Experiment 2. Determination of Heating Value of a Solid Pure Substance Using Bomb Calorimeter

I. Objectives1. To determine the heating value of a solid pure substance such as

naphthalene using the bomb calorimeter2. To compare the experimental net calorific value of naphthalene to its

theoretical value

II.Theory

Combustion is a process where a substance reacts rapidly with oxygen, releasing energy in the form of light and heat. It refers to the reaction of one mole of a substance with oxygen to produce combustion products (Encyclopedia Britannica, n.d.). Combustion is an exothermic reaction and the heat evolved from this reaction can be measured by the principles of calorimetry.

Calorimetry is the science of measuring the heat produced in a combustion process. It is commonly used in determining the calorific value or heating value of substances using a bomb calorimeter. The heating value is defined as the quantity of heat released by the complete combustion of a unit mass of fuel with oxygen at a constant volume process. It is expressed as a unit of energy per unit mass or volume of the substance such as kcal/kg, kJ/kg, J/mol and Btu/m³ (Spectro Analytical Labs, 2015).

Water vapor is a product of combustion along with carbon monoxide and carbon dioxide. Two techniques are used to recover the quantity of heat contained in the water vapor. The Higher Heating Value (HHV), also known as the Gross Calorific Value or Higher Calorific Value, is determined when the water vapor from the combustion process is entirely condensed. It is the amount of heat produced by the complete combustion of a unit quantity of fuel. The HHV is obtained when all products of combustion are cooled down to the pre-combustion temperature and when the water vapor produced from combustion is condensed (The Engineering Toolbox, n.d.).

On the other hand, when the water vapor from combustion remains as a steam and its heat is not recovered, the Lower Heating Value (LHV) is determined. It is also known as the Net Calorific Value or Lower Calorific Value. The LHV is obtained by subtracting the latent heat of vaporization of water vapor, the energy required to change the state of water from liquid to vapor at constant temperature, from the HHV (The Engineering Toolbox, n.d.). Equation 1 shows the calculation of LHV where W is the ratio of weight of water in the combustion products and weight of fuel burned. The factor K is the latent heat of vaporization at the partial pressure of the vapor in the gas at standard temperature (Perry and Green, 2008).

Net ∆ HC=Gross ∆H c−K·W (1)According to Bright Hub Engineering (2012), heating value is the most

important parameter that determines the economics of the power plant operation. In power plants, it indicates the amount of heat released when the coal is burned. The coal used in power plants has a heating value between 9500kJ/kg and 27000kJ/kg. This determines how much fuel is required for the operation of power plants. The higher the heating value of the fuel, the lesser the amount of coal required per unit of electricity. A high heating value also means that the cost of the coal is higher ut is offset by the lower cost of logistics, storage and ash disposal.

1

The heating value of substances is commonly determined using a bomb calorimeter. A sample of the substance is allowed to burn inside a constant volume and oxygen-filled bomb calorimeter. According to Roos et al. (2010), the temperature changes within the calorimeter, the amount of the substance burned by the combustion process and the heat capacity of the calorimeter are the primary requirements in determining the heating value. Understanding the principles behind the mechanism of the bomb calorimeter is another requirement in calculating the heating value.

The mechanism of bomb calorimeter follows the First Law of Thermodynamics which states that energy is neither created nor destroyed. As mathematically expressed by Equation 2, it states that the change in the internal energy of a system U is equal to the amount of heat Q transferred between the system and surroundings and work W done on or by the system (Smith et al., 2011).

∆U = ∆Q + ∆W (2)Since the reaction inside the bomb calorimeter takes place at constant

volume and it is an adiabatic process, the change in work and change in heat is both equal to zero. Therefore, the change in internal energy is equal to zero.

The insulating jacket of the bomb calorimeter isolates it from the surrounding environment. The reactants inside the bomb, the sample and oxygen, are then considered as the system while the rest of the calorimeter are the surroundings (Roos et al.,2010). The change in the total internal energy ∆U total of the calorimeter is then equal to the summation of change in internal energy of the system ∆U system and the change in internal energy of the surroundings ∆U surroundings

as shown by Equation 3. Since it was previously stated that ∆U total is equal to zero, Equation 3 can then be simplified to Equation 4.

∆U total = ∆U system + ∆U surroundings (3)∆U system = -∆U surroundings (4)

In an experiment using a bomb calorimeter, changes in the temperature of the water are measured. During the combustion process, the heat released by burning the sample is equilibrated through the walls of the bomb cylinder into the surrounding water bath where the change in temperature is recorded. The increase in temperature of the system due to combustion is related to the heat of combustion of the sample by a constant of proportionality (Lamp et al., 2013). If the heat capacity Cv of the bomb calorimeter is already known, the change in the internal energy of the calorimeter can be calculated using Equation 5.

