Calculating Enthalpy Change Using Heats Of Combustion A Thermochemical Approach

In the realm of chemical thermodynamics, understanding heat of combustion and enthalpy changes is crucial for predicting the energy released or absorbed during chemical reactions. This article delves into calculating the enthalpy change (ΔH) for the reaction C(s) + 2H2(g) → CH4(g) using the heats of combustion of C(s), H2(g), and CH4(g). We will explore the concepts, calculations, and significance of these thermochemical properties.

Before diving into the problem, let's define the key concepts:

• Heat of Combustion: The heat released when one mole of a substance is completely burned in oxygen at standard conditions.
• Enthalpy Change (ΔH): The change in heat content of a system at constant pressure. A negative ΔH indicates an exothermic reaction (heat is released), while a positive ΔH indicates an endothermic reaction (heat is absorbed).
• Hess's Law: States that the enthalpy change of a reaction is independent of the pathway taken. It allows us to calculate ΔH for a reaction by using the heats of combustion of reactants and products.

Understanding these concepts is essential for solving thermochemical problems and grasping the energy dynamics of chemical reactions. The heat of combustion provides a direct measure of the energy released when a substance undergoes complete oxidation, typically in the presence of oxygen. This value is crucial for various applications, including fuel efficiency calculations and industrial process design. The enthalpy change, denoted as ΔH, quantifies the heat exchanged between a system and its surroundings at constant pressure, offering insights into the energetic feasibility and spontaneity of reactions. Furthermore, Hess's Law serves as a cornerstone in thermochemistry, enabling the determination of enthalpy changes for complex reactions by breaking them down into simpler steps with known enthalpy values. This law is particularly useful when direct experimental measurement of ΔH is challenging or impractical. By mastering these fundamental concepts, one can effectively analyze and predict the energy transformations associated with chemical processes, fostering a deeper understanding of the principles governing chemical reactions.

Given the heats of combustion of C(s), H2(g), and CH4(g) as -94 kcal/mol, -68 kcal/mol, and -213 kcal/mol, respectively, we need to determine the enthalpy change (ΔH) for the reaction:

C(s) + 2H2(g) → CH4(g)

This problem is a classic application of Hess's Law, which allows us to calculate the enthalpy change of a reaction by using the heats of combustion of reactants and products. The heat of combustion values provide the necessary thermochemical data to determine the energy released or absorbed during the formation of methane (CH4) from its elements, carbon (C) and hydrogen (H2). By carefully manipulating these values and applying Hess's Law, we can effectively navigate through the energetic landscape of this reaction. The significance of this problem extends beyond theoretical calculations, as it has practical implications in fields such as energy production and chemical synthesis. Understanding the enthalpy change for the formation of methane is crucial for optimizing combustion processes, designing efficient energy systems, and developing new synthetic routes for valuable chemical compounds. Therefore, solving this problem not only reinforces our grasp of thermochemical principles but also highlights the relevance of these principles in real-world applications.

To solve this problem, we will use Hess's Law, which states that the enthalpy change for a reaction is the same whether it occurs in one step or multiple steps. We can express the given reaction as a combination of combustion reactions:

1. Combustion of C(s): C(s) + O2(g) → CO2(g) ΔH1 = -94 kcal/mol
2. Combustion of H2(g): H2(g) + 1/2 O2(g) → H2O(l) ΔH2 = -68 kcal/mol
3. Combustion of CH4(g): CH4(g) + 2O2(g) → CO2(g) + 2H2O(l) ΔH3 = -213 kcal/mol

Our target reaction is:

C(s) + 2H2(g) → CH4(g) ΔH = ?

