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Bomb Calorimeter: A Simulated Experiment Melina Holmes Arizona State University CHM 343

Abstract The purpose of this experiment was to determine the molar enthalpies of 4 substances: Naphthalene, Sucrose, Benzil, and Eicosane. The combustion benzoic acid was used to estimate the heat capacity of the calorimeter and each sample was ignited at 300 psi of oxygen. Each sample was weighed at approximately 1.000 grams and placed in a bomb calorimeter with a preweighed iron wire. The change in temperature due to combustion was determined through extrapolating the temperature vs. time graphs of each substance and finding the vertical lines that yielded equal areas on both sides of the graph. The change in temperature was then used to calculate ΔU and ΔH. The calculated values of ΔU for naphthalene, sucrose, benzil, and eicosane were -5326 kJ/mol, -5650.87 kJ/mol, -6818.99 kJ/mol, -13300.92 kJ/mol, respectively. The calculated values of ΔH for naphthalene, sucrose, benzil, and eicosane were -5330.97 kJ/mol, -5650.87 kJ/mol, -6826.44 kJ/mol, -13353.12 kJ/mol respectively. Possible sources of systematic error include observational errors from measuring the temperature of the calorimeter, the masses of the samples, and the time in which each temperature was measured. More systematic errors include differences in water temperature as well as how much oxygen was released during the combustion process.

Introduction The purpose of this experiment was to determine the change in both the enthalpy (ΔH) and the internal energy of a system (ΔU) when a system undergoes combustion or burning when exposed to an excess of oxygen. For the experiment in question, the combustion of four different substances: Naphthalene, Sucrose, Benzil, and eicosane was observed and measured. Generally, combustion holds a great significance in society as it serves as a primary source of energy. For instance, combustion is found in numerous situations, such as cooking food, heating water, and providing electricity (2). What makes these all possible is the energy that is produced when a particular substance reacts with oxygen (2). In other words, understanding the fundamental components of combustion (such as ΔH and ΔU) means understanding the underlying functions of the more general processes that people are more familiar with. Combustion also allows for a better understanding of some key elements of thermodynamics and the processes involved in this branch of chemistry. This is because combustion involves foundational concepts such as how heat is transferred between a system and its surroundings as well as the overarching change in energy. How can we investigate combustion in a feasible manner? One device we can use is a bomb calorimeter, a device with a relatively easy-to-understand design. Moreover, bomb calorimeters allow us to have a control of how much heat is transferred between the system and its surroundings. Since combustion reactions are always exothermic, we would mainly be concerned with how heat is transferred out of the system. Bomb calorimeters provide insight into many different elements of both the organic and inorganic worlds, such as how complex compounds are formed/broken, their energetic properties, and even their structures (2).

The first kinds of calorimeters were produced in 1761, with Antoine Lavoisier coining the term calorimeter in 1780 in order to name the apparatus that he used to measure heat (3). Lavoisier, along with Pierre-Simon Laplace, used ice calorimeters to determine the amount of heat involved in chemical reactions by measuring the amount of heat needed to melt ice (3).

Experimental A wire was connected to the electrodes and the sample pellet was placed in the cup. The cup was placed at the bottom of the electrodes so that the wire touched only the cup and nothing else. 1 mL of water was placed into the bomb. The electrode assembly was then placed into the bomb before the bomb was capped tightly. Afterwards, the bomb was filled and flushed with oxygen at about 300 psi. The bomb was then placed on top of the raised area of the bucket with about 2000 mL of distilled water. The bucket was then placed in the shell and connected to the firing box before the lid assembly was placed on top of the shell. A belt was then placed on the lid in order to spin the stirrer and a thermometer was set in place as well. The sample was then ready to be burned. The temperature was then recorded at thirty second intervals and linearity was observed for at 5 minutes before the ignition was initiated. When the rise in temperature slowed down, the temperature was taken at one minute intervals until linearity was observed for five minutes. The data was then extrapolated to determine the time in which ΔT occurred.

source: Gary L. Bertrand, University of Missouri

Analysis & Results

ΔT(o C)

ΔT(oC) error

Sample

Weight (g)

Wire Before (g)

Wire After (g)

Water Temp (oC)

Room Temp

Ti (oC)

Tf (oC)