∆U = -Cv ∆T (5)The heat capacity of a bomb calorimeter is commonly determined through

calibration. If the bomb calorimeter is frequently used, it can’t be avoided that inaccurate results will be gathered. Calibration of the bomb calorimeter is usually done to reduce the inaccuracy. It is conducted by introducing a known amount of heat into the calorimeter by the combustion of a reference sample under controlled and reproducible operating conditions (Parr Instrument Company, 2007). Benzoic acid is commonly used as the reference sample because it is available in pure form and it burns completely in oxygen. Equation 6 shows the equation for calculating the heat capacity of calorimeter.

C v=−[ (∆U sample ) (msample )+(∆U fuse ) (mfuse ) ]

∆T (6)

2

However, the bomb calorimeter is only approximately adiabatic. In a real situation, a small amount of heat escapes the insulating jacket. Therefore, the change in heat is not entirely equal to zero. The stirrer also does work on the calorimeter. Nonadiabaticity of the bomb calorimeter is corrected for with an empirical radiative correction RC. The following equations show the calculation of the change of temperature accounting for the radiative correction.

RC = (5 ) (T18−T 12 )+(T 6−T 0)

6 (7)

∆T = T 12 - T 6 – RC (8)

Although change in internal energy ∆U is a useful quantity, chemists find the change in enthalpy ∆H more relevant (Lamp et al., 2013). The relationship of internal energy and enthalpy is facilitated by definition of enthalpy as shown in Equations 9 and 10. When the pressure inside the bomb calorimeter remains constant, the change in enthalpy is then equal to change in internal energy. Moreover, the molar amount of gases changes during combustion. Assuming that the gaseous components inside the bomb behave according to the ideal gas law, Equation 10 can be simplified to Equation 11. Equation 11 is also recognized as the equation used for calculating the Gross Calorific Value of substances.

H = U + PV (9) ∆H = ∆U + ∆(PV) (10) ∆ H=∆U+RT ∆ngas (11)

This experiment aims to determine the heating value of a solid pure substance which is naphthalene. Naphthalene is an aromatic hydrocarbon with a chemical formula of C10H8. According to Wheet (2011), naphthalene is used as a fuel for combustion in bomb calorimeters because it is commercially available and easy to handle. The combustion equation for naphthalene is given below.

C10H8(s) + 12O2(g) → 10CO2(g) + 4H2O(l) (12) In order to ensure to complete combustion, combustion chambers are

usually fired with excess air. Excess air increases the amount of oxygen and nitrogen entering the chamber and increases the probability that the oxygen will react with the fuel. It also increases turbulence which means increased mixing of air and fuel (Biarnes et al, n.d.). As more excess air enter a combustion chamber, more of the fuel is burned until it finally reaches complete combustion. Equation 13 shows the formula in calculating the percentage of excess air.

% Excess air = (Molesof air supplied )−(Molesof theoretical air)

(Molesof theoretical air) x 100

(13)An energy balance for water is needed in the experiment. The following

equations show energy balance to be used in calculating the amount of cold water and ambient water needed to make sure that the water temperature is at standard condition which is 25OC.

mcoldCpcold(25oC−T cold) = - mambientCpambient (25oC−T ambient) (14)Assuming that the heat capacities and densities of the cold and ambient

water have a small difference, Equation 14 reduces to Equation 15. V cold (25oC−T cold ) = −V ambient (25oC−T ambient ) (15)

3

Figure 3. Bomb head inserted to the bomb cylinder

Figure 2. Bomb head placed on the support stand

Figure 1. Pelletizer

III.MethodologyBomb Calorimeter Platinum fuse TowelAnalytical Balance Naphthalene GlovesPelletizer Water BasinThermometer Ice MaskDigital thermometer Graduated cylinder (1000mL) RulerOxygen tank Stirring rod Watch glass

1. Approximately 0.5g of naphthalene was weighed in the analytical balance. Precautions were done in the experiment such as making sure that mass of the samples did not exceed 1.5g. Gloves, safety goggles and masks were used when handling the sample for safety reasons.

2. The 0.5g naphthalene was formed into a pellet using the pelletizer which is shown in Figure 1.Before the pelletized naphthalene was transferred to the capsule, the empty capsule was weighed first. The mass of the capsule with the pellet was measured after.

3. The calorimeter used 3000mL of water at 25OC. Using energy balance, the volume of cold water and ambient water were calculated and then mixed to make sure that the water temperature is 25OC. The cold water was prepared using ice.

4. A 7cm length of platinum fuse was weighed and cut. As shown in Figure 2, the bomb head was set on the support stand and the capsule with the pelletized naphthalene was placed in the capsule holder.

5. The fuse was fastened between the two electrodes and it was bent to make sure it touched the top surface of the pellet.

6. The bomb head was moved from the support stand to the bomb cylinder. It was carefully inserted to the bomb cylinder as shown in Figure 3.

7. The screw cap was then firmly set on the cylinder and the bomb cylinder was closed. The gas release valve was closed while the oxygen inlet valve was opened.

