Bomb Calorimetry
The goal of this experiment is to determine the enthalpy of combustion of naphthalene by means of a bomb calorimeter. First, the bomb calorimeter was standardized using benzoic acid and the average heat capacity of the bomb calorimeter was calculated to be 10.60.3205 kJ/K. From that, the
These results show that heats of combustions of unknown substances can be determined via bomb calorimetry.
Introduction
The first law of thermodynamics states that energy is conserved.2 Using that law it can be said that the change in the internal energy of a system () depends on the heat added (q) to the system and the work (w) done by the system.2 Equation 1 illustrates the relationship between the three variables. (1)
In this experiment, …show more content…
the bomb calorimeter is treated as a system in order to apply the calculations. This bomb calorimeter is used to determine the heat of combustion of naphthalene. Equation 2 shows the heat of combustion of naphthalene.
C10H8 (s) + 12O2 (g) 10CO2 (g) + 4H2O (l) (2)
It is also vital to show the heat of combustion of benzoic acid in equation 3 because it is used to standardize the bomb calorimeter. C6H5CO2H (s) +O2 (g)7CO2 (g) +3H2O (l) (3)
The standard heat of combustion is referred to as the amount of heat released by burning one mole of a substance at standard conditions (i.e. 1atm and 298K) to yield CO2 gas, N2 gas, SO2 gas and liquid water.3 To ensure that volume is kept constant during the experiment, the pail was filled with 2L of DI H2O each time. Equation 4 shows that since the volume is kept constant in this experiment (V=0), work done by the system is equal to 0. This corresponds to the first step in determining the experimental value of enthalpy and energy change. Equations 5 and 6 outline the general first and second steps in calculating the change in enthalpy (H) and change in energy (E). w=pΔV=0 (4)
A(P0, T0) + B(P0, T0) +S(P0, T0) = C(P1, T1) + D(P1, T1) + S(P1, T1) (5)
C(P1, T1) + D(P1, T1) +S(P1, T1) = C(P1, T1) + D(P0, T0) + S(P0, T0) (6)
A, B, C, and D refer to the reactants and products, while S refers to the reaction vessel. The total E (or U) will be the addition of both steps. As previously stated, the first step’s E will equal to 0. Therefore, the total E is composed of the second step’s E, which can be found using equation 7. This equation is also used to determine the heat capacity. That is why it is necessary to standardize the bomb calorimeter using benzoic acid.
ΔE= CVcal * ΔT (7)
The bomb calorimeter was not kept at constant pressure but the results found were from calculations assuming constant pressure. This assumption was made in order to claim that ΔH is again equal to the second step’s H, which can be found using equation 8.
ΔH= ΔE + RTΔn (8)
Methods
A pellet of the desired material, either benzoic acid or naphthalene, was made using a pill press. It was then weighed and placed on the dish inside the bomb. Almost 1g of benzoic acid and naphthalene was used for each individual trial. A 10cm piece of iron ignition wire was also weighed and then used to connect the terminals inside the bomb. Once the wire was positioned in a way to insure that it was in contact with the pellet only, not the pan, the bomb was inserted in the steel container and the top was tightened on by hand.
In order to pressurize the bomb, it was attached to an oxygen air tank and flushed with oxygen for a minute. Then it was filled to a pressure of 30 atm. The pressurized bomb was immersed in a pail that contained 2000ml of distilled water. A large 2L volumetric flask was used to accurately measure out the amount of water.
A propeller and thermometer were inserted into the pail. The steel container was connected to the wires then fully submerged in the water. Once temperature equilibrium was reached, five time-temperature readings one minute apart were recorded. Next, the firing switch was held down for five seconds. The temperature began to rise and temperature readings were taken every 30 seconds for about five minutes. Once temperature equilibrium was reached again, five post run temperature readings one minute apart were recorded.
In order to depressurize the bomb, the needle valve on top of the bomb was loosened slowly.
The remnants of the ignition wire were weighed at the end of each run. Before the start of the experiment and in between each run, the bomb and pan was wiped down to remove any remains of the substances. The pail was also refilled with 2L of distilled water. Each pellet was made before the start of its run to decrease the amount of water vapor in the air that could get inside of it.
Using the data obtained from the experiment a plot of time vs temperature was made and used to calculate the adiabatic temperature change. These plots can be seen in the appendix along with the equation of the trend lines. Equation 9 is used as well to calculate the adiabatic temperature change. However, equation 9 can be simplified to 10 because by inspection of figures 4 and 5 the slope of the line is small or simply 0. This slope corresponds to (dT/dt) in equation 9. Therefore, it is negligible. T= (Tf-Ti) – () (td-ti)- ()f (tf -td) …show more content…
(9)
Results
In total, four trials were run, two of benzoic acid and two of naphthalene. The raw data of these trials are shown in the appendix in Tables 3 through 6. First, the change in temperature (ΔT) was calculated using equation 10. Ti is the temperature right before the button was pressed and Tf was the post equilibrium temperature. The change in temperature for the first and second trials of the combustion of benzoic acid was 2.23oC and 2.30oC respectively. The change in temperature can also be expressed as 2.23K and 2.3K since the change in temperature is the same in Celsius and Kelvin.
