Question

From the following data, calculate the average bond enthalpy for the NH bond: $$ \begin{array}{cl} \mathrm{NH}_{3}(g) \longrightarrow \mathrm{NH}_{2}(g)+\mathrm{H}(g) & \Delta H^{\circ}=435 \mathrm{~kJ} / \mathrm{mol} \\ \mathrm{NH}_{2}(g) \longrightarrow \mathrm{NH}(g)+\mathrm{H}(g) & \Delta H^{\circ}=381 \mathrm{~kJ} / \mathrm{mol} \\ \mathrm{NH}(g) \longrightarrow \mathrm{N}(g)+\mathrm{H}(g) & \Delta H^{\circ}=360 \mathrm{~kJ} / \mathrm{mol} \end{array} $$

Short answer

The average NH bond enthalpy is 392 kJ/mol.

Step-by-step solution

Understanding the Problem

We need to calculate the average bond enthalpy for the NH bond by using the provided reactions and their respective enthalpy changes. These reactions involve breaking NH bonds in ammonia (\( \text{NH}_3 \)) step by step, eventually yielding nitrogen and hydrogen atoms.

Identify the NH Bonds

In ammonia (\( \text{NH}_3 \)), there are three NH bonds. Our task is to find the average bond enthalpy for one NH bond.

Calculate Total Enthalpy Change

Add the given enthalpies of the three reactions to find the total enthalpy change for breaking all NH bonds in a single \( \text{NH}_3 \) molecule:\[ \Delta H_{\text{total}} = 435 \text{ kJ/mol} + 381 \text{ kJ/mol} + 360 \text{ kJ/mol} = 1176 \text{ kJ/mol} \]

Calculate Average NH Bond Enthalpy

To find the average bond enthalpy for a single NH bond, divide the total enthalpy change by the number of bonds broken (three):\[ \text{Average NH bond enthalpy} = \frac{1176 \text{ kJ/mol}}{3} = 392 \text{ kJ/mol} \]

Key concepts

NH Bond

The NH bond is an essential component in ammonia, represented as \( \text{NH}_3 \). This means that each ammonia molecule contains three NH bonds, where a nitrogen atom is bonded to three hydrogen atoms. These bonds are strong due to the sharing of electrons between the nitrogen and hydrogen atoms.

In chemical reactions, these NH bonds may need to be broken, which requires energy. Understanding the strength of the NH bond is crucial for predicting how ammonia will behave in different chemical processes. This is why calculating the average bond enthalpy is important.

Enthalpy Change

Enthalpy change refers to the energy change during a chemical reaction. It is usually expressed in kilojoules per mole (kJ/mol). In the context of bond enthalpy, it represents the energy required to break specific bonds.

In our exercise, each step of breaking the NH bonds has an associated enthalpy change:

• The first reaction breaks an NH bond in \( \text{NH}_3 \), contributing 435 kJ/mol.
• The second step involves NH splitting further, requiring 381 kJ/mol.
• The final step breaks another NH bond, needing 360 kJ/mol.

Summing these values provides insight into the overall energy involved in bond breaking.

Bond Breaking

Breaking bonds in chemistry is an endothermic process, which means it consumes energy. This is because energy is needed to overcome the attraction between atoms in a bond.

In our case, breaking the NH bonds in ammonia is demonstrated in three successive steps. Each step represents the breaking of one NH bond, and the enthalpy changes reflect the energy required for each step. Calculating the total enthalpy change for the entire process helps us determine the strength of these bonds in a measurable way.

Ammonia

Ammonia, or \( \text{NH}_3 \), is a simple compound with vital industrial significance. Its molecular structure consists of one nitrogen atom covalently bonded to three hydrogen atoms.

This structure results in the presence of three NH bonds, making ammonia a key compound for studying bond enthalpies. Ammonia is not only a common product in fertilizers but also a starting material in many chemical syntheses. Understanding the bond energies in ammonia helps us grasp its stability and reactivity, allowing us to predict how it behaves under various conditions.