Question

Use bond energy values (Table 8.5\()\) to estimate \(\Delta H\) for each of the following reactions in the gas phase. a. \(\mathrm{H}_{2}+\mathrm{Cl}_{2} \rightarrow 2 \mathrm{HCl}\) b. \(\mathrm{N} \equiv \mathrm{N}+3 \mathrm{H}_{2} \rightarrow 2 \mathrm{NH}_{3}\)

Short answer

Using bond energy values and the formula \(\Delta H = \text{Energy of bonds broken} - \text{Energy of bonds formed}\), we calculated the change in enthalpy (\(\Delta H\)) for two reactions: a. \(\mathrm{H}_{2}+\mathrm{Cl}_{2} \rightarrow 2 \mathrm{HCl}\) \(\Delta H = -190\text{ kJ/mol}\) b. $\mathrm{N} \equiv \mathrm{N}+3 \mathrm{H}_{2} \rightarrow 2 \mathrm{NH}_{3}$ \(\Delta H = -93\text{ kJ/mol}\)

Step-by-step solution

Reaction a: H2 + Cl2 -> 2 HCl

In this reaction, one H-H bond and one Cl-Cl bond are broken, and two H-Cl bonds are formed. Look up the bond energy values for these bonds in Table 8.5: H-H bond: 432 kJ/mol Cl-Cl bond: 242 kJ/mol H-Cl bond: 432 kJ/mol

Reaction b: N≡N + 3 H2 -> 2 NH3

In this reaction, one N≡N triple bond and three H-H bonds are broken, and six N-H bonds are formed. Look up the bond energy values for these bonds in Table 8.5: N≡N triple bond: 941 kJ/mol H-H bond: 432 kJ/mol N-H bond: 391 kJ/mol **Step 2: Calculate \(\Delta H\) for each reaction** For each reaction, calculate \(\Delta H\) using the following formula: \(\Delta H = \text{Energy of bonds broken} - \text{Energy of bonds formed}\)

Reaction a: Calculate \(\Delta H\)

Calculate \(\Delta H\) for reaction a using the bond energies from Step 1: \(\Delta H = (1\cdot432 + 1\cdot242) - 2\cdot432 = -190\text{ kJ/mol}\)

Reaction b: Calculate \(\Delta H\)

Calculate \(\Delta H\) for reaction b using the bond energies from Step 1: \(\Delta H = (1\cdot941 + 3\cdot432) - 6\cdot391 = -93\text{ kJ/mol}\) Now, we have the change in enthalpy (\(\Delta H\)) for both reactions: a. \(\mathrm{H}_{2}+\mathrm{Cl}_{2} \rightarrow 2 \mathrm{HCl}\) \(\Delta H = -190\text{ kJ/mol}\) b. $\mathrm{N} \equiv \mathrm{N}+3 \mathrm{H}_{2} \rightarrow 2 \mathrm{NH}_{3}$ \(\Delta H = -93\text{ kJ/mol}\)

Key concepts

Chemical Reactions

Chemical reactions involve the transformation of one or more substances into different substances. In the context of bond enthalpy, we consider how the making and breaking of bonds drive these transformations. Reactants, which are the starting materials in a chemical reaction, will undergo changes to form products. During a chemical reaction, old bonds are broken and new bonds are formed. The energy required to break a bond is absorbed from the surroundings, while energy is released when a bond is formed.
For example, in the reaction between hydrogen gas and chlorine gas to form hydrogen chloride (\(\text{H}_2 + \text{Cl}_2 \rightarrow 2\text{HCl}\)), H-H and Cl-Cl bonds are broken in the reactants and H-Cl bonds are formed in the products.
This transformation of chemical bonds is central to understanding reactions and the resulting energetic changes, enabling chemists to predict the behavior of substances in reactions.

Enthalpy Change

Enthalpy change (\(\Delta H\)) is a measure of the total energy change in a chemical reaction. It reflects the difference between the energy required to break bonds in the reactants and the energy released when new bonds form in the products. When calculating \(\Delta H\), if more energy is released in forming new bonds than is absorbed in breaking the original bonds, the reaction is exothermic and \(\Delta H\) will be negative. Conversely, if less energy is released, the reaction is endothermic and \(\Delta H\) will be positive.
For example, in reaction (a), the calculation:\[\Delta H = (1\cdot432 + 1\cdot242) - 2\cdot432 = -190\text{ kJ/mol}\]shows that the overall reaction releases energy, making it exothermic. Understanding enthalpy change is crucial as it gives insight into the energy dynamics of a reaction, affecting how and if the reaction will spontaneously occur in natural conditions.

Bond Energy Calculation

Bond energy calculations involve determining the enthalpy change of a reaction by considering the bond energies of the reactants and the products. Bond energy is the measure of strength for a given bond, typically expressed in \(\text{kJ/mol}\), and varies between different types of bonds. To calculate the enthalpy change for a reaction:

• Identify all the bonds broken in the reactants and add their energies.
• Identify all the bonds formed in the products and add their energies.
• Apply the formula: \(\Delta H = \text{Energy of bonds broken} - \text{Energy of bonds formed}\).

This method allows for a simple estimation of a reaction's enthalpy change. In reaction (b), where nitrogen gas and hydrogen gas form ammonia (\(\text{N}\equiv\text{N} + 3 \text{H}_2 \rightarrow 2 \text{NH}_3\)), the calculation:\[\Delta H = (1\cdot941 + 3\cdot432) - 6\cdot391 = -93\text{ kJ/mol}\]shows the effective management of bond energies to predict the reaction’s energy outcome. This demonstrates bond energy calculations as an approachable way to understand and predict energy alterations in chemical processes.