ΔT= Tf-Ti (10)
Next, benzoic acid was used as a standard to calculate the heat capacity of the bomb calorimeter.
Equation 11 is used to find the heat released in combustion of naphthalene or the energy of combustion (ΔE). qcomb= ΔUcomb*(mBA) + ΔUwire*(mwire) (11)
ΔUcomb and ΔUwire are the specific energies of benzoic acid and the iron fuse wire. They correspond to the values -26.41 kJ/g for benzoic acid and -6.68 kJ/g for iron.1 The change in temperature is assumed to be entirely from the result of the combustion of a substance and not from heat from the universe, i.e. this part of the apparatus is adiabatic (quniv=0). This is assumption is displayed in equation 12. qcal is the heat absorbed by the calorimeter. qcomb + qcal= quniv qconb = -qcal (12)
In order to use equation 13 it is also assumed that the temperature change of the water is the temperature change in the bomb calorimeter. The heat capacity of the bomb calorimeter (CVcal) was found to be 10.9kJ/K for the first trial of benzoic acid and 10.4kJ/K for the second trial. This gives a mean of
10.6kJ/K. qconb= -CVcal * ΔT (13)
The average heat capacity was used to find ΔU in equation 14.
ΔU= CVcal * ΔT (14)
In general, the internal energy is equal to the heat absorbed minus the work done by the system. In turn, the work done is equal to the pressure multiplied by the change in volume. This experiment is performed in isochoric conditions (ΔV =0), therefore, the internal energy is equal to the heat absorbed. This is all shown below in equations 15 to 17. In order to find the molar internal energy change, simply divide by the number of moles.
ΔU=q-w (15)
ΔU=q-pΔV (16)
ΔU=q (17)
Finally, the enthalpy (ΔH) of naphthalene can be determined using equation 18.
ΔH= ΔU + RTΔn (18)
For this equation, the R constant used is 0.083145 kJ/mol*K and temperature is the average temperature of the system before and after the combustion. While, -2 moles is used for Δn because n is equal to the number of moles of gaseous products minus the number of moles of the gaseous reactants. This was found by using the balanced formula of the combustion of naphthalene (equation 2).
These results show that heats of combustions of unknown substances can be determined via bomb calorimetry.
Introduction
The first law of thermodynamics states that energy is conserved.2 Using that law it can be said that the change in the internal energy of a system () depends on the heat added (q) to the system and the work (w) done by the system.2 Equation 1 illustrates the relationship between the three variables. (1)
In this experiment, …show more content…
the bomb calorimeter is treated as a system in order to apply the calculations. This bomb calorimeter is used to determine the heat of combustion of naphthalene. Equation 2 shows the heat of combustion of naphthalene.
C10H8 (s) + 12O2 (g) 10CO2 (g) + 4H2O (l) (2)
It is also vital to show the heat of combustion of benzoic acid in equation 3 because it is used to standardize the bomb calorimeter. C6H5CO2H (s) +O2 (g)7CO2 (g) +3H2O (l) (3)
The standard heat of combustion is referred to as the amount of heat released by burning one mole of a substance at standard conditions (i.e. 1atm and 298K) to yield CO2 gas, N2 gas, SO2 gas and liquid water.3 To ensure that volume is kept constant during the experiment, the pail was filled with 2L of DI H2O each time. Equation 4 shows that since the volume is kept constant in this experiment (V=0), work done by the system is equal to 0. This corresponds to the first step in determining the experimental value of enthalpy and energy change. Equations 5 and 6 outline the general first and second steps in calculating the change in enthalpy (H) and change in energy (E). w=pΔV=0 (4)
A(P0, T0) + B(P0, T0) +S(P0, T0) = C(P1, T1) + D(P1, T1) + S(P1, T1) (5)
C(P1, T1) + D(P1, T1) +S(P1, T1) = C(P1, T1) + D(P0, T0) + S(P0, T0) (6)
A, B, C, and D refer to the reactants and products, while S refers to the reaction vessel. The total E (or U) will be the addition of both steps. As previously stated, the first step’s E will equal to 0. Therefore, the total E is composed of the second step’s E, which can be found using equation 7. This equation is also used to determine the heat capacity. That is why it is necessary to standardize the bomb calorimeter using benzoic acid.
ΔE= CVcal * ΔT (7)
The bomb calorimeter was not kept at constant pressure but the results found were from calculations assuming constant pressure. This assumption was made in order to claim that ΔH is again equal to the second step’s H, which can be found using equation 8.
