Problem 94 - Chemistry Matter and Change

Question

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

Step-by-Step Solution

Answer

The enthalpy change for the desired reaction, \(2A + B_2C_3 \rightarrow 2B + A_2C_3\), is \(\Delta H_{desired} = 1589 kJ\).

Step 1: Understand Hess's Law

Hess's law states that the change in enthalpy (?H) for a chemical reaction is independent of the path taken. In other words, if we can manipulate a series of reactions to form the desired reaction, the sum of the enthalpy changes for these reactions will equal the enthalpy change of the desired reaction.

Step 2: Identify our goal and given reactions

Our goal is to calculate ?H for the following reaction: \(2A + B_2C_3 \rightarrow 2B + A_2C_3\) Given reactions and their enthalpy changes are: Reaction 1: \( 2A + \frac{3}{2}C_2 \rightarrow A_2C_3, \quad \Delta{H_1} = -1874 kJ\) Reaction 2: \(2B + \frac{3}{2}C_2 \rightarrow B_2C_3, \quad \Delta{H_2} = -285 kJ\)

Step 3: Manipulate given reactions to match the desired reaction

We need to manipulate the given reactions in such a way that it matches our desired reaction. If we reverse Reaction 1 and add it to Reaction 2, it will form our desired reaction: Reverse Reaction 1: \(A_2C_3 \rightarrow 2A + \frac{3}{2}C_2\) Reaction 2: \(2B + \frac{3}{2}C_2 \rightarrow B_2C_3\) Sum of Reversed Reaction 1 and Reaction 2: \( A_2C_3 + 2B + \frac{3}{2}C_2 \rightarrow 2A + \frac{3}{2}C_2 + 2B + B_2C_3\) Which simplifies to the desired reaction: \(2A + B_2C_3 \rightarrow 2B + A_2C_3\)

Step 4: Calculate the ?H for the desired reaction

Since the desired reaction is the combination of the reversed Reaction 1 and Reaction 2, we can find the enthalpy change for the desired reaction, ?H, using their enthalpy changes: Reversing Reaction 1 changes the sign of its enthalpy change: \(\Delta H_1' = -(\Delta H_1) = 1874 kJ\) Now, add the enthalpy changes for the reversed Reaction 1 and Reaction 2: \(\Delta H_{desired} = \Delta H_1' + \Delta H_2 = 1874 kJ + (-285 kJ) = 1589 kJ\) The enthalpy change for the desired reaction is \(\Delta H_{desired} = 1589 kJ\).

Key Concepts

Enthalpy Change

Enthalpy is a concept used in thermochemistry to describe the total energy of a system. Specifically, it measures the energy required to create a system from nothing, taking account of both the internal energy and the work done to displace its environment. The change in enthalpy, represented by \( \Delta H \), indicates how much energy is absorbed or released during a chemical reaction.
When \( \Delta H \) is negative, the reaction releases energy (exothermic), and when it is positive, the reaction absorbs energy (endothermic).
For example, in the problem provided, the given reactions had their own enthalpy changes: \( \Delta H_1 = -1874 \text{kJ} \) and \( \Delta H_2 = -285 \text{kJ} \). These values signify that both reactions release heat energy into the surroundings.

• Enthalpy is expressed in units of energy, typically kilojoules (kJ).
• The change in enthalpy is crucial for understanding reaction energy requirements.

Using Hess's Law allows us to determine the \( \Delta H \) for reactions that might be difficult to measure directly by summing the \( \Delta H \) of multiple reactions.

Chemical Reactions

Chemical reactions involve the transformation of reactants into products. They are defined by a chemical equation that shows substances involved, their proportions, and the direction of the reaction.
The given problem requires understanding how specific reactions contribute their enthalpic values to achieve a desired chemical transformation.
The key here is to use provided reactions to manipulate them into the target reaction. Reactants and products can be added, subtracted, or their phases reversed (altering \( \Delta H \) accordingly) to meet the goal:

• Reactants are substances initially present in a chemical reaction.
• Products are substances formed as a result of a chemical reaction.

For instance, reversing Reaction 1 changes the direction in which reactants and products form, altering the sign of its enthalpy. Combining this reversed reaction with Reaction 2 enabled the desired transformation that matched the required reaction.

Thermochemistry

Thermochemistry is the study of heat and energy changes in chemical reactions. It involves calculating the energy exchanges as reactions occur, which provides insights into reaction feasibility and efficiency.
Hess's Law plays a significant role in thermochemistry by helping predict the enthalpy change of a reaction by manipulating known reactions. This law is instrumental when direct measurement of \( \Delta H \) is difficult or impossible.
By understanding individual enthalpy changes and the laws governing them, we can predict final energy changes even in complex reactions, like in the provided problem:

• Thermochemistry helps in calculating energy needs or releases in reactions.
• Understanding thermochemical principles is crucial in fields like material science and engineering.

The lesson from Hess's law is that pathway independence allows for flexible approaches in calculating \( \Delta H \), making thermochemical analysis powerful in both scientific and industrial applications.