Question

Consider the following two reactions: $$ \begin{array}{ll} \mathrm{A} \longrightarrow 2 \mathrm{~B} & \Delta H_{\mathrm{rxn}}^{\circ}=H_{1} \\\ \mathrm{~A} \longrightarrow \mathrm{C} & \Delta H_{\mathrm{rxn}}^{\circ}=H_{2} \end{array} $$ Determine the enthalpy change for the process $$ 2 \mathrm{~B} \longrightarrow \mathrm{C} $$

Short answer

The enthalpy change is \( H_{2} - H_{1} \).

Step-by-step solution

Analyze the given reactions

We have two reactions:1. \( \mathrm{A} \longrightarrow 2 \mathrm{~B} \) with \( \Delta H_{\mathrm{rxn}}^{\circ} = H_{1} \)2. \( \mathrm{A} \longrightarrow \mathrm{C} \) with \( \Delta H_{\mathrm{rxn}}^{\circ} = H_{2} \).Our goal is to find the enthalpy change for the reaction \( 2 \mathrm{~B} \longrightarrow \mathrm{C} \).

Reverse the necessary reaction

To find the enthalpy change for \( 2 \mathrm{~B} \longrightarrow \mathrm{C} \), reverse the first reaction \( \mathrm{A} \longrightarrow 2 \mathrm{~B} \) to get \( 2 \mathrm{~B} \longrightarrow \mathrm{A} \). This reversal changes the sign of \( \Delta H_{\mathrm{rxn}}^{\circ} \), so it becomes \( -H_{1} \).

Add reversed and given reactions

Combine the reversed reaction from step 2 with the second given reaction:Reversed: \( 2 \mathrm{~B} \longrightarrow \mathrm{A} \), \( \Delta H = -H_{1} \)Given: \( \mathrm{A} \longrightarrow \mathrm{C} \), \( \Delta H = H_{2} \)By combining, we get: \( 2 \mathrm{~B} \longrightarrow \mathrm{C} \).

Calculate the enthalpy change for the target reaction

Add the enthalpy changes from the combined reactions:\[\Delta H_{\text{total}} = (-H_{1}) + H_{2} = H_{2} - H_{1}\]This gives the enthalpy change for the reaction \( 2 \mathrm{~B} \longrightarrow \mathrm{C} \).

Key concepts

Chemical Reactions

Chemical reactions involve the transformation of substances through the breaking and forming of chemical bonds. This process results in the conversion of reactants to products. In the context of our original problem, we have two reactions where substance \( A \) reacts to form either \( 2B \) or \( C \).

These reactions can have different enthalpy changes (\( \Delta H \)), which represent the total heat absorbed or released during a reaction at constant pressure. These changes help us understand how energy flows in or out of a system. In the reactions provided, \( \Delta H_{\text{rxn}}^{\circ} = H_1 \) and \( \Delta H_{\text{rxn}}^{\circ} = H_2 \) are the respective enthalpy changes.

When manipulating chemical reactions, such as reversing or adding them, the enthalpy changes must also be adjusted accordingly. Understanding these transformations aids in calculating enthalpy changes for new reactions using known data from related reactions.

Hess's Law

Hess's Law is a fundamental principle in chemistry that states that the total enthalpy change of a chemical reaction is independent of the pathway taken. The law emphasizes that enthalpy is a state function, which means it depends only on the initial and final states, not on the steps in between.

In the exercise, Hess's Law allows us to find the enthalpy change for the desired reaction \( 2B \rightarrow C \) by combining and manipulating the given reactions and their corresponding enthalpies. Specifically, by reversing one reaction and adding it to another, we apply Hess's Law to calculate the enthalpy change \( \Delta H = H_2 - H_1 \) for the new reaction.

This method is incredibly useful when the direct determination of a reaction's enthalpy is challenging or impractical. It allows us to build on known enthalpies of simpler reactions to deduce the enthalpy changes of more complex reactions.

Thermochemistry

Thermochemistry is the branch of chemistry that studies the heat evolved or absorbed in chemical reactions. It focuses on the measurement and interpretation of enthalpy changes to understand energy transformations in chemical processes.

In practical applications, thermochemistry helps in predicting the feasibility of reactions, studying energy efficiency, and understanding the conditions under which reactions occur. By knowing the enthalpy change, scientists and engineers can gauge how much energy systems release or need, essential for diverse fields such as material science and environmental technology.

• Endothermic reactions absorb heat, having positive enthalpy changes.
• Exothermic reactions release heat, having negative enthalpy changes.

In our problem, tracking these changes through the given and reversed reactions illustrates thermochemistry's role in providing insights into energy exchanges during chemical transformations.