Question

For each generic reaction, determine the value of \(\Delta H_{2}\) in terms of \(\Delta H_{1} .\) a. \(\mathrm{A}+\mathrm{B} \longrightarrow 2 \mathrm{C} \quad \Delta H_{1}\) \(2 \mathrm{C} \longrightarrow \mathrm{A}+\mathrm{B} \quad \Delta H_{2}=?\) b. \(A+1 / 2 B \longrightarrow C\) \(\Delta H_{1}\) \(2 \mathrm{~A}+\mathrm{B} \longrightarrow 2 \mathrm{C} \quad \Delta H_{2}=?\) \(\begin{array}{ll}\text { c. } A \longrightarrow B+2 C & \Delta H_{1}\end{array}\) \(1 / 2 \mathrm{~B}+\mathrm{C} \longrightarrow 1 / 2 \mathrm{~A} \quad \Delta H_{2}=?\)

Short answer

\(\Delta H_{2}=-\Delta H_{1}\) for reaction A, \(\Delta H_{2}=2\Delta H_{1}\) for reaction B, and \(\Delta H_{2}=-\frac{1}{2}\Delta H_{1}\) for reaction C.

Step-by-step solution

Identify Reverse Reaction

Note that reaction A in the reverse is exactly the reverse of the given reaction. When a reaction is reversed, the sign of the enthalpy change is also reversed.

Calculate \(\Delta H_{2}\) for Reaction A

Since the reaction is reversed, \(\Delta H_{2} = -\Delta H_{1}\). The enthalpy change for reaction A in the reverse direction will have an opposite sign.

Identify the Multiple of the First Reaction

Reaction B involves the first reaction being multiplied by 2 as indicated by the coefficients of reactants and products.

Calculate \(\Delta H_{2}\) for Reaction B

For reaction B that has been scaled up by a factor of 2, \(\Delta H_{2} = 2 \times \Delta H_{1}\) since enthalpy is an extensive property.

Identify the Fraction of the Reverse Reaction

Reaction C in the reverse is 1/2 of the original reaction, as shown by the coefficients of the reactants and products.

Calculate \(\Delta H_{2}\) for Reaction C

Because reaction C is half and the opposite of the first reaction, \(\Delta H_{2} = -\frac{1}{2} \times \Delta H_{1}\).

Key concepts

Understanding Thermochemistry

Thermochemistry is a branch of physical chemistry that deals with the energy changes, particularly heat, involved in chemical reactions. When a reaction occurs, energy is either released or absorbed, and this energy change is referred to as the enthalpy change, symbolized by \( \Delta H \).

\[ \Delta H \] is an important concept in thermochemistry as it tells us whether a reaction is exothermic (releases heat, \( \Delta H < 0 \) ) or endothermic (absorbs heat, \( \Delta H > 0 \) ). Understanding how to calculate and interpret \( \Delta H \) is crucial for predicting the behavior of chemical reactions and for designing processes that require energy management, such as in industrial chemical production.

Applying Hess's Law

Hess's Law states that the total enthalpy change in a chemical reaction is the same, irrespective of the number of stages in which the reaction takes place. This is because enthalpy is a state function, meaning it only depends on the initial and final states of the system, not the path taken.

Using Hess's Law, we can determine \( \Delta H \) for complex reactions by breaking them down into simpler steps, whose enthalpy changes are known or can be measured easily. This principle is incredibly helpful in educational exercises because it allows us to manipulate equations algebraically. For example, if a reaction is reversed, the sign of \( \Delta H \) is also reversed, as noted in the step-by-step solution. This also applies when scaling reactions up or down; the \( \Delta H \) will scale accordingly with the stoichiometric coefficients.

Examining Enthalpy as an Extensive Property

An extensive property is one that changes when the size of the sample changes. Enthalpy is one such property, meaning that the value of \( \Delta H \) is directly proportional to the amount of substance involved in the reaction.

For instance, if a given reaction \( A \rightarrow B \) has an enthalpy change \( \Delta H_{1} \), then carrying out the same reaction with double the amount of reactant \( 2A \rightarrow 2B \) will result in \( \Delta H_{2} \) being \( 2 \times \Delta H_{1} \), as shown in the solution for reaction B. The concept of enthalpy being an extensive property is fundamental in thermochemistry and must be considered when predicting how \( \Delta H \) will behave in scaled-up or scaled-down reactions.

This property is especially useful when dealing with industrial processes, where reactions are being carried out on a much larger scale than those seen in a typical laboratory setting.