Bomb Calorimetry

University of Nebraska at Omaha
Bomb Calorimetry
Physical Chemistry 3354

Enthalpy of Combustion:
1,2-diphenylethane

January 6, 2014
Author:
Jon D. Paul

Signature

Professor:
Dr. Edmund Tisko

Date

Abstract
Experimentation involving constant volume calorimetry produces the heat of reaction for many substances. When choosing adiabatic conditions we are allowed to focus on the reaction system while neglecting everything else. The reactions that are studied should proceed relatively quick without interfering side reactions. In this experiment, three trial measurements were conducted on benzoic acid using a Parr 1241 calorimeter. Enthalpy values were compared to primary literature values in order to quantify the accuracy of the procedure as well as proper functionality of equipment. Finally, a
10 g sample of 1,2-diphenylethane was obtained and analyzed. four trial measurements were conducted and the mean enthalpy of combustion was obtained.

Table of Contents
1 Introduction to Bomb Calorimetry

2

2 Materials & Experimental Procedure
2.1 Safety . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.1 Combustion Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4
4
5
5

3 Conclusion: Experimental Results & Error Analysis

6

Appendix A. Derivation of [Acid/Base] using Beer’s Law

7

Appendix B. Data and Graphs

8

1

1

Introduction to Bomb Calorimetry
Calorimetry is a composed of the Latin word, calor (heat) and the Greek word, meter (measure).

From this, bomb calorimetry occurs when a substance is ignited in the presence of oxygen gas. The enthalpy of combustion is measured provided that we are at isochoric conditions. The most common components of a bomb calorimeter are depicted below:1

Figure 1: Cross Section of Series 1300 Plain Calorimeter. Bomb unit on right1
A thermistor is connected to measure both inner and outer jacket temperatures. We are most concerned with the inner jacket as this will allow us to calculate the internal energy given our final temperature. Notice the leads entering the bomb unit - this allows electricity to flow from the wire causing combustion upon exposure to oxygen gas. This ignition is controlled by a switch on the control machine which also contains water bath controls. The bomb unit contains a holder for the sample as well as holes to insert the fuse wire. There are two gas valves located on the bomb cover: an input and an output. The bomb should be flushed once or twice with oxygen gas before the experiment proceeds
- this ensures that all gases from the air are no longer trapped inside the bomb unit.
Accurate combustion analysis rests heavily on the inner jacket’s ability to restrict heat flow to the surroundings. With this in mind, the construction of the bomb unit allows us to make many assumptions that simplify our work. The first assumption is that the reaction occurs at constant volume. This implies there is no work or heat flow and the system is declared independent of its surrounds.2

wcalorimeter =
1
2

pdV = 0

http://ntweb.deltastate.edu/vp academic/jbentley/teaching/labman/bomb/bomb1.htm http://www.chem.hope.edu/∼polik/Chem345-2000/bombcalorimetry.htm 2

(1)

qcalorimeter = 0

(2)

qcalorimeter = −qreaction

(3)

Equation three emphasizes the isolation of the calorimeter from the rest of its surroundings. The sample mass and oxygen gas are the system; the bomb enclosure and water are the surroundings. From this we can see that:3
∆Utotal = ∆Usystem + ∆Usurrounding = 0

(4)

∆Usystem = −∆Usurrounding

(5)

If we know the specific heat of the calorimeter we can calculate the energy release. In this experiment benzoic acid is used to calculate the specific heat capacity of the calorimeter. Benzoic acid burns nicely with a known specific heat value of -26.43 kJ/g.4 We also use the specific heat of the fuse wire which was calculated to be -5.858 kJ/g.5 . From these values constant volume heat capacity can be determined from the following equations. q = −Ccalorimeter m∆T
Ccalorimeter = −

∆Q
∆T

(6)
(7)

∆c Qtotal = ∆c Qsample + ∆c Qf use

(8)

−Ccalorimeter ∆T = ∆c Qsample + ∆c Qf use

(9)

∆c Qsample =

−Ccalorimeter ∆T − ∆c Qf use
Msample
msample

(10)

Now that we have an equation calculating the enthalpy of combustion for benzoic acid, the change in enthalpy of combustion of the calorimeter is found by relating ∆H and ∆Q. We know that at constant pressure these two values would be the same; however, in a combustion reaction the moles of gas is always changing. We can express this equation by assuming that the gases behave ideally:6

∆c Hsample = ∆c Qsample + ∆ngas RTcombustion

(11)

Using standard enthalpy of reaction we must subtract the molar enthalpies of the reactants from the products; both the products and reactants are multiplied by their stoichiometric coefficient, υ. In
3

http://www.uni-ulm.de/∼hhoster/pc lecture/Calorimetry 1.pdf http://www.chm.davidson.edu/ronutt/che115/Bomb/Bomb.htm 5 http://www.unomaha.edu/tiskochem/Chem3354/Bomb calorimetry.pdf
6
http://www.csun.edu/∼jeloranta/CHEM355L/experiment1.pdf
4

