Bomb calorimetry. The goal of this experiment was to use temperature data over time from combustion reactions to calculate the heat released and then produce an experimental value for the heat of formation of naphthalene.

Considering the combustion of the system for both sample and the cotton fuse,

∆cUsample + ∆cUcotton = 0                                                                 (6)

The volume is constant (calorimeter bomb), and if the heat capacity Ccal of the calorimeter is known, the measurement of the water bath temperature change (∆T) provide directly a measurement of the internal change for the system:

∆cUsample + ∆cUcotton = -CV∆T                                                                 (7)

By definition of enthalpy, this in the present case is enthalpy of combustion:

∆H         = ∆U + ∆ (pV)         

        =∆U + ∆ (nRT)

        = ∆U + ∆ ngas RT                                                                (8)

∆H and ∆U would be identical only if the pressure in the bomb remains constant. However, for combustion reactions, the molar amount of gases changes (∆ ngas). Assuming that the gaseous components in the bomb behave according to the ideal gas law, Eq. (8) becomes:

∆cHosample         = ∆cUosample   + ∆ngas RTf

= - ∆cUocotton   -  CV∆T  + ∆ngas RTf                                         (9)

The temperature was approximated as the mean temperature of the system before and after the reaction.  This approximation probably resulted in significant error.

Enthalpies of formation of naphthalene

10C(s) + 4H2(g)  C10H8                                        ∆fHo                         (10)

C(s) + H2(g)  CO2 (g)                                        ∆Ho=-393 kJ/mol         (11)

H2(g) + 0.5 O2 (g)  H2O (l)                                        ∆Ho=-285 kJ/mol        (12)

C10H8 (s) + 12 O2 (g)  10 CO2 (g) + 4 H2O (l)                 ∆cHo                        (13)

By Hess’s Law, the sum of the change in enthalpy over the combustion cycle must be zero, and therefore

∆fHo        = ∆Ho1 - ∆cHo                                                                        (14)

Where ∆Ho1 is the standard enthalpy of combustion of the appropriate number of moles of carbon and hydrogen to form carbon dioxide and water, hence, the eq.(15) becomes:

∆fHonapthalene        = ∆Ho1 - ∆cHo

                = ∆HoCO2+  ∆HoH2O - ∆cHonaphthalene                                         (15)

Methods

The experimental method was similar to that used in the practical manual (CHEM220 chemical Reactivity, Laboratory note, UNE, 2012). The experiment was run twice, for benzoic acid and for naphthalene. The bomb calorimeter used is similar to that shown in figure 1.

Some of the precautions used to insure that experimental is successful. For example, the bomb was cleaned and dried; we made sure that no bits of iron were left on the terminal.

Figure 1. Schematic drawing of the bomb calorimeter (CHEM220 chemical Reactivity, Laboratory note, UNE, 2012).

The pellet and the wire and the cotton were installed into the bomb, the wire touching the terminals. See table1 below for the weights of the platinum wires and pellets and the cotton. The bomb was assembled carefully and the cap was screwed hand-tight. Then the bomb was attached to the oxygen filling apparatus at 1000 Pa.

Table 1. The samples data for the combustions

(± 2% is the accuracy on the fairly simple apparatus used)

The temperature were read and recorded every minute for 5 minutes (the first five results in Table 2) before firing the bomb. The bomb was then fired and recorded the time and temperature every 30 seconds until 15 minutes after the temperature reaches to maximum (From minute 5.30th to the end, Table 3).

After 48 minutes for benzoic acid combustion and 45 minutes for naphthalene combustion (Counting from the samples were burnt), all benzoic acid and naphthalene has been burnt and no specks of carbon on the walls.

Finally, all parts of the bomb were cleaned and dried.

Results

The heat of combustion of naphthalene was experimentally calculated to be -4982.66 ± 99.6532 kJ mol-1 and the enthalpy of combustion of naphthalene was experimentally determined to -4983.1522 ± 99.6630 kJ mol-1 which was a 3.44% error from the literature value of -5160 ± 20kJ/mol (NIST Chemistry WebBook, 2008). In order to calculate these results, the heat capacity of the calorimeter had to be determined by combusting benzoic acid, which had a known heat of combustion value.  The heat capacity of the calorimeter was 0.0699 kJ K-1.  The uncertainty of each calculation in this experiment was determined by completing a propagation of error calculation.

The thermodynamic of naphthalene combustion

Making the run:

We began time-temperature readings, reading the precision thermometer every 30 seconds and recording the time and temperature (Table 3).

Table 2. Temperature versus time recording for benzoic acid and naphthalene combustion

The plots of temperature vesus time for both from data plot given in table2 are shown in figure 2 and figure 3

Figure 2. Temperature versus time for benzoic acid combustion

Figure 3. Temperature versus time for naphthalene combustion

The data from Figure 2 was used to calculate the heat capacity of the calorimeter using equation (7).  This step was necessary since the purpose of this experiment was to calculate the enthalpy of combustion of naphthalene, which could only be accomplished if the heat capacity of the vessel in which it was combusted was known.  Figure 3 is a plot of the data obtained from the naphthalene combustion. To use the data in Figures 2 and 3, information needed to be known about the mass of substances being combusted during the process.  Also, in order to calculate the heat capacity of the calorimeter, the heats of combustion of both benzoic acid and the fuse wire were needed.  

