Calculating Enthalpy Of Combustion Of Acetylene A Step-by-Step Guide

The enthalpy of combustion is a crucial thermochemical parameter, representing the heat released when one mole of a substance completely combusts in oxygen under standard conditions. Determining the enthalpy of combustion is vital in various fields, including chemical engineering, materials science, and environmental science, as it provides essential data for energy balance calculations, reactor design, and assessing the energy content of fuels. In this article, we will delve into the calculation of the enthalpy of combustion for acetylene ($C_2H_2$), a highly versatile and energy-rich compound widely used in welding, cutting, and as a chemical feedstock. By employing Hess's Law and standard enthalpies of formation, we will meticulously determine the enthalpy change for the combustion reaction, providing a comprehensive understanding of the energy released during this process. Accurately determining the enthalpy of combustion is paramount for optimizing industrial processes, ensuring safety, and developing sustainable energy solutions. The combustion of acetylene is an exothermic reaction, meaning it releases heat into the surroundings. This heat release is what makes acetylene such a useful fuel. Understanding the enthalpy of combustion allows engineers to design efficient combustion systems and to predict the amount of heat that will be released in a given reaction. This knowledge is also crucial for safety considerations, as uncontrolled combustion can lead to explosions or fires. Furthermore, the enthalpy of combustion data is essential for comparing the energy content of different fuels, helping in the selection of the most suitable fuel for a particular application. In addition, the enthalpy of combustion plays a significant role in environmental studies. By knowing the amount of heat released during the combustion of a fuel, scientists can assess its impact on the environment, including its contribution to greenhouse gas emissions and air pollution. This information is vital for developing cleaner and more sustainable energy technologies. In this article, we will not only calculate the enthalpy of combustion for acetylene but also discuss the implications of this value in various practical applications. We will explore how this information is used in industry, research, and environmental studies, providing a comprehensive understanding of the significance of enthalpy of combustion in the broader context of chemistry and engineering.

Background

Acetylene ($C_2H_2$) is a colorless, highly flammable gas widely recognized for its exceptional energy content. Its high enthalpy of combustion makes it a popular fuel in welding and cutting torches, where its ability to produce intense heat is crucial for melting and cutting metals. Beyond its industrial applications, acetylene serves as a fundamental building block in organic synthesis, playing a vital role in the production of various chemical compounds, polymers, and pharmaceuticals. The enthalpy of combustion, symbolized as $\Delta H_c$, is a quantitative measure of the heat released when one mole of a substance undergoes complete combustion under standard conditions (298 K and 1 atm pressure). This value is inherently negative for exothermic reactions, signifying the release of heat, while it is positive for endothermic reactions, which require heat input. Understanding the enthalpy of combustion is essential for evaluating the energy potential of a fuel and for designing efficient combustion processes. The combustion of acetylene with oxygen is a highly exothermic reaction, producing carbon dioxide and water as the primary products. The balanced chemical equation for this reaction is:

$2 C_2 H_2(g) + 5 O_2(g) \rightarrow 4 CO_2(g) + 2 H_2 O(g)$

To accurately determine the enthalpy of combustion for acetylene, we can leverage Hess's Law. This fundamental principle of thermochemistry asserts that the enthalpy change for a reaction is independent of the pathway taken, depending solely on the initial and final states. In essence, this law allows us to calculate the enthalpy change for a reaction by summing the enthalpy changes for a series of steps that ultimately lead to the same overall reaction. One of the most powerful applications of Hess's Law involves using standard enthalpies of formation ($\Delta H_f^\circ$). The standard enthalpy of formation is defined as the enthalpy change when one mole of a compound is formed from its constituent elements in their standard states (the most stable form at 298 K and 1 atm). By utilizing tabulated values of standard enthalpies of formation for reactants and products, we can precisely calculate the enthalpy of combustion for acetylene. This method provides a robust and reliable approach to determine the energy released during the combustion process. In the subsequent sections, we will meticulously apply Hess's Law and standard enthalpies of formation to calculate the enthalpy of combustion for acetylene, providing a detailed and comprehensive analysis of the thermochemistry involved in this crucial reaction. This calculation is essential not only for understanding the energy potential of acetylene but also for optimizing its use in various industrial and scientific applications.

