Effect of Carbon Chain Length on MHC

1.0 Introduction

1.1 Research Question

How does increasing the carbon chain length of alcohols affect the molar heat of combustion?

1.2 Rationale

"The molar heat of combustion is the energy released when 1 mole of a substance undergoes complete combustion" (Ck12, 2013). Calorimetry is the science of measuring the change of heat associated with the system and its surroundings (Henderson, 2010). The amount of heat released during the combustion of the alcohol can be calculated by the change in temperature of the water. An equation was developed to calculate the molar heat of combustion:

MHC = ^mcΔT / n

This equation calculates the amount of heat released that the water absorbs.

However, some heat was lost to the aluminum milkshake can and to the surroundings. To increase the accuracy of the molar heat of combustion calculation, the milkshake can was included in this equation, using the formula:

MHC = ^m_waterc_waterΔT_water / n + ^m_canc_canΔT_can / n

Where MHC = Molar Heat of Combustion (kJ/mol), m = mass of water or can (g), c = specific heat capacity of water or aluminum, ΔT = change in temperature (°C), n = number of moles of the combustion substance (mol).

A combustion reaction involves a fuel reacting with excess oxygen and produces carbon dioxide and water. For example, when butanol undergoes complete combustion, the equation is:

C₄H₉OH + 6.5O₂ → 4CO₂ + 5H₂O

For this example, 1 mole of butanol reacts with 6.5 moles of excess oxygen and produces 4 moles of carbon dioxide and 5 moles of water.

According to Jim Clark, bond enthalpy is "the energy required to break 1 mole of the bond to give separated atoms - everything being in the gaseous state" (Clark, 2010).

Each chemical bond has a varied bond energy, and for a reaction to be exothermic, the total bond energy of the reactants must be greater than the total bond energy of the products, which ultimately releases energy. For an endothermic reaction, the products have a greater total bond energy than the reactants (Khan Academy, 2016).

Both types of reactions are represented on the graph below:

Reaction Type	Energy Change
Exothermic	Release of heat
Endothermic	Absorption of heat

The combustion reaction of the fuel is an exothermic reaction, releasing energy in the form of heat. This leads to the development of the research question. With the number of carbon atoms increasing, and subsequently the number of hydrogen atoms by one per alcohol (butanol, pentanol, hexanol, heptanol, octanol), the total number of bonds increases, and therefore, the bond enthalpy increases, resulting in an increase in the molar heat of combustion proportionally.

The original experiment needed to be modified to overcome limitations and make the results more accurate. These modifications included using a probe to measure the temperature of the water with LoggerPro, applying aluminum foil to the milkshake can to act as a lid and insulant, changing the height from the spirit burner to reduce the amount of heat loss, and increasing the water volume to reduce the rate of heat loss. Despite all these modifications, the experiment still wasn't a fair test due to the lack of accuracy, as there was still too much heat loss, significantly reducing the final calculated MHC values.

2.0 Methodology

2.1 Original Experiment

1. Weigh the spirit burner.
2. Pour 200mL of cool water (10-15°C below room temperature) into the milkshake can.
3. Measure the initial temperature of the water.
4. Place the can in the ring on the retort stand.
5. Light the spirit burner and immediately position it under the milkshake can.
6. Stir the water gently until the temperature rises to 10-15°C above room temperature.
7. Extinguish the burner by placing the lid on it.
8. Measure the maximum temperature reached by the water.
9. Re-weigh the spirit burner (with the lid on).
10. Empty the can and remove any soot, ensuring the can is dry.
11. Repeat steps 1-10 twice more.

2.2 Modifications

Several modifications were made to improve the accuracy and precision of the experiment:

• Utilized LoggerPro and a probe to measure the water's temperature, enhancing temperature recording accuracy.
• Applied aluminum foil as a lid on the can to minimize heat loss and retain more water inside.
• Conducted experiments with five different fuels instead of one to allow for a more extensive dataset and accurate determination of the relationship between chain length and MHC.
• Reduced the distance between the bottom of the can and the spirit burner to 2.5cm, minimizing heat loss and improving result accuracy.
• Increased the water volume in the can, enabling the water to absorb more heat, resulting in a lower temperature rise and reduced heat loss due to the water's increased heat capacity.