3

this case the reactant is oxygen gas and the product is carbon dioxide:7

dH =

δH δT δH δP dT +
P

(12)

0

0

υO2 µO2 CpO2 dP −

∆HP =

dP
T

1

υCO2 µCO2 CpCO2 dP

(13)

1

Using these corrections allows us to manipulate equation 11 to include standard temperature with fluctuating pressure. This reduces our equation to:5

o
∆c Hsample = ∆c H + ∆HP

(14)

The standard enthalpy of combustion for benzoic acid was determined using equation 14 and the following combustion reaction:8

C7 H6 O2 (s) +

15
O2 (g) → 7CO2 (g) + 3H2 O(l)
2

(15)

Experimentation was conducted on 1,2-diphenylethane to obtain the enthalpy of reaction using its combustion reaction:
C14 H14 (s) +

2

35
O2 (g) → 14CO2 (g) + 7H2 O(l)
2

(16)

Materials & Experimental Procedure

2.1

Safety

- Approximately 1.0000 g of primary reagent grade benzoic acid were used in each trial combustion.
Benzoic acid causes eye, skin, and respiratory irritation with symptoms of vomiting and diarrhea9
- Approximately 1.0000 g of primary reagent grade 1,2-diphenylethane were used in each trial combustion.
1,2-diphenylethane may cause irritation to bodily system and should be handled with care.10
- Distilled water is generally safe but should not be consumed due to possible contamination from other laboratory chemicals.
- The fuse wire containing zinc, copper, aluminum, silver, or alloys may cause skin irritation.
7

http://www4.ncsu.edu/∼franzen/public html/CH201/lecture/Lecture 7.pdf http://www.ualr.edu/rebelford/chem1402/q1402/X2/C6/6-3/6-3.htm 9 http://avogadro.chem.iastate.edu/MSDS/benzoic acid.htm
10
http://terpconnect.umd.edu/ choi/MSDS/Sigma-Aldrich/BIBENZYL.pdf
8

4

2.2
2.2.1

Procedure
Combustion Analysis

The beginning of the experiment involved burning benzoic acid to pinpoint laboratory accuracy through technique/methods and to verify mechanical operations in the bomb calorimeter are working properly. Results are only as good as the error in our machinery and technique. In a more important aspect, the mean enthalpy of combustion of benzoic acid will be used to calculate the enthalpy of reaction for 1,2-diphenylethane.
The outer and inner jacket were maintained at constant temperature using a chiller and heater.
Thermistors were connected and LabView was used to output digital temperature readings. Measuring the temperature allows us to conclude any change in temperature comes solely form the combustion reaction once the sample is ignited. Purging was done to allow the temperature of the outer bucket to equilibrate with the inner jacket temperature.
A sample of benzoic acid is weighed to approximately 1 gram on a 0.01 gram analytical balance.
The sample is compressed to a pellet using two punches and a die. The pellet is weighed accurately to
0.0001 g. A sample fuse wire was measured to the nearest 0.0001 g. The bomb unit was opened and a
1.00 mL of distilled water was added. This 1 mL saturates the atmosphere with water vapor allowing all water formed by the reaction to be converted to liquid water. The pellet is placed on the sample holder and the fuse wire is allowed to nest gently on the surface of the benzoic acid.
The bomb is flushed with 30 atm of oxygen gas to release all gaseous air trapped inside. The bomb is filled with 30 atm of oxygen gas and placed in the inner bucket. The bucket is filled with 2 L of distilled water. The accuracy of this measurement is crucial to ensure that all trial runs are done under constant heat capacity.11 The bucket is loaded into the inner jacket compartment and the inner and outer jacket temperatures were allowed to equilibrate.
Once the temperatures remained constant, the sample is ignited and the initial temperature is recorded. The temperature is allowed to reach its maximum peak - this is the final temperature used in the enthalpy calculation. Once this is finished, the procedure is repeated twice more. 1,2-diphenylethane is then combusted in three trials using the same procedure.
11

http://python.rice.edu/∼brooks/Chem381/LabManual/Ch4.pdf

5

3

Conclusion: Experimental Results & Error Analysis
The enthalpy of formation for 1,2-diphenylethane was calculated using the following manipulation

using equations 13 and 14; literature values for the molar enthalpies of formation were obtained:12

o
∆f Hsample (s) =

o
∆f Hsample (s) =

[∆Hi ]products −

−(7)285.820 − (14)393.520

[m∆HI ]reactants

kJ
35 kJ kJ −
0
51.55 mol 2 mol mol (17)
= −7561.52

kJ mol (18)

The constant volume heat capacity was determined using the mass benzoic acid and fuse wire. The standard enthalpy of combustion for the fuse wire and benzoic acid were provided and can be seen in appendix A. Statistical analysis was performed on the three trials runs to obtain the average internal energy of the system. The data is shown below:
Table 1: Statistical analysis performed on constant volume heat capacity for benzoic acid
Statistical Analysis
Sample Size
Mean Cυ
Standard Error
Standard Deviation
Student’s T 95%
Confidence Limits 95%