Objective

The primary objective of this article is to meticulously calculate the enthalpy of combustion for one mole of acetylene ($C_2H_2$) using the provided standard enthalpies of formation ($\Delta H_f^\circ$). This calculation will be performed by applying Hess's Law, a fundamental principle in thermochemistry that allows us to determine the enthalpy change of a reaction by summing the enthalpy changes of individual steps leading to the overall reaction. The provided reaction is:

$2 C_2 H_2(g) + 5 O_2(g) \rightarrow 4 CO_2(g) + 2 H_2 O(g)$

To achieve this objective, we will utilize the standard enthalpies of formation for each compound involved in the reaction, as outlined in the table. The standard enthalpy of formation is the enthalpy change when one mole of a compound is formed from its constituent elements in their standard states (298 K and 1 atm). By employing these values, we can accurately determine the enthalpy change for the combustion of acetylene. This calculation is crucial for understanding the energy released during the combustion process and for assessing the fuel potential of acetylene. Furthermore, this exercise provides a practical application of Hess's Law and highlights the importance of thermochemical data in chemical calculations. Accurately determining the enthalpy of combustion is essential for various applications, including industrial process design, energy balance calculations, and environmental impact assessments. In industrial settings, this value is critical for optimizing combustion processes, ensuring efficient energy utilization, and preventing hazardous conditions. In environmental studies, the enthalpy of combustion helps in evaluating the environmental impact of fuel combustion, including greenhouse gas emissions and air pollution. By calculating the enthalpy of combustion of acetylene, we gain insights into its energy content and its potential as a fuel source. This information is valuable for developing sustainable energy solutions and for comparing the energy potential of different fuels. Moreover, this calculation reinforces the fundamental concepts of thermochemistry and provides a solid foundation for further studies in chemical thermodynamics. In the subsequent sections, we will present a step-by-step calculation of the enthalpy of combustion for acetylene, providing a clear and concise explanation of the methodology and the results obtained.

Data Provided

To calculate the enthalpy of combustion of acetylene, we are provided with a table of standard enthalpies of formation ($\Delta H_f^\circ$) for the compounds involved in the reaction. The standard enthalpy of formation is a crucial thermochemical property, representing the enthalpy change when one mole of a compound is formed from its constituent elements in their standard states (298 K and 1 atm). These values are essential for applying Hess's Law and determining the enthalpy change for the combustion reaction. The table typically includes the following compounds:

• Acetylene ($C_2H_2$)
• Carbon Dioxide ($CO_2$)
• Water ($H_2O$)

The standard enthalpy of formation for oxygen ($O_2$) is, by definition, zero because it is an element in its standard state. This simplifies the calculation, as we only need to consider the enthalpies of formation for the compounds being formed or consumed in the reaction. The accurate values of the standard enthalpies of formation are critical for obtaining a precise calculation of the enthalpy of combustion. These values are experimentally determined and are typically available in thermochemical tables or databases. The units for standard enthalpy of formation are typically given in kilojoules per mole (kJ/mol). Understanding the significance of these values is paramount for correctly applying Hess's Law. The enthalpy of formation is a state function, meaning it depends only on the initial and final states and not on the path taken to reach those states. This property is what allows us to use Hess's Law to calculate the enthalpy change for a reaction. Moreover, the standard enthalpies of formation provide valuable information about the relative stability of compounds. Compounds with large negative enthalpies of formation are more stable than compounds with less negative or positive enthalpies of formation. This stability is directly related to the energy required to break the bonds in the reactants and form the bonds in the products. In the following sections, we will utilize the provided standard enthalpies of formation to calculate the enthalpy of combustion of acetylene, demonstrating the practical application of Hess's Law and the importance of thermochemical data in chemical calculations. This calculation will provide a clear understanding of the energy released during the combustion process and the role of acetylene as a fuel.

Compound	$\Delta H _{ f } (kJ/mol)$	Discussion Category
$C_2 H_2$	226.7	Chemistry
$CO_2$	-393.5	Chemistry
$H_2 O$	-285.8	Chemistry
$O_2$	0	Chemistry

Calculation Methodology

To calculate the enthalpy of combustion of acetylene, we will employ Hess's Law, a fundamental principle in thermochemistry. Hess's Law states that the enthalpy change for a reaction is independent of the pathway taken and depends only on the initial and final states. This allows us to calculate the enthalpy change for the combustion reaction by summing the enthalpies of formation of the products and subtracting the enthalpies of formation of the reactants, each multiplied by their stoichiometric coefficients from the balanced chemical equation. The balanced chemical equation for the combustion of acetylene is:

$2 C_2 H_2(g) + 5 O_2(g) \rightarrow 4 CO_2(g) + 2 H_2 O(g)$

The formula for calculating the enthalpy of reaction ($\Delta H_{rxn}$) using Hess's Law and standard enthalpies of formation ($\Delta H_f^\circ$) is:

$\Delta H_{rxn} = \sum [n \times \Delta H_f^\circ (products)] - \sum [n \times \Delta H_f^\circ (reactants)]$

where n represents the stoichiometric coefficient for each compound in the balanced chemical equation. In our case, the products are carbon dioxide ($CO_2$) and water ($H_2O$), and the reactants are acetylene ($C_2H_2$) and oxygen ($O_2$). We will use the provided standard enthalpies of formation for each compound and their respective stoichiometric coefficients to calculate the enthalpy of combustion. First, we will calculate the total enthalpy of formation for the products:

$\sum [n \times \Delta H_f^\circ (products)] = [4 \times \Delta H_f^\circ (CO_2)] + [2 \times \Delta H_f^\circ (H_2O)]$

Then, we will calculate the total enthalpy of formation for the reactants:

$\sum [n \times \Delta H_f^\circ (reactants)] = [2 \times \Delta H_f^\circ (C_2H_2)] + [5 \times \Delta H_f^\circ (O_2)]$

Finally, we will subtract the enthalpy of formation of the reactants from the enthalpy of formation of the products to obtain the enthalpy of reaction, which in this case is the enthalpy of combustion for 2 moles of acetylene. To find the enthalpy of combustion for 1 mole of acetylene, we will divide the result by 2. This step-by-step methodology ensures an accurate calculation of the enthalpy of combustion, providing valuable insights into the energy released during the combustion of acetylene. The correct application of Hess's Law and the use of standard enthalpies of formation are crucial for obtaining reliable thermochemical data. In the following section, we will apply this methodology using the provided data to calculate the enthalpy of combustion for acetylene.

Step-by-Step Calculation

Now, let's perform the step-by-step calculation of the enthalpy of combustion for acetylene using the provided data and the methodology outlined in the previous section. We will use the following standard enthalpies of formation ($\Delta H_f^\circ$) from the table:

• $\Delta H_f^\circ (C_2H_2) = 226.7 \, kJ/mol$
• $\Delta H_f^\circ (CO_2) = -393.5 \, kJ/mol$
• $\Delta H_f^\circ (H_2O) = -285.8 \, kJ/mol$
• $\Delta H_f^\circ (O_2) = 0 \, kJ/mol$

The balanced chemical equation for the combustion of acetylene is:

$2 C_2 H_2(g) + 5 O_2(g) \rightarrow 4 CO_2(g) + 2 H_2 O(g)$

Step 1: Calculate the total enthalpy of formation for the products

$\sum [n \times \Delta H_f^\circ (products)] = [4 \times \Delta H_f^\circ (CO_2)] + [2 \times \Delta H_f^\circ (H_2O)]$

Substitute the values:

$\sum [n \times \Delta H_f^\circ (products)] = [4 \times (-393.5 \, kJ/mol)] + [2 \times (-285.8 \, kJ/mol)]$

$\sum [n \times \Delta H_f^\circ (products)] = -1574 \, kJ/mol - 571.6 \, kJ/mol$

$\sum [n \times \Delta H_f^\circ (products)] = -2145.6 \, kJ/mol$

Step 2: Calculate the total enthalpy of formation for the reactants

$\sum [n \times \Delta H_f^\circ (reactants)] = [2 \times \Delta H_f^\circ (C_2H_2)] + [5 \times \Delta H_f^\circ (O_2)]$

Substitute the values:

$\sum [n \times \Delta H_f^\circ (reactants)] = [2 \times (226.7 \, kJ/mol)] + [5 \times (0 \, kJ/mol)]$

$\sum [n \times \Delta H_f^\circ (reactants)] = 453.4 \, kJ/mol + 0 \, kJ/mol$

$\sum [n \times \Delta H_f^\circ (reactants)] = 453.4 \, kJ/mol$

Step 3: Calculate the enthalpy of reaction ($\Delta H_{rxn}$)

$\Delta H_{rxn} = \sum [n \times \Delta H_f^\circ (products)] - \sum [n \times \Delta H_f^\circ (reactants)]$

Substitute the values:

$\Delta H_{rxn} = -2145.6 \, kJ/mol - 453.4 \, kJ/mol$

$\Delta H_{rxn} = -2599 \, kJ/mol$

This value represents the enthalpy of combustion for 2 moles of acetylene. To find the enthalpy of combustion for 1 mole of acetylene, we divide by 2:

$\Delta H_{combustion} (1 \, mole \, C_2H_2) = \frac{-2599 \, kJ/mol}{2}$

$\Delta H_{combustion} (1 \, mole \, C_2H_2) = -1299.5 \, kJ/mol$

Therefore, the enthalpy of combustion for 1 mole of acetylene is approximately -1299.5 kJ/mol. This negative value indicates that the combustion of acetylene is an exothermic reaction, meaning it releases heat. In the next section, we will discuss the significance of this result and its implications.