4

Figure 4. Ignition wires connected to terminal sockets of the bomb head

Figure 5. Calorimeter cover

8. Assistance from the laboratory technician was needed in filling the bomb with oxygen. The hose from the oxygen tank was securely attached to the bomb. The oxygen control valve of the tank was slowly opened to supply oxygen to the bomb and the bomb pressure was observed. After the desired pressure was reached, the oxygen control valve was closed and the hose was removed.

9. The oxygen-filled bomb was then placed in the center of the bucket of water. It was made sure that there was no continuous flow of gas bubbles after the bomb was submerged in the water.

10.The two ignition wires were then attached to the terminal sockets of the bomb head as shown in Figure 4 and the cover of the calorimeter was closed as shown in Figure 5.

11.The digital thermometer was inserted in the calorimeter cover and made sure that it touched the water. It was also made sure that there was enough space for the stirrer.

12.The stirrer was then turned on for six minutes while the temperature for every 30 seconds was recorded.

13.After 6 minutes, the firing button was pressed for 1-2 seconds on the ignition unit and the temperature was recorded for every 30 seconds up to 12 minutes after firing.

14.The stirrer was turned off and the calorimeter cover was opened. The bomb was lifted and it was dried using a clean towel. It was then taken outside into an open area.

15.Before the screw cap of the bomb cylinder was removed, the gas release valve was slowly opened to get rid of residual gas pressure and observations were taken.

16.The cap was unscrewed and the bomb head was lifted. The interior of the bomb cylinder was inspected for any signs of incomplete combustion.

17.The mass of the capsule after combustion and the mass of the unburned fuse were measured. The interior of the bomb and the combustion capsule were washed and dried using the towel.

18.The same procedure was followed for Trial 2.

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IV. Results and Discussion

Table 1. Calculated Data from Combustion of Benzoic AcidParameters Trial 1

Mass of combusted benzoic acid (g) 0.4640Mass of burned fuse (g) 0.0096Radiative correction, RC (OC) 0Change in temperature accounting RC (OC)

0.8

Heat of combustion of fuse (cal/mol) -12575.81Heat capacity of bomb calorimeter (cal/K)

3665.21

Percent of excess air (%) 328.62%

Table 2. Calculated Data from Combustion of NaphthaleneParameters Trial 1 Trial 2

Mass of combusted naphthalene (g) 0.4969 0.4912Mass if burned fuse (g) 0.0108 0.0065Radiative correction, RC (OC) 0.0167 0.0167Change in temperature accounting RC (OC)

1.28331.1833

Heat of combustion of fuse (cal/mol) -12575.81 -12575.81Heat of combustion of naphthalene (cal/g)

-9464.42-8828.64

Percent of excess air (%) 165.18% 166.03%

Table 3. Heating Value of NaphthaleneHeating Value Trial 1 Trial 2

Gross ΔHC (cal/g) -9473.6685 -8837.8848Net ΔHc (cal/g) -9800.7467 -9164.9630Average Net ΔHc (cal/g) - 9482.85Theoretical Net ΔHc (cal/g) - 9284.17Percent difference % 2.14%

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Figure 6. Graph of temperature as a function of time for combustion of benzoic acid

Table 4. Temperature of Water for the Combustion of Benzoic Acid and Naphthalene

Time (min)

Benzoic AcidNaphthalene

Trial 1 Trial 2

Pre-firing

T 0 25.4 25.3 25.5T 1 25.4 25.3 25.5T 2 25.4 25.4 25.5T 3 25.4 25.4 25.5T 4 25.4 25.4 25.6T 5 25.4 25.4 25.6T 6 25.4 25.4 25.6

Post - firing

T 7 25.8 26.0 26.2T 8 25.9 26.4 26.6T 9 26.1 26.6 26.8T 10 26.1 26.6 26.8T 11 26.2 26.7 26.8T 12 26.2 26.7 26.8T 13 26.2 26.7 26.8T 14 26.2 26.7 26.8T 15 26.2 26.7 26.8T 16 26.2 26.7 26.8T 17 26.2 26.7 26.8T 18 26.2 26.7 26.8

7

0 2 4 6 8 10 12 14 16 18 2025

25.2

25.4

25.6

25.8

26

26.2

26.4

Time (min)

Tem

pera

ture

(°C

)

The previous experiment aims to calibrate the bomb calorimeter by determining its heat capacity using benzoic acid as the reference sample. A specified amount of benzoic acid was burned inside the bomb cylinder and changes in temperature within the bucket were recorded. However, due to errors encountered in the previous experiment, the heat capacity of the calorimeter was not calculated. Therefore, another trial for determining the heat capacity of the calorimeter was conducted in this experiment.

Table 1 shows the calculated data for the calibration of the bomb calorimeter. The heat capacity of the calorimeter can be calculated using Equation 6. The only given parameter in this equation is the heat of combustion of benzoic acid which is -6318 cal/g. Therefore, the unknown values of Equation 6 which are mass of combusted benzoic acid, heat of combustion of fuse, mass of burned fuse and change in temperature can be calculated using the raw data gathered in the experiment.

