digital
conversion. The LabView-Thermocouple setup samples discrete data at intervals of
1mV, which corresponds to 0.022 0C. In the worst case scenario, the percent error due to
LSB was calculated to be 3.1%. This calculation was done using equation 1. The values
of m, W, and the correction values do not affect the percent error possibly due to the
LSB. The corrected t value is the only concern. (rewritten here for convenience.)
t = tc – ta –r1(b-a) – r2(c-b) (corrected temperature)
a and c are the firing time and the quiescent time, respectively. Because of the stability
of the thermocouple data, c should be unaffected by temperature values. a is always
independent of temperature. The last two terms in Equation 2 are assumed to be
independent of temperature for the following reasons. Each point in the rise may be
separately affected by the LSB, but statistically (comparing the minimum and maximum),
the slope is not greatly affected. Therefore, the 60% point, b, should be more or less
unaffected by any deviation in the rise due to the digital conversion. Furthermore, r1 and
r2, although very small in the thermometer data (~10-3) are most often zero in the
thermocouple case. This is obvious considering that the thermocouple data is very stable
and the variations in the r1 and r2 regions are in the thousandths of a degree, while the
thermocouple measures with accuracy of 0.022 0C. Therefore, the error due to the LSB
can be assumed to be contained completely within tc and ta. One more assumption that is
made is the initial value of t. Out of the eight trials performed, the lowest t value, 1.47
(highest value in all trials is 1.58), is used, which will result in the highest percent error.
Using this information the maximum error due to the digital conversion is estimated to be
3.1%. In practice, the error between thermometer and thermocouple averages 1.14% with
a maximum value of 1.86%.
15
Discussion
The average heat of combustion of cystine was found to be 3852.14 + 69.97 cal/g,
while the average heat of combustion of cysteine was found to be 4140.90 + 23.50 cal/g.
In order to find the precision of our experiment, we applied the t-test with 95%
confidence limits between each trial; the t-stat value was always found to be less than the
t-critical value, indicating that there is no significant difference between the means. (see
Table 5, Results) When compared to the literature value of the heat of combustion of
cystine and cysteine, the experimentally determined values deviated from the literature
value by 8.83% for cystine, and 7.43% for cysteine. (see Table 2 and 3, Results)
“Literature value 3” was used for comparison, since it was established more recently, and
consequently more contemporary methods and equipment were used.
The deviation of our results from the literature value could be associated with
both experimental and systematic error. As shown by the t-test, the error in the
experiment was most likely due to sampling error. This embodied itself in several forms.
For one, the conditions in the laboratory varied week to week, and as a result, it was
difficult to maintain a consistent environment. Several sources of error can be identified
as to why the experimental heat of combustion varied from the literature value. First of
all, the conditions of the water we used were not ideal. Instead of using deionized water,
we used regular tap water, and without checking to see if it contained less than the 250
ppm of dissolved solids. The unknown content of the water may have affected the rise in
temperature during the experiment.
Another source of error lies in the initial temperatures of the trials, as we were
unable to achieve the same initial temperature for each of the trials. After measuring the
water, we allowed it to either cool down or warm up to room temperature. However, we
found that the temperature of the room was constantly fluctuating due to random
conditions (i.e. movement in the room, the draft from an opening door) and was closer to
23 C rather than the standard 25 C. This created a problem due to the fact that the
lowest marker on the thermometer was at 23.8 C. If the water we used was to be
approximately 1.5 C below room temperature, we would not have been able to read the
temperature of the water. Part of the error in the thermometer was taken into account by
adding the appropriate values from the thermometer correction table supplied by the Parr
Instrumentation Company, and part was corrected by the formula supplied for the rise in
temperature (see Background). Since the variation in initial temperature was not believed
to have a great effect on experimental error, these corrections were considered sufficient.
During the experiment, there was also a degree of measurement and human error.
Errors in measurement may have occurred during the reading of the length of the fuse
wire following the completion of the combustion process. Since it was difficult to get
perfectly straight, the measurement of the wire was inaccurate to a certain degree. The
ruler used during the reading also had an error of 0.5 mm.
The uncertainty due to systematic error was quantified by the method of
estimation of systematic uncertainty interval.(see Results) In the results attained by use
of the thermometer, the error in the heat of combustion was calculated to be 12.84 cal/g.
A major source of systematic error can be attributed to the procedure and equipment
used, as will be discussed later.
16
The Parr manual uses certain error corrections to account for side reactions that
generate an appreciable amount of heat, which cannot be credited to the sample. These
equations are based upon the heat of formation of 0.1N HNO3 and 0.17N H2SO4, as
described briefly in the background and in detail in “Discussion of Calculations” of the
Parr manual. As seen in Table 2, we found the heat of combustion for all our trials of
cystine deviated significantly from the most recent NIST literature value, 4225.14 cal/g,
existed for each trial. Our mean value for the percent deviation was 8.83+ 1.66%. One
observation we made was that when the acid and sulfur corrections were eliminated from
our calculations for the heat of combustion, the percent deviation decreased to
approximately 1.05 + 0.63%. This observation was also made for the heat of combustion
of cysteine, as seen in Table 3. Using the standard t-test, our data was proven to be
consistent, meaning that little variation existed between our trials. This consistency in
our data and the large percent deviation existing between our value and the literature
value for the heat of combustion of both cystine and cysteine lead us to believe that our
procedure for acid and sulfur corrections were different than those used in calculating the
NIST values.