The calculating the temperature rise in the calorimeter is as in the following equation:

T = Tf -Ti-(dT/dt)i(td-ti)-(dT/dt)f(tf-ti) 

From the graphs in figure 2 and figure 3 we determined the initial and final drift rates as follows: (dT/dt)i =0, (dT/dt)f =0

Thus,         For benzoic acid, ∆T= 20.3 – 12.3 - 0 - 0 = 8.0 oC = 281K

For naphthalene, ∆ T= 23.2 – 15.5 – 0 - 0 = 7.7 oC = 280.7K

The eq. (7) rearranges to CV = (∆cUbenzoic acid+ ∆cUcotton)/(- ∆Tbenzoic acid) 

CV         = (-26.434 kJ/g x 0.7408 g– 0.059 kJ)/[- 281 K]

        = 0.0699 kJ K-1

Moles of  C10H8 used = nnapthalene=  0.5025g(1mol/128g)] = 0.003926 mol

Moles of O2=(0.003926 mol C10H8 )x(12mol O2/1mol C10H8)= 0.047112 mol O2

Moles of CO2=(0.003926 mol C10H8)x(10molCO2/1molC10H8)= 0.03926mol CO2

Thus, ∆ngas= Moles of CO2 -Moles of O2= 0.03926mol - 0.047112 mol = -0.0007852 mol

Hence the eq.(7) give ∆cUonapthalene = [- ∆cUcotton -CV∆Tnapthalene]/ nnapthalene

 ∆cUonapthalene          = [-(-0.059kJ) – 0.0699 kJ K-1x 280.7K]/ 0.003926 mol

  = -4982.66 kJ mol-1

From the eq.(9), the enthalpy of naphthalene combustion ∆cHonapthalene is

∆cHonapthalene          = [-4982.66 kJ mol-1x 0.003926 mol -0.0007852 mol x 8.3145 x 10-3 kJ mol-1K-1x (23.2+273)K]/ 0.003926 mol

= -4983.1522 kJ mol-1

However, ± 2% is the accuracy on the fairly simple apparatus used, hence, ∆cUonapthalene and

∆cHonapthalene  in this combustion are

∆cUonapthalene = -4982.66 ± 99.6532 kJ mol-1

∆cHonapthalene  = -4983.1522 ± 99.6630 kJ mol-1

Enthalpies of formation of naphthalene

From the eq.(15), Theoretical Enthalpies of formation of naphthalene using Hess’s Law is

∆fHonapthalene        = (10x(-393kJ/mol)+4x(-285kJ/mol)) - (-4983.1522 kJ/mol)

                =  -86.8478 kJ/mol

However, ± 2% is the accuracy on the fairly simple apparatus used, hence, ∆fHonapthalene is

∆fHonapthalene = -86.8478 ± 1.736956kJ/mol

Percent Error (ΔHcombustion,naph(s))

The literature value for the enthalpy of naphthalene combustion from NIST Chemistry WebBook (2008) was -5160 ± 20kJ/mol

% error = |1-Experimental value/literature value|x100%

        = |1-(-4982.66)/(-5160)|x 100%

        = 3.44%                                  

Discussions

This experiment was a success as each objective of the experiment was completed and the experimentally determined enthalpy of combustion of solid naphthalene was very close to its literature value.  There was a 3.44% error between the experimental enthalpy of combustion of solid naphthalene and the literature value from NIST Chemistry WebBook (2008). There were some main sources of error in this experiment associated with the bomb calorimeter such as balance, themometer and the graphical estimation of ∆T, etc. For example, one source of error was that exactly the same amount of water needed to be used to immerse the bomb in both trials for the best results.  The water was measured out using the human eye and therefore, the accuracy of its measurement is not reliable.  The other main source of error is that the actual combustion of either solid was not the only source of heat transfer in the calorimeter.  Stirring in the calorimeter produced a certain amount of heat and then another certain amount of heat was lost through the walls of the calorimeter.

The results of this experiment would be useful for calculating other thermodynamic properties of naphthalene, since many of those calculations would require that the enthalpy of combustion of naphthalene be known. 

Consequently, the heat of combustion of naphthalene was experimentally calculated to be -4982.66 ± 99.6532 kJ mol-1 and the enthalpy of combustion of naphthalene was experimentally determined to -4983.1522 ± 99.6630 kJ mol-1 which was a 3.44% error from the literature value of -5160 ± 20kJ/mol (NIST Chemistry WebBook, 2008) and the enthalpy of formation was -86.8478 ± 1.736956kJ mol-1. In order to calculate these results, the heat capacity of the calorimeter had to be determined by combusting benzoic acid, which had a known heat of combustion value.  The heat capacity of the calorimeter was 0.0699 kJ K-1.  The use of bomb calorimetry to calculate the heat of combustion of naphthalene was successful due to the low error between the experimental results and literature values.

References

Experiment 1, CHEM220 chemical Reactivity, Laboratory note, UNE, 2012

F. Daniels, J.W. Williams, P. Bender, R.A. Alberty, C.D. Cornwell, and J.E. Harriman, (1970). 'Experimental Physical Chemistry', 7th ed, McGraw-Hill, 18

G.P. Mathews, (1985). “Experimental Physical Chemistry”, Oxford University Press,80.

Mashkevich S. V., (1995). “Statistical Theory of an Adiabatic Process”, Phys. Rev. E. 51: 245 – 253

NIST Chemistry WebBook. (2008). NIST Standard Reference Database Number 69. Material Measurement Laboratory. United States Secretary of Commerce.

P.W. Atkins, (1998).  “Physical Chemistry,” 6th ed, Oxford University Press .55

R.J. Sime, (1988). “Physical Chemistry. Methods, Techniques and Experiments” , Saunders College Publishing,420