Benzoic Acid

1.0063

0.0240

0.0151

24.2

24.3

24.2 02

26.6 2.461 63

0.002

Naphthalene

1.0589

0.0246

0.0187

24.3

24.3

24.3 00

28.3 4.068 68

0.002

Sucrose

0.9884

0.0253

0.0166

24.2

24.3

24.2 00

25.7 1.512 12

0.002

Benzil

0.9965

0.0237

0.0211

24.4

24.3

24.3 99

27.3 2.987 86

0.002

Eicosane

1.0347

0.0269

0.0236

24.1

24.3

24.1 02

28.6 4.501 03

0.002

ΔT was extracted from each data plot by extrapolating the slope of the graph before ignition and the slope of the graph after ignition. The vertical line that yielded an equal area on both sides of the vertical line was created in order to find the moment in which the temperature changed in the sample. For benzoic acid, or the standard, ΔT was found in order to determine the approximate energy of the apparatus. The heats of combustion of the samples following benzoic acid were also determined using ΔT. An illustration of how ΔT was determined for all samples is provided here:

source: Gary L. Bertrand, University of Missouri

Sample

ΔT (K)

Ccal (J/K) 

ΔU (kJ/mol)

ΔnRT (J/mol)

ΔH (kJ/mol)

ΔHc (lit.) kJ/mol

Naphthalen 4.068 e

10826.33

-5326

-4971.77

-5330.97

-5150.09

Sucrose

1.512

10826.33

-5650.87

0

-5650.87

-5643.4

Benzil

2.987

10826.33

-6818.99

-7457.66

-6826.44

-6784.0

Eicosane

4.501

10826.33

-13300.92

-52203.60

-13353.12

-13316.4

Source for ΔHc (lit.) values: NIST Chemistry Webbook https://www.nist.gov/

Calculations:

Graph of all combustion reactions:

Group values for ΔU and ΔH:

Napthalene

Sucrose

Benzil

Eicosane

dH dU dH dU dH dU dH dU (J/mol) (J/mol) (J/mol) (J/mol) (J/mol) (J/mol) (J/mol) (J/mol)

Group -51320 -51320 -56477 -56476 -68005 -68004 -13297 -13297 62.11 25.94 11.33 84.57 34.23 90.84 606.84 574.43 1:

Group 2:

Ranel, Hope, and Nam

Leo, Dante, -52911 -52861 -52208 -52208 -66270 -66196 -13302 -13250 Clint, 48.88 94.93 39.24 39.24 96.126 63.41 050.18 021.17 and D

Group -51657 -51657 -56718 -56718 -68053 -68053 -13334 -13334 3: 12.33 12 32.13 32 40.24 40 723.02 723 Andrew

Group 4:

Alaa, Clare, -52466 -52417 -57272 -57272 -67998 -67961 -13521 -13495 Brianna, 87.88 29.94 97.71 97.71 38.64 20.19 952.86 923.69 Farshid

Hritik, Gilian, -51620 -51620 -56021 -56021 -68091 -68091 -13310 -13310 Tristin, 74.9 35.4 33 18.6 87 74 995.8 977.9 Hunter

Group 5:

Statistical Analysis:

Sample

Avg ΔU (J/mol)

Avg ΔH (J/mol)

Standard Deviation for ΔU (J/mol)

Standard Deviation for ΔH (J/mol)

Naphthalene

-5197539.642

-5199537.22

63988.54

59525.32

Sucrose

-5573954.424

-5573962.682

202493.13

181118.00

Benzil

-6766157.688

-6768399.2472

82040.76

79082.14

Eicosane

-13337844.038

-13353465.74

93615.17

95271.54

Discussion During the process of calculating ΔH for each unknown substance, there were many errors that could have possibly come into play. The first was the assumption of the ideal gas law in ΔH = ΔU + RTΔn. The value for T for each calculation was 299 K, which could have been different for others analyzing the same set of data. The temperature of combustion may have also been different for each sample, although the variance of the temperatures was not assessed in this report. Another source of error when making assumptions about the ideal gas law was that there was an exact loss of moles of oxygen that is demonstrated in each balanced chemical equation. Some oxygen may not have been fully converted to CO2 in the reaction, leading to a slight error

in determining Δn. Not knowing the specific heats for each substance was another hurdle that needed to be worked around. The magnitude of uncertainty in this experiment from the lack of knowledge about specific heat values of the sample can be demonstrated by the following Initial, Change, and Equilibrium (ICE) tables for each sample: C10H8 (s) + 12O2 (g) → 10CO2 (g) + 4H2O (l) Species

Initial moles

Upon rxn

After combustion X = 0.00824

C10H8 (s)

0.00824

0.00824-x

0

O2 (g)

256.899

256.899-12x

256.89933

CO2 (g)

0

10x

0.0824

H2O (l)

0

4x

0.03296

Fe (s)

4.405*10-4

4.405*10-4  -1.171*10-4  3.234*10-4

Fe2O3 (s)

0

1.171*10-4

1.171*10-4

Cv, prod = (256.89933)( Cv, O2) + (0.0824)(Cv, CO2) + (0.03296)(Cv, H2O) + (3.234*10-4)(Cv,Fe) + (1.171*10-4)(Cv,Fe2O3)