As shown in Table 1, the mass of combusted benzoic acid and mass of burned fuse were determined from the experiment to be 0.4640g and 0.0096g, respectively. The heat of combustion of the platinum fuse was calculated using the equation below where T2 is the stabilized temperature, T1 is the melting point and Cp is the heat capacity of platinum. This equation was integrated and calculated as shown in the sample calculations to determine the heat combustion of fuse which is -12575.81cal/mol.

∆ Ufuse = ∫T 1

T 2

C pdT

Table 4 shows the recorded temperature of water for every 1 minute during the combustion of benzoic acid while Figure 6 shows the graph of the temperature of water as a function of time. As shown in Figure 6, the temperatures obtained during the pre-firing stage forms a straight line. This suggests that a constant temperature of 25.4OC was obtained before the combustion process was initiated. From 25.4OC, it can be observed that the temperature escalated as the combustion process was initiated 6 minutes after stirring. As seen in the graph, there is a gradual change of temperature between 6 and 10 minutes. After 4 minutes of firing, the temperature became constant at 26.2OC

It was previously stated that the bomb calorimeter is not fully adiabatic because in reality, a small amount of heat escapes from its insulating jacket. This

8

0 2 4 6 8 10 12 14 16 18 2024.5

25

25.5

26

26.5

27

Time (min)

Tem

pera

ture

( °

C)

Figure 7. Graph of temperature as a function of time for combustion of naphthalene

nonadiabaticity is corrected by the radiative correction. Using Equations 7 and 8, the change in temperature accounting for radiative correction was calculated to be 0.8OC.

Since the values of the needed parameters in Equation 6 are already known, the heat capacity of the calorimeter can be calculated. Substituting the known values to the equation, the calculated heat capacity of the bomb calorimeter is 3665.21cal/K. The percent excess of air for the combustion of benzoic acid was also calculated to be 328.62%. The high percentage of excess air suggests that there was a large amount of oxygen supplied to react with the benzoic acid until it reaches complete combustion. However, the presence of soot and the evolution of gas signifies incomplete combustion.

After determining the heat capacity of the bomb calorimeter, the following experiment aims to determine the heating value of a pure solid substance. For this experiment, naphthalene was used as the sample. As recommended in the Materials Safety Data Sheet (MSDS) of naphthalene, personal protection equipment such as gloves, masks and safety goggles were used in handling the naphthalene. This experiment also aims to compare the experimental net calorific value of naphthalene to its theoretical value. Two trials were conducted for the experiment and the calculated data for the two trials are presented in Table 2.

The calculation of the Gross Calorific Value (Gross ΔHC) of naphthalene utilizes the values of the heat of combustion of naphthalene and the change of molar amount of gases during its combustion as shown by Equation 11. The values for these parameters should be determined first in order to calculate the Gross ΔHC of naphthalene.

For the calculation of the heat of combustion of naphthalene, Equation 6 was used. The known values of Equation 6 are the previously calculated heat capacity of the calorimeter and heat of combustion of fuse which are 3665.21cal/K and -12575.81cal/mol, respectively. The values for the mass of burned fuse, mass of combusted naphthalene and change in temperature were then calculated using the data gathered in the experiment. As shown in Table 2, the mass of combusted naphthalene for Trials 1 and 2 are 0.4969g and 0.4912g, respectively. The mass of the burned fuse was determined to be 0.0108g and 0.0065g for Trials 1 and 2, respectively.

The changes in temperature of water during the combustion of naphthalene for Trials 1 and 2 are shown in Table 4. On the other hand, the graphs of temperature of water as a function of time for the two trials are shown in Figure 7. The graph for Trial 1 is represented by the red color while Trial 2 is represented by the green one. It can be observed from Figure 7 that the recorded temperatures for both trials during the pre-firing stage were constant. Trial 1 has a constant temperature of 25.4OC before the combustion process started while Trial 2 has a constant temperature of 25.6OC. The temperature for both trials escalated as the combustion process was initiated 6 minutes after firing. For Trial 1, the temperature gradually increases between 6 and 10 minutes and becomes constant at 26.7OC after 4 minutes from firing. On the other hand, the temperature in Trial 2 gradually increases between 6 and 9 minutes and becomes constant at 26.8OC after 3 minutes from firing.

As previously stated, the radiative correction was determined using Equation 7 in order to correct the nonadiabaticity of the bomb calorimeter. Using Equation 8, the change in temperature accounting radiative correction was then calculated to be 0.0167OC for both trials.

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With the calculated values of mass of combusted naphthalene, mass of burned fuse and change in temperature; the heat of combustion of naphthalene can be determined. Substituting the known values to Equation 6, the heat of combustion of naphthalene for Trial 1 is -9464.42cal/g and for Trial 2 is -8828.64cal/g. Both values of heat of combustion are negative since the reaction inside the bomb is exothermic.

