Question

If the \(\Delta H\) for \(2 \mathrm{Na}+\mathrm{Cl}_{2} \rightarrow 2 \mathrm{NaCl}\) is \(-772 \mathrm{~kJ},\) what is the \(\Delta H\) for this reaction: \(2 \mathrm{NaCl} \rightarrow 2 \mathrm{Na}+\mathrm{Cl}_{2}\)

Short answer

The \(\Delta H\) for the reverse reaction is \(+772 \mathrm{~kJ}\).

Step-by-step solution

Understanding Reaction Enthalpy

The given reaction is the formation of sodium chloride (NaCl) from sodium (Na) and chlorine gas (\( \mathrm{Cl}_2 \)), releasing energy, so the enthalpy change \( \Delta H \) is \(-772 \mathrm{~kJ}\). This is an exothermic reaction.

Identifying the Reverse Reaction

The exercise asks for the enthalpy change of the reverse reaction: decomposition of sodium chloride into sodium and chlorine gas, which is \(2 \mathrm{NaCl} \rightarrow 2 \mathrm{Na} + \mathrm{Cl}_2 \).

Applying the Concept of Reaction Reversibility

The enthalpy change for a reaction and its reverse are equal in magnitude but opposite in sign. Thus, if forming \(2 \mathrm{NaCl} \) releases \(772 \mathrm{~kJ}\), decomposing \(2 \mathrm{NaCl} \) requires \(772 \mathrm{~kJ}\).

Calculating \(\Delta H\) for the Reverse Reaction

Since \(\Delta H\) for the formation is \(-772 \mathrm{~kJ}\), the \(\Delta H\) for the reverse reaction where \(2 \mathrm{NaCl}\) decomposes is \(+772 \mathrm{~kJ}\), indicating it is endothermic.

Key concepts

Exothermic Reactions

In chemical reactions, energy changes can determine whether a reaction is exothermic or not. An exothermic reaction releases energy, typically in the form of heat, to its surroundings. This release occurs because the energy needed to break the bonds in the reactants is less than the energy released when forming the products. As a result, enthalpy change (\(\Delta H\)) for exothermic reactions is negative.
For example, the reaction \(2\, \text{Na} + \text{Cl}_2 \rightarrow 2\, \text{NaCl}\) is exothermic. It releases 772 kJ of energy for every two moles of \(\text{NaCl}\) formed. The molecules are more stable after the reaction, as they have lower energy levels than the initial reactants.
In summary, exothermic reactions are characterized by the release of heat, leading to a decrease in the system's enthalpy and making the surrounding environment warmer.

Endothermic Reactions

In contrast to exothermic reactions, endothermic reactions absorb energy from their surroundings. These reactions require more energy to break the bonds of the reactants than is released when forming the products. This means that the enthalpy change (\(\Delta H\)) is positive in endothermic reactions.
The reverse reaction of forming sodium chloride is an example of this phenomenon: \(2\, \text{NaCl} \rightarrow 2\, \text{Na} + \text{Cl}_2\). This decomposition process requires an input of 772 kJ of energy, making it an endothermic reaction. The energy is absorbed because the products have a higher energy level than the reactants.
Endothermic reactions, therefore, result in a decrease of temperature in the surrounding environment, as the system absorbs energy.

Reaction Reversibility

In chemistry, many reactions are reversible, meaning the products can react to form the original reactants under the right conditions. The concept of reaction reversibility is crucial in determining the enthalpy of the reverse reaction.
The principle states that if a forward reaction releases an amount of energy, the reverse reaction will absorb the same amount of energy. In other words, the enthalpy change for the reverse reaction is equal in magnitude but opposite in sign to that of the forward reaction. For instance, if the formation of sodium chloride releases 772 kJ, then its decomposition requires 772 kJ.
This concept helps us understand energy relationships in chemical reactions and plays a significant role in processes like equilibrium where both forward and reverse reactions occur simultaneously.