From the protocol of Cox and Pilcher in Thermochemistry of Organic and
Organometallic Compounds, we found that a difference in procedure for sulfur correction
did exist. From Tables 2 and 3 we can see that of the three literature values presented,
our results deviated the least (7.81 + 1.67% for cystine and 5.82 + 0.53% for cysteine)
from the literature number one values, found by Becker and Roth in 1934. This may
have been due to the fact that the procedure for the static bomb used by Becker and Roth
was the most similar to ours. However, during their experiment, Becker and Roth were
able to show that when combustion calorimetry is performed with static bombs, the
sulfuric acid solution produced varies in concentration at different parts of the bomb.
This imposes a limitation on overall accuracy due to the relatively large heat of dilution
of sulfuric acid and the uncertainty from the multiplicity of acid concentrations. Huffman
and Ellis, who found the literature number 2 values in 1935, attempted to reduce this
uncertainty by not adding water to the bomb before combustion. The theory behind their
procedure was that the sulfuric acid would form a fine mist of uniform concentration on
the walls of the bomb. However, Cox and Pilcher, who found the literature number 3
values, found that the sulfuric acid could be brought to a single, definite concentration
more satisfactorily by the use of rotating bomb calorimeter. They found that by initially
adding a known volume of water (~10 ml) to the bomb before combustion, and rotating
the bomb after combustion, the sulfuric acid solution produced was of a definite
concentration. With the known concentration, the appropriate heat of formation of
sulfuric acid could be found and applied in determining the correct sulfur correction.
The variation of sulfuric acid concentration in different areas of our bomb reduces
the accuracy of the correction for sulfur. The sulfur correction is directly dependent upon
the heat of formation of sulfuric acid and the concentration of the sulfuric acid. This
affect of sulfur concentration on heat of formation can be seen in the Appendix. Because
the sulfuric acid concentration within our bomb is not constant and therefore unknown,
we cannot base our sulfur correction on the heat of formation of 0.17N H2SO4 as stated in
the Parr manual.
Other correction factors used by Cox and Pilcher may have also contributed to the
deviation between their literature value and our actual value. For example, their
17
calculations for the heat of combustion of organosulfur compounds were derived from the
analysis of all combustion products. This analysis included gravimetric determination of
carbon dioxide, titrimetric determination of total acid in the bomb solution, and
gravimetric determination of sulfuric acid content of an aliquot of the neutralized
solution. The amount of nitric acid was estimated by subtracting the number of
equivalents of sulfuric acid from the number of equivalents of total acid and form an
aliquot of the neutralized bomb solution. Sulfur dioxide as a minor product was
determined by a suitable reagent (e.g. acid potassium dichromate solution) or by a
colorimetric test. Tests for nitrogen oxides in the bomb gases were also applied as well
as an analysis for nitrous acid by the Griess-Ilosvay reagent.
In order to compare the consistency in data acquisition between the thermocouple
and the Parr thermometer, several statistical analyses were performed. To prove that, in
all likelihood, the differences in the results between the two techniques were only due to
sampling error, the analysis of variance test was performed. The logic of the test is that
under the null hypothesis, the differences between the group means will be small relative
to the variability within the groups. The two groups are considered to be the heat of
combustion data acquired by the thermocouple and the heat of combustion data acquired
by the thermometer; the group mean is the mean of the heat of combustion found for
each group.(see Table 4, Results) Furthermore, the test assumes that the samples are
normally distributed, and that there is not a great deal of variance in sampling error
within any group. Applying the appropriate formulas, the ratio was found to be 0.1858,
much less than the number that would have to result for something other than sampling
error to be considered to be playing a role in the variance between the groups.
Additionally, this result allows one to state that there is more variability within each
group relative to the difference between the group means. As a result, it is safe to
conclude that the thermocouple is a viable alternative to the thermometer for the
acquisition of combustion data.
When the t-test was performed within each group, the t-stat was always found to
be less than the t-critical. However, the difference between the t-stat and the t-critical
was not always the same, indicating there was a certain degree of variance within each
group. Thus the thermocouple data is also fairly precise, further lending itself to being an
alternative to the thermometer for gathering data. The advantages of using the
thermocouple are its superior timing, readability, and its “fire and forget” capability.