The calculation for the change of molar amount of gases ngas during the combustion of naphthalene is shown in the sample calculations. It was calculated based on the combustion reaction of naphthalene which is shown below. The calculated ngas are -7.8099 x 10-3 moles and -7.7850 moles for Trials 1 and 2, respectively.

C10H8(s) + 12O2(g) → 10CO2(g) + 4H2O(l)With the calculated values of heat of combustion of naphthalene and change

in molar amount of gases during combustion, the enthalpy of combustion of naphthalene for both trials can be calculated. Putting in the known values to Equation 11, the enthalpy of combustion of naphthalene for Trials 1 and 2 were determined to be -9473.67cal/g and -8837.88cal/g, respectively. These values are the Gross ΔHC of naphthalene.

The Net Calorific Value (Net ΔHC) of naphthalene is calculated by subtracting the latent heat of vaporization of water vapor from the Gross ΔHC as shown by Equation 1. The Gross ΔHC for Trials 1 and 2 were previously calculated. The latent heat of vaporization of water ∆ H v can be calculated using the equation obtained from the Perry’s Chemical Engineering Handbook as shown in the sample calculations. For both trials, the calculated ∆ H v is 581.60 cal/g. With the known values of Gross ΔHC and ∆ H v, the calculated Net Calorific Value for Trial 1 is - 9800.75 cal/g and for Trial 2 is - 9164.96 cal/g.

An average Net ΔHC was obtained from the calculated values of Net ΔHC for Trials 1 and 2. The average Net ΔHC was then compared to the theoretical Net ΔHC of naphthalene. As shown in Table 3, the average Net ΔHC was determined to be -9482.85cal/g. It was compared to the theoretical Net ΔHC which is -9284.17cal/g by obtaining a percent difference. The calculated percent difference between the experimental and theoretical Net ΔHC of naphthalene is 2.14%. The small percent difference suggests that the Net ΔHC obtained from the experiment is accurate and acceptable. This means that here is no significant difference between the experimental and theoretical net calorific value of naphthalene.

The percentage of excess air for the combustion of naphthalene was also calculated. Table 2 shows a 165.18% excess air for Trial 1 and 166.03% excess air for Trial 2. The high percentage of excess air suggests that a large amount of oxygen and nitrogen were supplied in order to achieve a complete combustion. This means that a large amount of oxygen reacted with naphthalene until it finally reaches a complete combustion. However the presence of soot suggests that the combustion was incomplete. There was also evolution of gas when the bomb cylinder was opened after combustion. The common gases that can evolve from a combustion process are carbon monoxide, carbon dioxide and hydrogen gas. It can be confirmed that carbon monoxide is one of the residual gases since the combustion process inside the bomb was incomplete. It was also observed that moisture was present in the bomb cylinder. This is because water is one of the products of combustion.

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RecommendationsThe fuse should be securely attached to the electrodes. It should be bent in

the manner shown in Figure 8 rather than the one shown in Figure 9. It should be made sure that neither the wire nor the pellet is touching the sides of the cup. If the wire touches any metal between the two electrodes, it will short out. Figure 9 shows a great possibility for the fuse to touch the sides of the capsule.This should be avoided.

V. Conclusion

The heating value of naphthalene was determined using the bomb calorimeter. The Gross Calorific Value of Naphthalene for Trials 1 and 2 were determined to be -9473.67cal/g and -8837.88cal/g, respectively. The average Net Calorific Value of naphthalene was also determined to be - 9482.85cal/g. It was compared to the theoretical value of - 9284.17cal/g by obtaining the percent difference. The 2.14% difference of experimental and theoretical net calorific values of naphthalene suggests that the results of the experiment are accurate and acceptable.

References

Biarnes, M., Freed, B. & Esteves, J. (n.d.). Combustion. E Instruments International LLC. Retrieved from http://www.e-inst.com/docs/Combustion-Booklet-2013.pdf

Bright Hub Engineering. (2012). Burning Coal in Power Plants – Calorific Value and Moisture. Retrieved from http://www.brighthubengineering.com/power-plants/22202-burning-coal-in-power-plants-calorific-value-and-moisture/

Encylopedia Britannica. (2015). Combustion. Retrieved from http://www.britannica.com/science/combustion

Lamp, B. D., Humphry, T., Pultz, V. M., & McCornick, J. M. (2013). Enthalpies of Solution. Retrieved from http://chemlab2.truman.edu/files/2015/07/Enthalpies-of-Solution.pdf

Roos, M., Kucerova, G., & Brimaud, S. (2010). Experiement 9 – Calorimetry. Ulm University. Retrieved from http://www.uni-ulm.de/~hhoster/pc_lecture/Calorimetry_1.pdf

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Figure 8. Correct attachment of fuse to the electrodes

Figure 9. Incorrect attachment of fuse to the electrodes

Smith, J. M., Van Ness, H., & Abbott, M. (2011). Introduction to Chemical Engineering Thermodynamics (7th ed). New York: McGraw-Hill Book Company

Spectro Analytical Labs. 2015. Coal Testing Definition. Retrieved from http://www.spectro.in/Coal-definition.html

The Engineering Toolbox. (n.d.). Heating Value. Retrieved from http://www.engineeringtoolbox.com/gross-net-heating-value-d_824.html

Wheet, R. (2011). Organic Chemistry Laboratory Procedures: Naphthalene, Vol.4. Department of Chemical Technology Texas State Technical College, USA.