2.3 Equipment

The following equipment and materials were used in the experiment:

• Scrubbing tools
• Matches
• Ruler (30cm)
• Balance
• Timer
• Measuring Cylinder (250mL)
• Water (≈19°C)
• Laptop with LoggerPro
• Retort Stand
• Ring
• Heatproof mat
• Probe
• Aluminum foil
• Spirit Burner (Butanol, Pentanol, Hexanol, Heptanol, Octanol)
• Aluminum milkshake can

2.4 Risk Management

During the experiment, several risks associated with naked flames and fuels were managed to ensure safety:

• Contact with skin and clothing: Lab coats were worn if clothing needed to be removed quickly, although the risk was unlikely as the fuel was in a container.
• Hot metal: After each trial, the can was placed in the sink with tap water to cool it down, as this risk was certain.
• Eyes being contaminated by fuel: Safety goggles were worn at all times, and careful handling of fuel minimized the risk of fuel entering the eyes (unlikely).
• Fumes of the fuel: Constant ventilation was maintained in the room to address this certain risk.
• Fuel spill: An extinguisher was on standby, but careful handling and constant monitoring of the flame minimized this risk (very likely).
• Fuel ingestion: In case of ingestion, water could be given if the person was conscious, but medical advice would be required. Initial warnings not to drink the fuel minimized this very unlikely risk.

3.0 Results

3.1 Raw Data

Below is the raw data obtained from the experiments, including the molar mass, initial and final mass of the burner, and initial and final temperature of the water for each trial:

Fuel	Trial	Molar Mass (amu)	Initial Mass Burner (g)	Final Mass Burner (g)	Initial Temp Water (°C)	Final Temp Water (°C)
Butanol	1	74.12	326.48	325.99	19.1	26.2
	2	74.12	324.52	323.91	19.7	28.2
	3	74.12	322.76	322.22	19.2	26.6
Pentanol	1	88.15	291.03	290.67	19.3	25
	2	88.15	290.05	289.71	19.4	24.5
	3	88.15	293.99	293.55	19.8	26.6
Hexanol	1	102.162	323.5	323.25	19.2	22.7
	2	102.162	325.46	325.1	19.4	25.4
	3	102.162	323.51	323.17	19.4	27.3
Heptanol	1	116.88	326.3	325.87	19.3	26.2
	2	116.88	325.91	325.5	19.5	26.1
	3	116.88	324.98	324.54	19.7	25.9
Octanol	1	130.2279	314.34	313.79	19	28.1
	2	130.2279	313.78	313.24	19.7	27.9
	3	130.2279	319.08	318.68	19.6	27.7

3.2 Observations

General:

• Air conditioning and fast movement from students created air flow, causing the flame to flicker and not stay constantly underneath the can.
• For a few trials, the spirit burner wasn't centered underneath the can, resulting in disproportionality.
• There was only a small amount of blue flame compared to the amount of yellow or orange flame.

Butanol:

• Thin layer of soot with light amounts on the side.
• Small yellow/blue flame with no smoke.
• Little condensation on the bottom.

Pentanol:

• Thin layer of soot on the bottom.
• Small yellow/blue flame with no smoke.
• Little condensation on the sides and bottom.

Hexanol:

• Medium layer of soot, with additional soot on the sides in Trials 2 and 3.
• In Trial 1, there was only a small area of concentrated soot on the base.
• Small yellow/blue flame with no smoke.
• Condensation on the bottom and sides.

Heptanol:

• Thick layer of soot on the base and extending up the sides.
• Condensation on sides and bottom.
• Medium yellow/blue flame with no smoke.

Octanol:

• Very thick layer of soot on the bottom with soot reaching up the sides of the can.
• Condensation on the bottom and sides.
• Medium yellow/blue flame.

3.3 Processed Data

Table 1: Butanol Trial 1

Mass of Water (g)	Initial Mass (g)	Final Mass (g)	Initial Temp (°C)	Final Temp (°C)	Mass of Can (g)	Molar Mass (amu)
250	326.48	325.99	19.1	26.2	183.33	74.117

All calculations below use data from Butanol Trial 1:

Moles of Butanol (C₄H₉OH) = 0.00661...