Another test that was performed in the experiment was the variation of the
percentage of sulfur in the compound combusted. This was done to verify our
combustion data from pure cystine, and calculations were preformed as follows. We
assumed that the total heat of combustion of the cystine and elemental sulfur mixture in
trials 8 and 9 could be divided into its component parts. Because 78.72% of the
compound was composed of cystine, we assumed that this portion of the total generated
heat of combustion was comparable to that of the pure cystine trials. Enough sulfur was
added to maintain a 53% sulfur concentration (which is approximately double the original
26.7% sulfur concentration of cystine) which reacted in the bomb by reducing oxygen to
form SO2 and oxidizing less electronegative elements such as hydrogen and carbon. All
of this sulfur eventually formed sulfur dioxide (S + O2 = SO2), and in lesser
concentration, sulfur trioxide (2S + 3O2 = 2SO3), which then combined with water vapor
to form sulfuric acid. We used the value of the heat of combustion for cystine
18
determined experimentally in our calculations to find the heat of formation of H2SO4. If
the heat of formation calculated compared well with the handbook value, then the heat of
combustion found for cystine must be fairly accurate. When compared to the literature
value for the heat of formation of sulfuric acid (814 kJ/mol), the calculated heat of
formation was approximately 8.86% accurate between the thermocouple and the
thermometer.
The accuracy of this calculation may have been limited by the exact percentages
of both sulfur and cystine in the pellet. When these chemicals were weighed individually
on the Mettler BD6000 electronic balance their mass was correct to the hundredth of a
gram. However, after being thoroughly mixed and pelleted, the samples lost between 0.01
and 0.023 g. The composition of the mass lost was unknown; it may have been pure sulfur,
cystine, or any combination of the two. This would slightly vary the percentages of the
original components in the pellet, which may have ultimately led to a deviance from the
literature value.
Another factor that may have caused the 8.86% error was the formation of SO2
and SO3 that did not go on to form H2SO4. Enough water was formed from the
combustion of cystine convert only 76% of the sulfur to sulfuric acid. The rest of the
sulfur present in the bomb most likely remained as SO2 and in a lesser concentration,
SO3. For this reason, the heat of formation of these additional components may have
distorted the value of the heat of formation of sulfuric acid found mathematically. In our
calculations, we assumed that the difference between the heat of combustion of the
experimental mass and the overall heat of combustion of the mixture could be attributed
to the heat of formation of H2SO4. However, if all of the sulfur did not ultimately form
sulfuric acid, part of this difference must be due to the heats of formation of other
compounds, such as SO2 and SO3. As the heat of formation calculated for sulfuric acid
was found to be 8.86% higher than the handbook value, it stands to reason that the value
is elevated due to a fraction of this number arising from other compounds.
The value of the heat of formation of sulfuric acid could also have been affected
by the varying pH of sulfuric acid as discussed above. This was not believed to play a
major role, however, this was a factor that could have led to some error.
In conclusion, based on these findings, the Parr Instrument Model 1341 Oxygen
Bomb Calorimeter does adequately combust sulfur and nitrogen containing compounds
such as cysteine and cystine. Additionally, the thermocouple was proven to be a viable
alternative to the thermometer for collecting combustion data.
19
Appendix
Effects of Concentration on the Heat of Formation of Sulfuric Acid
Negative Heat of
Formation at Constant
Volume (calories)
Concentration vs. Heat of Formation of Sulfuric Acid
y = -938.51x 2 + 6790.1x + 125337
R2 = 0.9878
140000
138000
136000
134000
132000
130000
128000
126000
124000
Series1
Poly. (Series1)
0
1
2
3
4
5
Moles of Water/Moles of Sulfuric Acid
Huffman and Ellis used the value of the heat of formation of sulfuric acid given by Roth,
Grau, and Meischner and the data of Bronsted for the heat of dilution of concentrated
solutions to calculate the values of the heat of formation of sulfuric acid at several
concentrations. The above plot was made from their data values. It was found that as the
concentration of sulfuric acid becomes more dilute, its heat of dilution increases,
decreasing its heat of formation (increasing the negative heat of formation).
20
References
1. BE 210 Bioengineering Laboratory II Laboratory Manual.
2. Bull, Henry B. An Introduction to Physical Biochemistry. Philadelphia: F.A. Davis
Company, 1971, pp. 32-38.
3. Campbell, Neil. Biology. 4th Edition.
4. Cox, J.D.; Pilcher, G, Thermochemistry of Organic and Organometallic Compounds,
Academic Press, New York, 1970, 1-636.
5. CRC Handbook of Chemistry and Physics. 49th Editions. The Chemical Rubber Co.,
1969, p. D-188.
6. Hamburg, Morris. Statistical Analysis for Decision Making. Harcourt Brace & Co.,
Orlando, FL, 1994.
7. Huffman, H.M.; Ellis, E.L., “Thermal Data. II. The heats of combustion of l-cysteine,
of l-cystine, b-thiolactic acid and b,b'-dithiodilactic acid”, J. Am. Chem.
Soc., 1935, 57, 41-46.
8. Tinoco, Ignacio, Sauer, Kenneth, and Wang, James C. Physical Chemistry: Principles
and Applications in Biological Sciences. NJ: Prentice-Hall, Inc., 1978, pp. 42 44.
9. Zumdahl, Steven S. Chemical Principles. Lexington: D.C. Heath and Company,
1995, pp. 344-345.
21