AppendicesRaw Data Table 5. Measured Data for Benzoic Acid

Parameters Trial 1Mass of benzoic acid (g) 0.5008Mass of fuse (g) 0.0115Mass of the capsule (g) 12.6678Mass of capsule and soot (g) 12.6755Mass of unburned fuse (g) 0.0019

12

Pressure (psig) 115Mass of capsule and pelletized benzoic acid (g)

13.1395

Volume of the bomb (mL) 345

Table 6. Measured Data for NaphthaleneParameters Trial 1 Trial 2

Mass of naphthalene (g) 0.5036 0.5017Mass of fuse (g) 0.0117 0.0117Mass of the capsule (g) 12.8027 12.4503Mass of capsule and pelletized naphthalene (g)

13.3032 12.9492

Mass of capsule and soot (g) 12.8063 12.4580Mass of unburned fuse (g) 0.0009 0.0052Pressure (psig) 115 115Volume of the bomb (mL) 345 345

Table 7. Temperature of Water for Combusting Benzoic AcidTime (min) Temperature

(OC)

Pre-Firing

T0 0.00 25.40.30 25.4

T1 1.00 25.41.30 25.4

T2 2.00 25.42.30 25.4

T3 3.00 25.43.30 25.4

T4 4.00 25.44.30 25.4

T5 5.00 25.45.30 25.4

13

T6 6.00 25.4

Post-Firing

6.30 25.5T7 7.00 25.8

7.30 25.9T8 8.00 25.9

8.30 26.0T9 9.00 26.1

9.30 26.1T10 10.00 26.1

10.30 26.2T11 11.00 26.2

11.30 26.2T12 12.00 26.2

12.30 26.2T13 13.00 26.2

13.30 26.2T14 14.00 26.2

14.30 26.2T15 15.00 26.2

15.30 26.2T16 16.00 26.2

16.30 26.2T17 17.00 26.2

17.30 26.2T18 18.00 26.2

Table 8. Temperature of Water for Combusting NaphthaleneTime (min) Temperature (OC)

Trial 1 Trial 2

Pre-Firing

T0 0.00 25.3 25.50.30 25.3 25.5

T1 1.00 25.3 25.5130 25.4 25.5

T2 2.00 25.4 25.52.30 25.4 25.5

T3 3.00 25.4 25.53.30 25.4 25.6

T4 4.00 25.4 25.64.30 25.4 25.6

T5 5.00 25.4 25.65.30 25.4 25.6

T6 6.00 25.4 25.66.30 25.6 25.8

T7 7.00 26.0 26.27.30 26.3 26.5

T8 8.00 26.4 26.6

14

Post-Firing

8.30 26.5 26.7T9 9.00 26.6 26.8

9.30 26.6 26.8T10 10.00 26.6 26.8

10.30 26.7 26.8T11 11.00 26.7 26.8

11.30 26.7 26.8T12 12.00 26.7 26.8

12.30 26.7 26.8T13 13.00 26.7 26.8

13.30 26.7 26.8T14 14.00 26.7 26.8

14.30 26.7 26.8T15 15.00 26.7 26.8

15.30 26.7 26.8T16 16.00 26.7 26.8

16.30 26.7 26.8T17 17.00 26.7 26.8

17.30 26.7 26.8T18 18.00 26.7 26.8

Sample Calculations Calculations for the water used in the experiment

Using energy balance(mCp∆T )cold + (mCp∆T )ambient = 0(mCp∆T )cold = - (mCp∆T )ambientmcoldCpcold(25oC−T cold) = - mambientCpambient (25oC−T ambient)

Since mass = (densityρ) (volume V), therefore ρcoldCpcoldV cold(25oC−T cold) = −ρambient CpambientV ambient (25oC−T ambient)

Assumptions: a. heat capacities of cold and ambient water have a small difference b. densities of cold and ambient water have a small difference

V cold (25oC−T cold ) = −V ambient (25oC−T ambient )

The measured temperatures are Tcold = 14.8OC, Tambient=26.1OC V cold (25oC−T cold ) = −V ambient (25oC−T ambient )

Vcold = −3000mL(25oC−26.1oC )

(25oC−14.8oC )