Mass of Water (m_water) = 250 ± 1g

Change in Mass (Δm) = 0.49 ± 0.02g

Change in Temperature (ΔT) = 7.1 ± 0.2°C

Mass of Can (m_can) = 183.33 ± 0.01g

Relative Uncertainty:

m_water = 250 ± 0.4%g

Δm = 0.49 ± 4.08%g

ΔT = 7.1 ± 2.82%°C

m_can = 183.33 ± 5.46x10^-3g

Absolute Error of MHC = Accepted – Experimental

Absolute Error of MHC = 2676 – 1299.488

Absolute Error of MHC = 1376.51

Relative Error of MHC:

Relative Error of MHC = (Absolute Error of MHC / Accepted) x 100

Relative Error of MHC = (1376.51 / 2676) x 100

Relative Error of MHC = 51.44%

Average MHC of Butanol Trials:

Average MHC of Butanol Trials = 1259.386 kJ/mol

3.2 Calculated MHC Values

Table 2: Calculated MHC values

Fuel	Trial	MHC (kJ/mol)	Average (kJ/mol)	Average (kJ/mol)
Butanol	1	1299.488	1259.386	1259.386
	2	1249.681
	3	1228.989
Pentanol	1	1688.765	1645.671	1645.671
	2	1599.883
	3	1648.364
Hexanol	1	1730.581	2220.994	1895.399
	2	2060.216
	3	2872.183
Heptanol	1	2269.318	2179.537	2179.537
	2	2276.538
	3	1992.755
Octanol	1	2607.098	2730.229	2499.928
	2	2392.758
	3	3190.830

4.0 Evaluation of Experimental Process

4.1 Limitations of Evidence

The outliers, Hexanol T3 and Octanol T3, did not significantly impact the results, but they were excluded from averaged calculations and certain graphs to ensure accuracy. The primary limitation of the evidence was the substantial heat loss due to experimental methods, not the accuracy of the materials used. The equipment, including the LoggerPro temperature probe with an absolute uncertainty of ±0.1ºC, the balance with an absolute uncertainty of ±0.01g, and the 250mL measuring cylinder with an absolute uncertainty of ±1mL, was precise. There was a sufficient variety of fuels used to establish the relationship between chain length and MHC.

4.2 Reliability

The experiment demonstrated reliability in some trials, such as Butanol and Pentanol, which showed precision with results within 100kJ/mol of each other. However, Hexanol, Heptanol, and Octanol exhibited a wider range of 300kJ/mol for each fuel, excluding outliers. The uncertainty was relatively high, with the highest absolute uncertainty being ±350.17kJ/mol for Hexanol T1 and the lowest being ±109.85kJ/mol for Butanol T2. Factors contributing to random errors included air drafts caused by fast movement around the apparatus, inconsistent starting temperatures, and variations in the centring of the spirit burner under the can.

4.3 Validity

The experiment generated results that addressed the research question but yielded inaccurate MHC values, with a large average relative error of 52%. The primary systematic error was the substantial heat loss to the surrounding environment, primarily due to the open flame and insufficient oxygen supply. This resulted in incomplete combustion, visible through the flame's orange appearance, and substantial soot buildup. Incomplete combustion led to reduced heat transfer to the water and lower MHC values, rendering the results invalid.

4.4 Improvements & Extensions

To minimize heat loss and improve accuracy, several enhancements can be made:

• Use heatproof mats as a heat/wind shield to insulate the apparatus.
• Implement a Styrofoam cylinder around the can as an insulator.
• Extend the trial duration to 4 minutes to allow for complete combustion.
• Modify the can base to prevent the flame from coming up the sides.

To extend the investigation, compare the combustion of alcohols to alkanes, alkenes, and alkynes to explore the impact of functional groups and hydrogen atoms on MHC.

5.0 Conclusion

The aim of this investigation was to examine the impact of carbon chain length in alcohols on the molar heat of combustion (MHC). It was hypothesized that increasing the number of carbon atoms in the chain would proportionally increase the MHC. The results supported this hypothesis, demonstrating that alcohols with longer carbon chains indeed exhibit higher MHC values than those with shorter chains.

For instance, Butanol with 4 carbon atoms displayed the lowest average MHC of 1259.39 ± 122.8 kJ/mol, while Octanol with 8 carbon atoms exhibited the highest average MHC of 2499.93 ± 227.5 kJ/mol. The graphical representation of the results confirmed a linear trend, suggesting that for each additional carbon atom, the MHC increased by approximately 301.5 kJ/mol.

