Calculate Reaction Enthalpy With Standard Formation Enthalpies

Introduction

In the realm of thermochemistry, understanding and calculating reaction enthalpies is paramount for predicting the feasibility and energy changes associated with chemical reactions. Reaction enthalpy, a crucial thermodynamic parameter, quantifies the heat absorbed or released during a chemical reaction at constant pressure. Standard conditions, defined as 298 K (25 °C) and 1 atm pressure, provide a reference point for comparing the thermodynamic properties of various reactions. One powerful method for determining reaction enthalpy under standard conditions involves utilizing the table of standard formation enthalpies, commonly found in resources like the ALEKS Data tab. This article delves into the methodology of calculating reaction enthalpy using standard formation enthalpies, specifically focusing on the combustion reaction of ethane ($C_2H_6$) with oxygen ($O_2$).

Understanding Standard Formation Enthalpies

Standard formation enthalpy (ΔHf°) is the enthalpy change when one mole of a compound is formed from its constituent elements in their standard states. The standard state refers to the most stable form of an element under standard conditions. For instance, the standard state of oxygen is gaseous diatomic oxygen ($O_2(g)$), and the standard state of carbon is solid graphite (C(s)). The standard formation enthalpy of an element in its standard state is, by definition, zero. This concept serves as a foundation for calculating enthalpy changes for more complex reactions.

Hess's Law and Reaction Enthalpy

The cornerstone of calculating reaction enthalpies from standard formation enthalpies is Hess's Law. This fundamental principle states that the enthalpy change for a reaction is independent of the pathway taken, meaning that the overall enthalpy change is the same whether the reaction occurs in one step or multiple steps. Hess's Law allows us to treat chemical reactions as algebraic equations, where the enthalpy change of the overall reaction can be calculated by summing the enthalpy changes of individual steps.

In the context of standard formation enthalpies, Hess's Law can be expressed as follows:

ΔH°rxn = ΣnΔHf°(products) - ΣmΔHf°(reactants)

Where:

• ΔH°rxn is the standard reaction enthalpy.
• Σ represents the summation.
• n and m are the stoichiometric coefficients of the products and reactants, respectively, in the balanced chemical equation.
• ΔHf°(products) are the standard formation enthalpies of the products.
• ΔHf°(reactants) are the standard formation enthalpies of the reactants.

This equation highlights the essence of the calculation: the standard reaction enthalpy is the difference between the sum of the standard formation enthalpies of the products (each multiplied by its stoichiometric coefficient) and the sum of the standard formation enthalpies of the reactants (each multiplied by its stoichiometric coefficient).

Calculating the Reaction Enthalpy of Ethane Combustion

Let's apply this methodology to the given reaction: the combustion of ethane ($C_2H_6$) with oxygen ($O_2$) to produce carbon dioxide ($CO_2$) and water ($H_2O$):

$2 C_2 H_6(g) + 7 O_2(g) ightarrow 4 CO_2(g) + 6 H_2 O(l)$

Step 1: Identify Standard Formation Enthalpies

The first step is to obtain the standard formation enthalpies (ΔHf°) for each reactant and product from a reliable source, such as the ALEKS Data tab or a standard thermochemical table. These values are typically given in kJ/mol.

• ΔHf°($C_2H_6(g)$) = -84.0 kJ/mol
• ΔHf°($O_2(g)$) = 0 kJ/mol (by definition, as it's an element in its standard state)
• ΔHf°($CO_2(g)$) = -393.5 kJ/mol
• ΔHf°($H_2O(l)$) = -285.8 kJ/mol

Step 2: Apply Hess's Law Formula

Now, we apply the Hess's Law formula:

ΔH°rxn = [4 * ΔHf°($CO_2(g)$) + 6 * ΔHf°($H_2O(l)$)] - [2 * ΔHf°($C_2H_6(g)$) + 7 * ΔHf°($O_2(g)$)]

Step 3: Substitute Values and Calculate

Substitute the standard formation enthalpy values into the equation:

ΔH°rxn = [4 * (-393.5 kJ/mol) + 6 * (-285.8 kJ/mol)] - [2 * (-84.0 kJ/mol) + 7 * (0 kJ/mol)]

ΔH°rxn = [-1574 kJ/mol - 1714.8 kJ/mol] - [-168 kJ/mol + 0 kJ/mol]

ΔH°rxn = -3288.8 kJ/mol + 168 kJ/mol

ΔH°rxn = -3120.8 kJ/mol

Step 4: Round the Answer

Round the final answer to the appropriate number of significant figures. In this case, let's round to one decimal place:

ΔH°rxn ≈ -3120.8 kJ/mol

Therefore, the reaction enthalpy for the combustion of ethane under standard conditions is approximately -3120.8 kJ/mol. The negative sign indicates that this reaction is exothermic, meaning it releases heat to the surroundings.

Significance of Reaction Enthalpy

The reaction enthalpy provides valuable insights into the energy changes associated with a chemical reaction. A negative reaction enthalpy signifies an exothermic reaction, where energy is released, often in the form of heat. Conversely, a positive reaction enthalpy indicates an endothermic reaction, where energy is absorbed from the surroundings. Understanding the reaction enthalpy allows us to predict whether a reaction will spontaneously occur (thermodynamically favorable) and the amount of energy involved.

In the case of ethane combustion, the large negative reaction enthalpy (-3120.8 kJ/mol) underscores the highly exothermic nature of the reaction. This explains why ethane is an effective fuel; its combustion releases a significant amount of energy, making it suitable for various applications, including power generation and heating.

Applications and Implications

The calculation of reaction enthalpies using standard formation enthalpies has widespread applications in various fields:

Chemical Engineering

In chemical engineering, reaction enthalpies are crucial for designing and optimizing chemical processes. Understanding the heat released or absorbed during a reaction is essential for reactor design, heat management, and process safety.

Materials Science

In materials science, reaction enthalpies play a role in predicting the stability and reactivity of materials. They are used in the development of new materials with specific properties, such as high thermal stability or controlled reactivity.

Environmental Science

In environmental science, reaction enthalpies are used to assess the environmental impact of chemical processes. For example, understanding the enthalpy changes associated with combustion reactions is crucial for evaluating the greenhouse gas emissions from power plants and vehicles.

Research and Development

In research and development, reaction enthalpies are used to explore new chemical reactions and pathways. They help scientists understand the energetics of chemical transformations and design more efficient and sustainable processes.

Conclusion

Calculating reaction enthalpies using standard formation enthalpies is a powerful tool for understanding and predicting the energy changes associated with chemical reactions. By applying Hess's Law and utilizing standard formation enthalpy data, we can determine whether a reaction is exothermic or endothermic and quantify the amount of heat released or absorbed. This knowledge is essential in various fields, including chemistry, chemical engineering, materials science, and environmental science. The example of ethane combustion illustrates the practical application of this methodology and its significance in understanding the energy associated with chemical reactions. Understanding the principles and applications discussed in this article provides a strong foundation for further exploration into the fascinating realm of thermochemistry and its role in shaping our understanding of the world around us.

Calculate the standard reaction enthalpy for the reaction $2 C_2 H_6(g) + 7 O_2(g) ightarrow 4 CO_2(g) + 6 H_2 O(l)$ using the table of standard formation enthalpies.

Calculate Reaction Enthalpy with Standard Formation Enthalpies