Vcold = 323.52 mL V ambient = 2676.27 mL

15

Heat of combustion of fuse ∆U fuse

Using the following equation

∆ Ufuse = ∫T 1

T 2

C pdT

where: T2 = Stabilized temperature = 17550C +273.15 = 2028.15 K

T1 = Melting Point Temperature = 25 0C + 273.15 = 298.15 K Heat Capacity of Platinum = 5.92 + 00.116T Source: Perry’s Chemical EngineersHandbook, 8th edition (Table 2-

151)

∆ Ufuse = -∫T 1

T 2

(5.92+0.00116T )dT

∆ Ufuse = -[5.92T + 0.00116T 2

2 ] ⃒T1

T2

∆ Ufuse = -5.92 (T 2−T1) - 0.00116(T22−T 1

2)2

∆ Ufuse = -5.92 (2028.15K−298.15K) - 0.00116 (2028.15K2−298.15K2)

2

∆ Ufuse =-12575.8094 calmol

Solving for radiative correction, R C For the combustion of benzoic acid

RC = (5 ) (T18−T 12 )+(T 6−T 0)

6

= (5 ) ( 26.2OC−26.2OC )+(25.4OC−25.4OC )

6 = 0

For the combustion of naphthalene in Trial 1

RC = (5 ) (T18−T 12 )+(T 6−T 0)

6

= (5 ) ( 26.7OC−26.7OC )+(25.4OC−25.3OC)

6 = 0.01667 OC

Solving for ∆T For the combustion of benzoic acid

∆T = T 12 - T 6 – RC = 26.2OC – 25.4OC – 0 = 0.8OC

For the combustion of naphthalene in Trial 1

16

∆T = T 12 - T 6 – RC = 26.7OC – 25.4OC – 0.01667OC = 1.2833OC

Heat capacity of the bomb calorimeter Using benzoic acid as sample

Cv = −⌊(∆U sample)¿¿Cv =

−⌊ (−6318cal / g)(0.4640 gbenzoicacid)+(−12575.8094calmol )(0.0096 g platinum fuse )( 1mol Pt

195.08 g Pt) ⌋

0.8Cv = 3665.213579 cal/KCv = 3665.2136 cal/K

Heat of combustion of naphthalene Using naphthalene in Trial 1Since heat capacity of bomb calorimter is Cv = 3665.213579 cal/K

C v=−[ (∆U naphthalene) (mnaphthalene )+(∆U fuse ) (mfuse ) ]

∆T

Rearranging the equation above to solve for ∆U naphthalene

∆U naphthalene = −[ (∆U fuse ) (mfuse )+C v∆T ]

mnaphthalene

=

−[(−12575.8094calmol ) (0.0108 g )( 1mol

195.08g Pt)+(3665.213579cal /K )(1.2833)]

0.4969 g = -9464.42416 cal/g = -9464.4242 cal/g

Solving for n gas

From the combustion of naphthalene in Trial 1C10H8(s) + 12O2(g) → 10CO2(g) + 4H2O(l)ngas = nproduct – nreactants

= (moles of naphthalene)(10) – (moles of naphthalene)(12)

= (0.5005g C10H8)( 1molC10 H 8

128.17 g )(10) – (0.5005g C10H8)( 1molC10 H 8

128.17 g )(12)

= -7.809939924 x10-3 moles = -7.8099 x 10-3 moles

Solving for enthalpy of combustion of naphthalene, H naphthalene For the combustion of naphthalene in Trial 1

Hnaphthalene = Unaphthalene + RTngas

17

= (-9464.42416 calg

) +

(1.987cal

mol K)(298.15K )(−7.809939924 x 10−3moles)

0.5005g = -9473.668508 cal/g

Since Gross ΔHC = Hnaphthalene,

Gross ΔHC = -9473.6685 cal/g

Latent heat of vaporization of water, ∆ H v

From Table 2-150, Perry’s Chemical engineering Handbook 8th edC1 = 5.2053x107 C2 = 0.3199C3 = -0.212 C4 = 0.25795

From Table 2-141, Perry’s Chemical engineering Handbook 8th edTC = 647.096 K

Tr = TTc

= 295.18K

647.096K = 0.4607508005

Solving for latent heat of vaporization ∆ H v=C1(1−Tr)

C 2+C 3T r+C 4T r2+C 5T r

3

= (5.2053x107)(1−0.4608)( 0.3199 )+(−0.212) (0.4608 )+(0.25795)(0.4608)2

= 43868870.73J

kmolx

1kmol1000mol

x1cal

4.1858Jx

1mol18.02 gH 2O

= 581.5983887 cal/g

Lower Heating Value, Net ΔHC Using naphthalene in Trial 1

Net ΔHC = Gross ΔHC - K·W Where: Gross ΔHC = Hnaphthalene = -9473.6685 cal/g K = ∆ H v=¿ 581.5983887 cal/g