However, the experiment encountered a significant limitation due to a major systematic error: heat loss to the surrounding environment. This error resulted from the absence of insulation and insufficient oxygen supply, leading to incomplete combustion. As a consequence, the heat transferred to the water was lower than expected, causing all experimental MHC values to be substantially lower than the accepted values. The average MHC for Butanol, for instance, was 1259.39 ± 122.8 kJ/mol, while the accepted value was 2676 kJ/mol, resulting in an error of 53%. Octanol, excluding outliers, had an average MHC of 2499.93 ± 227.5 kJ/mol, compared to the accepted value of 5294 kJ/mol, with an error of 52%. These significant errors rendered the data inaccurate and the results unreliable.

Therefore, a method with more controlled conditions is required to obtain conclusive results that align with accepted MHC values for alcohols.

6.0 Reference List

1. Bandos, G. (2019). Chain Length. Retrieved 30 July 2019, from http://chemteacher.chemeddl.org/joomla/index.php?option=com_content&view=article&id=59
2. BBC. (2019). Calorimetry - Revision 1 - GCSE Chemistry (Single Science) - BBC Bitesize. Retrieved 30 July 2019, from https://www.bbc.co.uk/bitesize/guides/znp4jxs/revision/1
3. BBC. (2019). Alkanes and alkenes - Revision 2 - GCSE Chemistry (Single Science) - BBC Bitesize. Retrieved 30 July 2019, from https://www.bbc.co.uk/bitesize/guides/z3mpk7h/revision/2
4. Brown, P. (2009). Doc Brown's A Level Chemistry - Advanced Level Theoretical Physical Chemistry Revision Notes - Basic Thermodynamics. Retrieved 30 July 2019, from http://www.docbrown.info/page07/delta1Hd.htm
5. cK-12. (2012). Activation Energy. Retrieved 30 July 2019, from https://www.ck12.org/c/physical-science/activation-energy/lesson/Activation-Energy-MS-PS/
6. cK-12. (2013). Heat of Combustion. Retrieved 30 July 2019, from https://www.ck12.org/chemistry/heat-of-combustion/lesson/Heat-of-Combustion-CHEM/
7. Clark, J. (2010). bond enthalpy (bond energy). Retrieved 30 July 2019, from http://www.chemguide.co.uk/physical/energetics/bondenthalpies.html
8. Henderson, T. (2010). Calorimeters and Calorimetry. Retrieved 30 July 2019, from https://www.physicsclassroom.com/class/thermalP/Lesson-2/Calorimeters-and-Calorimetry
9. Khan Acadamy. (2019). Bond enthalpy and enthalpy of reaction. Retrieved 30 July 2019, from https://www.khanacademy.org/science/chemistry/thermodynamics-chemistry/enthalpy-chemistry-sal/a/bond-enthalpy-and-enthalpy-of-reaction
10. Libre Texts. (2019). Calorimetry. Retrieved 30 July 2019, from https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Supplemental_Modules_(Physical_and_Theoretical_Chemistry)/Thermodynamics/Calorimetry
11. Neutrium. (2014). Heat of Combustion – Neutrium. Retrieved 30 July 2019, from https://neutrium.net/heat_transfer/heat-of-combustion/

7.0 Appendices

MHC of Alcohols (outliers)

MHC (kJ/mol)
122.805
214.525
318.693
252.646
265.942
122.805
214.525
318.693
252.646
265.942

MHC of Alcohols (excluding outliers)

MHC (kJ/mol)
122.805
214.525
318.693
252.646
265.942

No Anom

4	5	6	7	8
MHC (kJ/mol)	1259.386	1645.671	1895.398	2179.537	2499.928

MHC values of all Trials

T1	T2	T3
4	5	6	7	8
MHC (kJ/mol)	1299.488	1688.765	1730.581	2269.318	2607.098
T2	4	5	6	7	8
MHC (kJ/mol)	1249.681	1599.883	2060.216	2276.538	2392.758
T3	4	5	6	7	8
MHC (kJ/mol)	1228.989	1648.364	2872.183	1992.755	3190.830

MHC of Alcohols - Theoretical vs Experimental

Experimental	Accepted
4	5	6	7	8
MHC (kJ/mol)	1259.386	1645.671	1895.398	2179.537	2499.928
Accepted	4	5	6	7	8
MHC (kJ/mol)	2676	3331	3984	4638	5294