ΔH= ΔE + RTΔn (8)
Methods
A pellet of the desired material, either benzoic acid or naphthalene, was made using a pill press. It was then weighed and placed on the dish inside the bomb. Almost 1g of benzoic acid and naphthalene was used for each individual trial. A 10cm piece of iron ignition wire was also weighed and then used to connect the terminals inside the bomb. Once the wire was positioned in a way to insure that it was in contact with the pellet only, not the pan, the bomb was inserted in the steel container and the top was tightened on by hand.
In order to pressurize the bomb, it was attached to an oxygen air tank and flushed with oxygen for a minute. Then it was filled to a pressure of 30 atm. The pressurized bomb was immersed in a pail that contained 2000ml of distilled water. A large 2L volumetric flask was used to accurately measure out the amount of water.
A propeller and thermometer were inserted into the pail. The steel container was connected to the wires then fully submerged in the water. Once temperature equilibrium was reached, five time-temperature readings one minute apart were recorded. Next, the firing switch was held down for five seconds. The temperature began to rise and temperature readings were taken every 30 seconds for about five minutes. Once temperature equilibrium was reached again, five post run temperature readings one minute apart were recorded.
In order to depressurize the bomb, the needle valve on top of the bomb was loosened slowly.
The remnants of the ignition wire were weighed at the end of each run. Before the start of the experiment and in between each run, the bomb and pan was wiped down to remove any remains of the substances. The pail was also refilled with 2L of distilled water. Each pellet was made before the start of its run to decrease the amount of water vapor in the air that could get inside of it.
Using the data obtained from the experiment a plot of time vs temperature was made and used to calculate the adiabatic temperature change. These plots can be seen in the appendix along with the equation of the trend lines. Equation 9 is used as well to calculate the adiabatic temperature change. However, equation 9 can be simplified to 10 because by inspection of figures 4 and 5 the slope of the line is small or simply 0. This slope corresponds to (dT/dt) in equation 9. Therefore, it is negligible. T= (Tf-Ti) – () (td-ti)- ()f (tf -td) …show more content…
(9)
Results
In total, four trials were run, two of benzoic acid and two of naphthalene. The raw data of these trials are shown in the appendix in Tables 3 through 6. First, the change in temperature (ΔT) was calculated using equation 10. Ti is the temperature right before the button was pressed and Tf was the post equilibrium temperature. The change in temperature for the first and second trials of the combustion of benzoic acid was 2.23oC and 2.30oC respectively. The change in temperature can also be expressed as 2.23K and 2.3K since the change in temperature is the same in Celsius and Kelvin.
ΔT= Tf-Ti (10)
Next, benzoic acid was used as a standard to calculate the heat capacity of the bomb calorimeter.
Equation 11 is used to find the heat released in combustion of naphthalene or the energy of combustion (ΔE). qcomb= ΔUcomb*(mBA) + ΔUwire*(mwire) (11)
ΔUcomb and ΔUwire are the specific energies of benzoic acid and the iron fuse wire. They correspond to the values -26.41 kJ/g for benzoic acid and -6.68 kJ/g for iron.1 The change in temperature is assumed to be entirely from the result of the combustion of a substance and not from heat from the universe, i.e. this part of the apparatus is adiabatic (quniv=0). This is assumption is displayed in equation 12. qcal is the heat absorbed by the calorimeter. qcomb + qcal= quniv qconb = -qcal (12)
In order to use equation 13 it is also assumed that the temperature change of the water is the temperature change in the bomb calorimeter. The heat capacity of the bomb calorimeter (CVcal) was found to be 10.9kJ/K for the first trial of benzoic acid and 10.4kJ/K for the second trial. This gives a mean of
10.6kJ/K. qconb= -CVcal * ΔT (13)
The average heat capacity was used to find ΔU in equation 14.
ΔU= CVcal * ΔT (14)
In general, the internal energy is equal to the heat absorbed minus the work done by the system. In turn, the work done is equal to the pressure multiplied by the change in volume. This experiment is performed in isochoric conditions (ΔV =0), therefore, the internal energy is equal to the heat absorbed. This is all shown below in equations 15 to 17. In order to find the molar internal energy change, simply divide by the number of moles.
ΔU=q-w (15)
ΔU=q-pΔV (16)
ΔU=q (17)
Finally, the enthalpy (ΔH) of naphthalene can be determined using equation 18.
ΔH= ΔU + RTΔn (18)
For this equation, the R constant used is 0.083145 kJ/mol*K and temperature is the average temperature of the system before and after the combustion. While, -2 moles is used for Δn because n is equal to the number of moles of gaseous products minus the number of moles of the gaseous reactants. This was found by using the balanced formula of the combustion of naphthalene (equation 2).