Results and Discussion

Based on the calculations performed, the enthalpy of combustion for 1 mole of acetylene ($C_2H_2$) is approximately -1299.5 kJ/mol. This negative value signifies that the combustion reaction is highly exothermic, meaning it releases a significant amount of heat into the surroundings. The large magnitude of the enthalpy of combustion underscores the potential of acetylene as a high-energy fuel. The release of heat during the combustion process is what makes acetylene suitable for applications such as welding and cutting, where high temperatures are required to melt or vaporize metals. The calculated enthalpy of combustion is a crucial parameter for various applications, including industrial process design, energy balance calculations, and safety assessments. In industrial settings, this value is used to optimize combustion processes, ensuring efficient energy utilization and minimizing fuel consumption. For example, engineers can use the enthalpy of combustion data to design combustion chambers and burners that maximize heat transfer and minimize energy losses. In energy balance calculations, the enthalpy of combustion is a key component in determining the overall energy efficiency of a system. This is particularly important in power generation and chemical manufacturing, where energy efficiency directly impacts operational costs and environmental footprint. Furthermore, the enthalpy of combustion plays a vital role in safety assessments. Understanding the amount of heat released during combustion is essential for preventing hazardous conditions, such as explosions or fires. This information is used to design safety systems and procedures that mitigate the risks associated with the handling and storage of flammable materials like acetylene. The high enthalpy of combustion of acetylene also has implications for environmental studies. While acetylene itself is not a significant greenhouse gas, the combustion process produces carbon dioxide ($CO_2$), a major contributor to global warming. Therefore, the efficient combustion of acetylene is crucial to minimize $CO_2$ emissions. Moreover, the formation of other pollutants, such as nitrogen oxides ($NO_x$) and particulate matter, needs to be controlled to mitigate air pollution. In conclusion, the calculated enthalpy of combustion for acetylene provides valuable insights into its energy potential and its role in various applications. The exothermic nature of the combustion reaction and the large amount of heat released make acetylene a versatile fuel, but also necessitate careful management and control to ensure safety and minimize environmental impact. In the next section, we will summarize the key findings and discuss the implications of this calculation.

Conclusion

In this article, we have successfully calculated the enthalpy of combustion for 1 mole of acetylene ($C_2H_2$) using Hess's Law and the provided standard enthalpies of formation. The step-by-step calculation revealed that the enthalpy of combustion is approximately -1299.5 kJ/mol. This significant negative value confirms that the combustion of acetylene is a highly exothermic reaction, releasing a substantial amount of heat into the surroundings. The calculated enthalpy of combustion has several important implications across various fields, including industrial engineering, energy production, and environmental science. In industrial applications, the high enthalpy of combustion of acetylene makes it an ideal fuel for processes requiring high temperatures, such as welding and cutting. The precise knowledge of this value allows engineers to design efficient combustion systems, optimize fuel consumption, and ensure safe operating conditions. By understanding the amount of heat released during combustion, engineers can develop systems that maximize heat transfer and minimize energy losses, leading to improved energy efficiency and reduced operational costs. In the realm of energy production, the enthalpy of combustion is a key parameter in assessing the energy potential of acetylene. This information is crucial for comparing acetylene with other fuels and for evaluating its suitability for various energy applications. While acetylene is not as widely used as other fuels like natural gas or propane, its high enthalpy of combustion makes it a viable option for specialized applications where high energy density is required. From an environmental perspective, the enthalpy of combustion is essential for assessing the environmental impact of acetylene combustion. The combustion process produces carbon dioxide ($CO_2$), a major greenhouse gas, and other pollutants. By quantifying the enthalpy of combustion, scientists and engineers can evaluate the carbon footprint of acetylene combustion and develop strategies to mitigate its environmental effects. This includes optimizing combustion processes to minimize $CO_2$ emissions and exploring alternative combustion technologies that produce fewer pollutants. Furthermore, the calculation of the enthalpy of combustion for acetylene serves as a valuable exercise in applying thermochemical principles, particularly Hess's Law. This fundamental law allows us to determine the enthalpy change for a reaction by summing the enthalpy changes of individual steps, providing a powerful tool for thermodynamic calculations. The accurate determination of the enthalpy of combustion requires a thorough understanding of Hess's Law, standard enthalpies of formation, and stoichiometric relationships. In summary, the enthalpy of combustion for acetylene, calculated to be -1299.5 kJ/mol, is a critical thermochemical property with wide-ranging implications. This value provides valuable insights into the energy potential of acetylene, its applications in industry and energy production, and its environmental impact. The principles and methodologies used in this calculation are fundamental to thermochemistry and are essential for various scientific and engineering disciplines. Understanding the enthalpy of combustion is crucial for developing sustainable energy solutions, optimizing industrial processes, and ensuring environmental stewardship.