Problem 94 - Chemistry Matter and Change

Question

Use Hess' law and the changes in enthalpy for the following two generic reactions to calculate \(\Delta H\) for the reaction \(2 \mathrm{A}+\mathrm{B}_{2} \mathrm{C}_{3} \rightarrow 2 \mathrm{B}+\mathrm{A}_{2} \mathrm{C}_{3}\) \(2 \mathrm{A}+\frac{3}{2} \mathrm{C}_{2} \rightarrow \mathrm{A}_{2} \mathrm{C}_{3} \quad \Delta \mathrm{H}=-1874 \mathrm{kJ}\) \(2 \mathrm{B}+\frac{3}{2} \mathrm{C}_{2} \rightarrow \mathrm{B}_{2} \mathrm{C}_{3} \quad \Delta H=-285 \mathrm{kJ}\)

Step-by-Step Solution

Answer

\(\Delta H = -1589\,\text{kJ}\) for the reaction.

Step 1: Write the Target Reaction

We need to determine the enthalpy change \(\Delta H\) for the reaction:\[ 2 \mathrm{A} + \mathrm{B}_{2} \mathrm{C}_{3} \rightarrow 2 \mathrm{B} + \mathrm{A}_{2} \mathrm{C}_{3} \]

Step 2: Identify Given Reactions and Their Enthalpies

The given reactions are: 1. \(2 \mathrm{A} + \frac{3}{2} \mathrm{C}_{2} \rightarrow \mathrm{A}_{2} \mathrm{C}_{3}\) with \(\Delta \mathrm{H} = -1874\,\text{kJ}\) 2. \(2 \mathrm{B} + \frac{3}{2} \mathrm{C}_{2} \rightarrow \mathrm{B}_{2} \mathrm{C}_{3}\) with \(\Delta \mathrm{H} = -285\,\text{kJ}\)

Step 3: Reverse the Second Given Reaction

Reverse the second reaction to match the target reaction's product and reactant placement, changing the sign of \(\Delta H\):\[ \mathrm{B}_{2} \mathrm{C}_{3} \rightarrow 2 \mathrm{B} + \frac{3}{2} \mathrm{C}_{2} \] with \(\Delta H = +285\,\text{kJ}\)

Step 4: Combine the Reactions

Add the first given reaction and the reversed second reaction to achieve the target reaction: 1. \(2 \mathrm{A} + \frac{3}{2} \mathrm{C}_{2} \rightarrow \mathrm{A}_{2} \mathrm{C}_{3}\) 2. \(\mathrm{B}_{2} \mathrm{C}_{3} \rightarrow 2 \mathrm{B} + \frac{3}{2} \mathrm{C}_{2}\) When combined:\[ 2 \mathrm{A} + \frac{3}{2} \mathrm{C}_{2} + \mathrm{B}_{2} \mathrm{C}_{3} \rightarrow \mathrm{A}_{2} \mathrm{C}_{3} + 2 \mathrm{B} + \frac{3}{2} \mathrm{C}_{2} \] Removing \(\frac{3}{2} \mathrm{C}_{2}\) from both sides, results in:\[ 2 \mathrm{A} + \mathrm{B}_{2} \mathrm{C}_{3} \rightarrow 2 \mathrm{B} + \mathrm{A}_{2} \mathrm{C}_{3} \]

Step 5: Calculate \(\Delta H\) for the Target Reaction

Sum the enthalpy changes for the combined reactions:\[ \Delta H = -1874\,\text{kJ} + 285\,\text{kJ} \]\[ \Delta H = -1589\,\text{kJ} \]

Step 6: Conclusion

The enthalpy change \(\Delta H\) for the reaction \(2 \mathrm{A} + \mathrm{B}_{2} \mathrm{C}_{3} \rightarrow 2 \mathrm{B} + \mathrm{A}_{2} \mathrm{C}_{3}\) is \(-1589\,\text{kJ}\).

Key Concepts

Enthalpy Change

In the context of chemical reactions, enthalpy change \( \Delta H \) is a vital concept. It represents the heat absorbed or released during a chemical reaction at constant pressure. When we talk about \( \Delta H \), it's essential to remember that it can either be positive (endothermic) or negative (exothermic). An endothermic reaction absorbs heat from the surroundings, while an exothermic reaction releases heat.
In our exercise, we computed \( \Delta H \) for a target reaction using Hess' Law. Hess' Law states that if a reaction is the sum of two or more other reactions, the enthalpy change for the net reaction is the sum of the enthalpy changes for the individual reactions. This principle allows us to break down complex reactions into simpler steps and calculate the overall enthalpy change by simply adding the enthalpy changes of these steps.
The use of Hess' Law ensures that no matter the route taken to convert reactants to products, the total enthalpy change remains consistent. So whether 2 A + B2C3 evolves directly into 2 B + A2C3, or follows a multiple-step pathway, the \( \Delta H \) remains \(-1589 \text{kJ}\).

Chemical Reactions

Chemical reactions are processes where reactants are transformed into products, involving the breaking and forming of chemical bonds.
During this transformation, energy is either absorbed or released, which is measured as the enthalpy change. Each chemical reaction has its own unique enthalpic characteristics. Some reactions need energy input to proceed, referred to as endothermic, while others release energy, known as exothermic reactions.
By understanding the nature of these reactions and their enthalpic profiles, scientists can predict reaction behavior and manipulate them accordingly. For instance, knowing that a reaction such as \( 2 A + B2C3 \rightarrow 2 B + A2C3 \) is exothermic can help in determining the feasibility and conditions under which the reaction should be carried out. Exploring the enthalpy change through exercises like ours enables students to grasp how energy considerations influence reactions and their practical applications.

Thermodynamics

Thermodynamics is the branch of physical science that deals with the relationships between heat and other forms of energy. In chemistry, it helps us understand how energy changes occur during chemical processes. Since chemical reactions involve making and breaking bonds, thermodynamics provides critical insights into these energy shifts.
One core concept in thermodynamics is the principle of conservation of energy. It implies that energy cannot be created or destroyed, only converted from one form to another. This is closely linked to enthalpy, as the enthalpy change represents a form of energy transfer during chemical reactions.
For instance, Hess' Law is grounded in thermodynamic principles by stating that since enthalpy is a state function, the \( \Delta H \) for a reaction is independent of the pathway taken. Thus, thermodynamics provides foundational principles that enable us to predict, calculate, and manipulate energy changes within reactions to achieve desired outcomes.

Reaction Energetics

Reaction energetics focuses on the energy changes that occur during chemical reactions. Understanding these energetics is pivotal in determining whether a reaction will occur spontaneously, and if it does, how fast it will proceed.
Various factors influence the energetics of a reaction, including bond energies, temperature, pressure, and the presence of catalysts. In our Hess' Law exercise, we calculated the energy change using known enthalpies of sub-reactions, thus determining the energetics of the target reaction.
These calculations are vital in the industrial and chemical engineering fields where controlling reaction energetics for processes like synthesis, combustion, or even in biological systems is crucial for efficiency and safety. By mastering reaction energetics, one can predict and control the course and extent of chemical transformations effectively.