We can obtain the target reaction by manipulating the combustion reactions. First, we multiply the second equation by 2:

2H2(g) + O2(g) → 2H2O(l) 2 * ΔH2 = 2 * (-68 kcal/mol) = -136 kcal/mol

Next, we reverse the third equation:

CO2(g) + 2H2O(l) → CH4(g) + 2O2(g) -ΔH3 = -(-213 kcal/mol) = 213 kcal/mol

Now, we add the first equation, the modified second equation, and the reversed third equation:

C(s) + O2(g) → CO2(g) ΔH1 = -94 kcal/mol

2H2(g) + O2(g) → 2H2O(l) 2 * ΔH2 = -136 kcal/mol

CO2(g) + 2H2O(l) → CH4(g) + 2O2(g) -ΔH3 = 213 kcal/mol

Adding these equations gives us the target reaction:

C(s) + 2H2(g) → CH4(g)

The enthalpy change for the target reaction is the sum of the enthalpy changes of the manipulated reactions:

ΔH = ΔH1 + 2 * ΔH2 + (-ΔH3)

ΔH = -94 kcal/mol + (-136 kcal/mol) + 213 kcal/mol

ΔH = -94 - 136 + 213 kcal/mol

ΔH = -17 kcal/mol

Therefore, the enthalpy change (ΔH) for the reaction C(s) + 2H2(g) → CH4(g) is -17 kcal/mol.

Hess's Law is a fundamental principle in thermochemistry that allows us to calculate the enthalpy change (ΔH) for a reaction by summing the enthalpy changes of individual steps, regardless of the pathway taken. In this problem, we utilize Hess's Law to determine the enthalpy change for the formation of methane (CH4) from its constituent elements, carbon (C) and hydrogen (H2), using the given heats of combustion. The heat of combustion is the energy released when one mole of a substance is completely burned in oxygen under standard conditions. By strategically manipulating and combining the combustion reactions of C(s), H2(g), and CH4(g), we can construct a pathway that leads to the target reaction, C(s) + 2H2(g) → CH4(g). The process involves several key steps:

1. Identifying the Combustion Reactions: We start by writing out the balanced chemical equations for the combustion of each substance: carbon, hydrogen, and methane. These reactions represent the individual steps for which we have known enthalpy changes (heats of combustion).
2. Manipulating the Equations: The goal is to arrange the combustion reactions in such a way that, when added together, they yield the target reaction. This may involve multiplying equations by stoichiometric coefficients, reversing equations (which changes the sign of ΔH), or both. In our case, we multiply the combustion of hydrogen by 2 to match the stoichiometry in the target reaction, and we reverse the combustion of methane, changing the sign of its enthalpy change.
3. Adding the Equations: Once the equations are properly manipulated, we add them together, ensuring that any species appearing on both sides of the equation cancel out. The resulting equation should be the target reaction.
4. Summing the Enthalpy Changes: According to Hess's Law, the enthalpy change for the target reaction is the sum of the enthalpy changes for the manipulated combustion reactions. This sum gives us the overall enthalpy change for the formation of methane from carbon and hydrogen.

By meticulously following these steps, we can accurately determine the enthalpy change for complex reactions using Hess's Law and the heats of combustion of reactants and products. This method is particularly valuable when direct experimental measurement of ΔH is difficult or impossible.

The heat of combustion is a critical parameter in various fields, including chemistry, engineering, and environmental science. It represents the total energy released as heat when a substance undergoes complete combustion with oxygen under standard conditions. This value is essential for several reasons:

1. Fuel Efficiency: In engineering, the heat of combustion is used to determine the efficiency of fuels. Fuels with higher heats of combustion release more energy per unit mass or volume, making them more desirable for applications such as power generation and transportation. For example, the heat of combustion of methane is significantly higher than that of wood, which is why methane is a more efficient fuel source.
2. Calorimetry: In chemistry, the heat of combustion is measured experimentally using calorimeters. These measurements provide valuable data for determining the energy content of substances and for studying the thermodynamics of chemical reactions. The heat of combustion data can be used to calculate other thermodynamic properties, such as enthalpy of formation and bond energies.
3. Industrial Processes: Many industrial processes involve combustion reactions, such as the production of electricity in power plants and the manufacturing of cement and steel. The heat of combustion is a key factor in designing and optimizing these processes. Understanding the heat of combustion helps engineers select the most efficient fuels and design systems that maximize energy output while minimizing waste.
4. Environmental Impact: The heat of combustion is also important for assessing the environmental impact of fuels. Combustion releases greenhouse gases, such as carbon dioxide, which contribute to climate change. Fuels with lower carbon content and higher heats of combustion are generally considered more environmentally friendly. The heat of combustion helps in evaluating the trade-offs between energy production and environmental sustainability.

In summary, the heat of combustion is a fundamental property with wide-ranging applications. It provides critical information for fuel selection, process design, and environmental assessment. By understanding and utilizing heat of combustion data, scientists and engineers can develop more efficient and sustainable energy systems.

Understanding and calculating enthalpy changes, especially using heats of combustion, has numerous practical applications and significant implications across various fields:

1. Industrial Chemistry: In industrial chemistry, knowing the enthalpy change of reactions is crucial for designing and optimizing chemical processes. For instance, in the production of ammonia via the Haber-Bosch process, the enthalpy change helps determine the optimal temperature and pressure conditions to maximize yield while minimizing energy consumption. Similarly, in the petrochemical industry, the enthalpy changes of cracking and reforming reactions are vital for efficient fuel production. The heats of combustion are also essential for evaluating the safety and feasibility of industrial-scale reactions, ensuring that exothermic reactions are controlled to prevent thermal runaways and explosions.

2. Fuel Development: The heat of combustion is a key parameter in fuel development. Fuels with high heats of combustion are desirable because they release more energy per unit mass or volume. Researchers use enthalpy change calculations to evaluate the potential of new fuels, such as biofuels and synthetic fuels. For example, the heat of combustion data helps in comparing the energy content of different biofuels, such as ethanol and biodiesel, and in optimizing their production processes. Furthermore, understanding the combustion characteristics of fuels is critical for designing efficient engines and combustion systems.

3. Environmental Science: Enthalpy change calculations are important in environmental science for assessing the impact of combustion processes on the environment. The heat of combustion of fuels is related to the amount of greenhouse gases, such as carbon dioxide, released during combustion. By understanding these relationships, scientists can develop strategies to reduce emissions and mitigate climate change. For example, the enthalpy change data helps in evaluating the environmental benefits of using alternative fuels, such as hydrogen or renewable biofuels, which have lower carbon emissions compared to fossil fuels.

4. Energy Storage: The enthalpy change concept is also relevant to energy storage technologies. For example, in chemical energy storage systems, such as hydrogen storage and thermochemical energy storage, the enthalpy changes of reactions are used to evaluate the energy storage capacity and efficiency of the system. Understanding the enthalpy changes of reversible reactions is crucial for designing efficient energy storage and release cycles. Additionally, in battery technology, the enthalpy changes associated with electrochemical reactions determine the energy density and performance of batteries.

In conclusion, the practical applications of understanding enthalpy changes and heats of combustion are vast and span across multiple disciplines. From optimizing industrial processes to developing sustainable energy solutions, these thermochemical concepts play a vital role in addressing real-world challenges and advancing technological innovations.

In summary, we have calculated the enthalpy change (ΔH) for the reaction C(s) + 2H2(g) → CH4(g) using the heats of combustion of C(s), H2(g), and CH4(g). By applying Hess's Law, we determined that the ΔH for the reaction is -17 kcal/mol. This calculation demonstrates the importance of thermochemical principles in understanding and predicting energy changes in chemical reactions. The heat of combustion serves as a critical parameter in evaluating fuel efficiency, designing industrial processes, and assessing environmental impacts. Mastering these concepts is essential for anyone studying chemistry or related fields.

The final answer is (A) -17 kcal/mol.