3
10059.0332 ◦J
C
4.0803
7.0673
4.303
17.5572

Once this data was obtained, the average constant volume heat capacity was converted to

J
.
C◦

This

value was converted to ∆U for the total system by multiplying by the change in temperature. ∆c Uf use was found using the provided ∆c Uf use value (-5858 J ). The enthalpy of combustion was then found and g corrected at each temperature. The moles of O2 and CO2 were found and converted to atmospheres.
This was then used to find ∆Hpressure . Equation 14 was then applied to find the enthalpy of combustion at standard conditions. The results are depicted below:
◦
Table 2: Statistical analysis performed on ∆c Hbibenzyl

Statistical Analysis
Sample Size
Mean Cυ
Standard Error
Standard Deviation
Student’s T 95%
Confidence Limits 95%

3
-7492.9308 ◦J
C
90.2164
156.2594
4.303
388.1699

Th
12

http://www.ohio.edu/mechanical/thermo/property tables/combustion/Enth Formation.html

6

Appendix A. Derivation of [Acid/Base] using Beer’s Law

1

Aλ1 =

HA
1

Aλ1 −

1

HA

[HA]

2

HA

= [A− ]

HA

2

[HA]

1

A−

HA

2

1

A−

HA

1

2

A−

=

A−

(Aλ1 ) −

1

A−

1

I = 0.5

2
A−

(Aλ1 ) −

(Aλ1 ) −
1
−
HA

1

A−

(Aλ2 )

1

HA

A−

1

A−

(A-7)

(A-8)

2

(A-9)

HA

(Aλ2 )

1
A−

−

HA

1

2

(0.005L)(0.04M N aOAc) 2
(0.005L)(0.04M N aOAc)
|1| +
| − 1|2 +
(.100L)
(.100L)
(0.0096L)(0.5N aCl) 2
(0.0096L)(0.5M N aCl)
0.5
|1| +
| − 1|2
(.100L)
(.100L)

7

(A-6)

1

A−
2

2

− Aλ2

1
A−

A−

A−

(Aλ1 )

(Aλ2 )

A−

[HA] =

A−

(A-5)

− Aλ2

1
A−

1
A−

2

HA

1
A−

2

[HA] =

−

[HA]

1

HA

(Aλ1 )

A−

A−

=

HA

(A-4)

1
A−

2

2

−

1
A−

2

[HA]

HA

[HA] =

HA

1

A−

2

A−

2

2

[HA]

1

HA

−

1
A−

−

1
A−

[HA]

A−

[HA] +

(A-3)

1
A−

(Aλ1 )

2

2

Aλ2 =

(A-2)

Aλ1 −

2
A−

[HA] +

(A-1)

[A− ]

A−

1
A−

Aλ2 =

[A− ]

1

[HA] =

HA

Aλ1 −

1
A−

[HA] +

(A-10)

(A-11)

Appendix B. Data and Graphs
Absorbance of 2,4-dinitrophenolate & 2,4-dinitrophenol
Molar Mass
Concentration (g/L)
[A− ] or [HA]
0.02031
0.01625
0.01219
0.008124
0.004062

of 2,4-dinitrophenol = 184.10636
Absorbance 320 nm Absorbance 253 nm
[A− ]
[HA]
[A− ]
[HA]
0.7732
1.2929
0.6019
0.6658
0.6040
1.0377
0.4833
0.5339
0.4540
0.7791
0.3689
0.3988
0.3084
0.5141
0.2429
0.2692
0.1542
0.2599
0.1185
0.1364

Table B-1 - Molarity and obtained absorbance values for acid and base forms of 2,4-dinitrophenol

Absorbance & pH of Buffers units of g/L−1 cm−1
[A-] 320 nm
36.80
[HA] 320 nm
63.97

320 nm
0.6776
0.6725
0.6656
0.6581
0.6538
0.6367

[A-] 253 nm
30.04
[HA] 253 nm
32.55

Table B-2 constants obtained from absorbance vs. concentration regression analysis

253 nm
1.1662
1.1453
1.1191
1.1019
1.0840
1.0280

pH
3.039
3.238
3.377
3.492
3.613
3.889

Corr. pH
3.076
3.275
3.414
3.529
3.650
3.926

Table B-3 - pH & absorbance of buffer solutions

2,4-dinitrophenol Buffer Solutions
2,4-DNP 0.2031g/L
10mL
10mL
10mL
10mL
10mL
10mL

0.04 M NaOAc
5mL
10mL
15mL
20mL
25mL
50mL

0.05 M NaCl
9.6mL
9.2mL
8.8mL
8.4mL
8.0mL
6.0mL

Table B-4 - Method of creating buffer solutions

8

1.0 M HOAc
10mL
10mL
10mL
10mL
10mL
10mL