W = weight of water∈the combustion products

weight of water burned

= (0.5005 gC10 H 8)( 1molC10H 8

128.17g )¿( 4mol H 2O

1molC10H 8)( 18.02 g H 2O

1mol H 2O ) ¿0.5005g

= 0.5623780916 = 0.5624

Solving for Net ΔHC

Net ΔHC = Gross ΔHC - K·W = (-9473.668508 cal/g) – (0.5623780916)(581.5983887 cal/g)

= - 9800.7467 cal/g = - 9800.75 cal/g

Using naphthalene in Trial 2Net ΔHC = Gross ΔHC - K·W

18

Where: Gross ΔHC = Hnaphthalene = -8837.884833 cal/g K =∆ H v=¿ 581.5983887 cal/g

W = weight of water∈the combustion products

weight of water burned

= (0.49 89 gC10 H 8)( 1molC10H 8

128.17g )¿( 4mol H 2O

1molC10H 8)( 18.02 gH 2O

1mol H 2O ) ¿0.49 89g

= 0.5623780916 = 0.5624

Solving for Net ΔHC

Net ΔHC = Gross ΔHC - K·W = (-8837.884833 cal/g) – (0.5623780916)(581.5983887 cal/g) = - 9164.963025 cal/g = - 9164.96 cal/g

Solving for average Net ΔHC from the two trials

Net ΔHC ave = Net ΔH c¿Trial1+Net ΔH c¿Trial2 ¿2

= (−9800.7467cal / g )+(−9164.963025cal /g)

2= - 9482.854863 cal/g= - 9482.85 cal/g

Percent difference of experimental Net ΔHC and theoretical Net ΔHC of naphthalene

% difference = Net ΔH cave−Net ΔH ctheo

Net ΔH c theo x 100

= (−9482.854863

calg )−(−9284.1674

calg

)

−9284.1674calg

x 100

= 2.140067649% = 2.14%

Moles of O 2 suppliedFor the combustion of benzoic acidUsing the Ideal Gas Law

R = 82.057atm•cm3

mol •K (Perry’s Chemical Engineering Handbook, 8th edition)

Measured volume of bomb cylinder = 345mL

PV = nRT

n = PVRT

19

moles O2 =

(129.7 psia)( 1atm14.7 psi

)(345mL)( 1 L1000mL

)

(82.057atm• cm3

mol •K)( 1m

100cm )3

( 1000 L1m3 )(298.15K )

moles O2 supplied = 0.1244203124 molesmoles O2 supplied = 0.1244 moles

Theoretical number of moles of oxygen for the combustion of benzoic acid For the combustion of benzoic acid

C7H6O2 (s) + 15/2 O2 (g) → 7 CO2 (g) + 3H2O (l)

moles O2 = 0.4717 gC7H 5O2×1molC7H 5O2

122.12gC7 H6O2

×7.5molO2

1molC7H 6O2

= 0.02896945627 moles = 0.02897 moles

For the combustion of fuse Pt (s) + O2 (g) → PtO2

moles O2 = 0.0115g Pt ×1mol Pt

195.08g Pt×

1mol oxygen1mol Pt

= 0.00005895017429 moles = 5.8950 x 10-5 moles

Theoretical moles O2 = moles O2 combusted with benzoic acid + moles O2

combusted with fuse = 0.02896945627 moles + 0.00005895017429 moles = 0.02902840644 moles = 0.02903 moles

Theoretical number of moles of oxygen for the combustion of naphthalene

For the combustion of naphthalene in Trial 1C10H8(s) + 12O2(g) → 10CO2(g) + 4H2O(l)

moles O2¿0.5005 gC10 H 8×1molC10 H 8

128.17 gC10H8

×12molO2

1molC10H 8

= 0.04685963954 moles = 0.04686 moles

For the combustion of fuse Pt (s) + O2 (g) → PtO2

moles O2 = 0.0117g Pt ×1mol Pt

195.08g Pt×

1mol oxygen1mol Pt

= 0.00005997539471 moles = 5.9975 x 10-5 moles

Theoretical moles O2 = moles O2 combusted with naphthalene + moles O2

combusted with fuse = 0.04685963954 moles + 0.00005997539471 moles = 0.04691961493 moles = 0.04692 moles

20

Percent of excess air For the combustion of benzoic acid

% excess air =supplied moles of O2−theoreticalmolesof O2

theoreticalmolesof O2

x 100

= 0.1244203124moles−0.02902840644moles

0.02902840644moles x 100

= 328.615717% = 328.62%

For the combustion of naphthalene in Trial 1

% excess air =supplied moles of O2−theoreticalmolesof O2

theoreticalmolesof O2

x 100

= 0.1244203124moles−0.04691961493moles

0.04691961493moles x 100

= 165.1776077% = 165.18%

Hazel Jan B. Fuertes ChE124 - 2Groupmates: Rodgin Grace Regencia

Viena Mae VillaruzDate performed: September 15, 2015Date submitted: September 22, 2015

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