C12H22O11 (s) + 12O2 (g) = 12CO2 (g) + 11H2O (g)  Species

Initial moles

Upon rxn

After combustion X = 0.003093

C12H22O11 (s) 

0.003093

0.003093-x

0

O2 (g)

256.899

256.899-12x

256.89939

CO2 (g)

0

12x

0.037116

H2O (l)

0

11x

0.034023

Fe (s)

4.531*10-4

4.531*10-4  -1.0395*10 3.4915*10-4 -4

Fe2O3 (s)

0

1.0395*10-4

1.0395*10-4

Cv, prod = (256.89939)( Cv, O2) + (0.037116)(Cv, CO2) + (0.034023)(Cv, H2O) + (3.4915*10-4)(Cv,Fe) + (1.0395*10-4)(Cv,Fe2O3)

2C14H10O2 (s) + 31O2 (g) → 28CO2 (g) + 10H2O (g) Species

Initial moles

Upon rxn

After combustion X = 0.00474

C14H10O2 (s) 

0.00474

0.00474-x

0

O2 (g)

256.899

256.899-31x

256.89928

CO2 (g)

0

28x

0.13272

H2O (l)

0

10x

0.0474

Fe (s)

4.244*10-4

4.244*10-4  -1.3213*10 2.9227*10-4 -4

Fe2O3 (s)

0

1.3213*10-4

1.3213*10-4

Cv, prod = (256.89928)( Cv, O2) + (0.13272)(Cv, CO2) + (0.0474)(Cv, H2O) + (2.9227*10-4)(Cv,Fe) + (1.3213*10-4)(Cv,Fe2O3)

2C20H42 (s) + 61O2 (g) → 40CO2 (g)+ 42H2O (l) Species

Initial moles

Upon rxn

After combustion X = 0.003662

C20H42 (s)

0.003662

0.003662-x

0

O2 (g)

256899.43

256899.43-61x

256899.20

CO2 (g)

0

40x

0.14646

H2O (l)

0

42x

0.153804

Fe (s)

4.817*10-4

4.817*10-4  -1.477*10-4  3.34*10-4

Fe2O3 (s)

0

1.477*10-4

1.477*10-4

Cv, prod = (256.89920)( Cv, O2) + (0.14646)(Cv, CO2) + (0.153804)(Cv, H2O) + (3.34*10-4)(Cv,Fe) + (1.477*10-4)(Cv,Fe2O3)

These ICE tables and the underlying equations demonstrate how we can determine the heat of combustion of each substance through using stoichiometry as well as the specific heats for each species involved in the reactions. Depending on the values of these specific heats, the uncertainties for each sample will differ.

ΔH pertains to the both the final and the initial temperatures. This is because the difference between the final and initial temperatures, or ΔT, is used to determine the enthalpy of the reaction. The enthalpy of the reaction could not be determined without either value. The uncertainty in ΔT can also be used to estimate the uncertainty in ΔH. For example, the uncertainty in ΔT for naphthalene was +/- 0.002. The percent uncertainty equation can then be used with the calculation: 0.002/4.680 *100% = This equation can then be used to estimate the uncertainty for ΔH by creating the equation: 0.002 4.680

* 100% =

x 5330.97

* 100% solving for x, we get +/- 2.62 which can be a reasonable

estimate of the uncertainty for ΔH. The statistical errors from the group data is expressed by using averages as well as standard deviations. One noteworthy aspect of the above section is the standard deviation for the ΔU of sucrose, which was 202493.13 J/mol. This was the largest error among all other standard deviations, which could have been the result of many factors. The error in which this value was calculated could have been the result of the use of a different R value among each lab student. Another source of error could have been from a different mass of the substance for not only sucrose but the other samples as well. Because the simulator produced different masses at random, the difference between the masses for sucrose could have been the greatest among the differences for the other masses. Additionally, if the experiment were to be conducted in person, different mass likely would have been measured for any lab student.

References (1) Santos, A.; Ribeiro da Silva, M. Molecular Energetics Of Alkyl Pyrrolecarboxylates: Calorimetric And Computational Study. The Journal of Physical Chemistry 2013, 117, 5195-5204.

(2) What is combustion? https://www.bbc.co.uk/bitesize/topics/zypsgk7/articles/zcwxcj6#:~:text=The%20energy %20that%20the%20reaction,compounds%20of%20oxygen%2C%20called%20oxides (accessed Sep 25, 2020).

(3) Helmenstine, A. What Is a Calorimeter? https://www.thoughtco.com/definition-of-calorimeter-in-chemistry-604397 (accessed Sep 25, 2020)....