Enthalpy of Reaction

Introduction

Key Concepts

Definition of Enthalpy of Reaction

The enthalpy of reaction ($\Delta H_{\text{rxn}}$) refers to the heat evolved or absorbed when reactants undergo a chemical change to form products at constant pressure. It is a state function, meaning it depends only on the initial and final states of the system, not on the pathway taken. The sign of $\Delta H_{\text{rxn}}$ indicates the nature of the reaction: exothermic ($\Delta H_{\text{rxn}} < 0$) or endothermic ($\Delta H_{\text{rxn}} > 0$).

Endothermic and Exothermic Reactions

Reactions can be broadly classified based on the direction of heat transfer between the system and its surroundings:

• Exothermic Reactions: These reactions release heat energy to the surroundings, resulting in a negative $\Delta H_{\text{rxn}}$. Combustion reactions are typical examples of exothermic processes.
• Endothermic Reactions: These reactions absorb heat energy from the surroundings, leading to a positive $\Delta H_{\text{rxn}}$. Photosynthesis is a quintessential endothermic reaction.

Hess’s Law

Hess's Law states that the total enthalpy change for a reaction is the same, no matter how many steps the reaction is carried out in. Mathematically, if a reaction can be expressed as a sum of two or more reactions, the enthalpy change of the overall reaction is the sum of the enthalpy changes of the individual steps:

$$\Delta H_{\text{overall}} = \sum \Delta H_{\text{steps}}$$

This principle is particularly useful for calculating enthalpy changes that are difficult to measure directly by using known enthalpy changes of other reactions.

Calculating Enthalpy of Reaction

The enthalpy of reaction can be calculated using the standard enthalpies of formation of the reactants and products. The standard enthalpy change of reaction ($\Delta H_{\text{rxn}}^\circ$) is given by:

$$\Delta H_{\text{rxn}}^\circ = \sum \Delta H_f^\circ (\text{products}) - \sum \Delta H_f^\circ (\text{reactants})$$

where $\Delta H_f^\circ$ is the standard enthalpy of formation of a compound.

Example: Calculate the enthalpy change for the reaction:

$$\text{CH}_4(g) + 2\text{O}_2(g) \rightarrow \text{CO}_2(g) + 2\text{H}_2\text{O}(l)$$

Using standard enthalpies of formation:

• $\Delta H_f^\circ (\text{CH}_4(g)) = -74.8 \text{ kJ/mol}$
• $\Delta H_f^\circ (\text{CO}_2(g)) = -393.5 \text{ kJ/mol}$
• $\Delta H_f^\circ (\text{H}_2\text{O}(l)) = -285.8 \text{ kJ/mol}$
• $\Delta H_f^\circ (\text{O}_2(g)) = 0 \text{ kJ/mol}$

Substituting into the formula:

$$\Delta H_{\text{rxn}}^\circ = [(-393.5) + 2(-285.8)] - [(-74.8) + 2(0)]$$

$$\Delta H_{\text{rxn}}^\circ = (-393.5 - 571.6) - (-74.8) = -965.1 + 74.8 = -890.3 \text{ kJ/mol}$$

This negative value indicates the reaction is exothermic.

Standard Enthalpy Changes

Standard enthalpy changes are measured under standard conditions, typically 1 atm pressure and a specified temperature (usually 25°C). They include:

• Standard Enthalpy of Formation ($\Delta H_f^\circ$): The enthalpy change when one mole of a compound is formed from its constituent elements in their standard states.
• Standard Enthalpy of Combustion ($\Delta H_c^\circ$): The enthalpy change when one mole of a substance undergoes complete combustion with oxygen under standard conditions.
• Standard Enthalpy of Reaction ($\Delta H_{\text{rxn}}^\circ$): The enthalpy change when reactants interact to form products under standard conditions.

Bond Enthalpies and Enthalpy Changes

The bond enthalpy method involves calculating the enthalpy change of a reaction by considering the energies required to break bonds in the reactants and the energies released when new bonds form in the products. The general formula is:

$$\Delta H_{\text{rxn}} = \sum (\text{Bond enthalpies of bonds broken}) - \sum (\text{Bond enthalpies of bonds formed})$$

Example: For the reaction:

$$\text{H}_2(g) + \text{Cl}_2(g) \rightarrow 2\text{HCl}(g)$$

Using average bond enthalpies:

• H–H: 436 kJ/mol
• Cl–Cl: 243 kJ/mol
• H–Cl: 428 kJ/mol

Calculating bonds broken:

• 1 mole H–H bonds: 436 kJ/mol
• 1 mole Cl–Cl bonds: 243 kJ/mol

Calculating bonds formed:

• 2 moles H–Cl bonds: 2 × 428 = 856 kJ/mol

Therefore:

$$\Delta H_{\text{rxn}} = (436 + 243) - 856 = 679 - 856 = -177 \text{ kJ/mol}$$

The negative value indicates an exothermic reaction.

Applications of Enthalpy of Reaction

Understanding the enthalpy of reaction is vital in various applications, including:

• Chemical Engineering: Designing reactors and processes that optimize energy efficiency.
• Pharmaceuticals: Assessing the thermodynamic feasibility of drug synthesis pathways.
• Environmental Science: Evaluating the energy requirements and emissions of chemical processes.
• Materials Science: Formulating materials with desired thermal properties.

Challenges in Measuring Enthalpy of Reaction

Accurately measuring the enthalpy of reaction can be challenging due to factors such as:

• Heat Loss: Unintended heat exchange with the surroundings can distort measurements.
• Reaction Completeness: Incomplete reactions require corrections to enthalpy calculations.
• Phase Changes: The enthalpy associated with phase transitions can complicate analysis.
• Strong Temperature Dependence: Enthalpy changes can vary with temperature, necessitating precise control.

Comparison Table

Summary and Key Takeaways