Question

Consider the following reaction: $$A_{2}+B_{2} \longrightarrow 2 A B \quad \Delta H=-285 \mathrm{kJ}$$ The bond energy for \(\mathrm{A}_{2}\) is one-half the amount of the AB bond energy. The bond energy of \(\mathrm{B}_{2}=432 \mathrm{kJ} / \mathrm{mol}\) . What is the bond energy of \(\mathrm{A}_{2}\) ?

Short answer

The bond energy of A₂ is 147 kJ/mol.

Step-by-step solution

Write the equation for the enthalpy change of the reaction

The change in enthalpy (ΔH) for the reaction can be represented by the formula: ΔH = Bond energy of reactants - Bond energy of products For our given reaction, A₂ + B₂ → 2AB, we have: ΔH = (Bond energy of A₂ + Bond energy of B₂) - 2 × (Bond energy of AB)

Find bond energy of A₂ using the given relationship

We are given that the bond energy of A₂ is one-half of the bond energy of AB. Therefore, we can write: Bond energy of A₂ = (1/2) × (Bond energy of AB)

Solve for the bond energy of A₂

Now, we can substitute the information given in the problem into the enthalpy change equation, and solve for the bond energy of A₂: -285 kJ = (Bond energy of A₂ + 432 kJ) - 2 × (Bond energy of AB) We can also substitute the relationship between bond energies of A₂ and AB: -285 kJ = ((1/2) × (Bond energy of AB) + 432 kJ) - 2 × (Bond energy of AB) Now, let's solve for the Bond energy of AB: -285 kJ = - (3/2) × (Bond energy of AB) + 432 kJ -147 kJ = -(3/2) × (Bond energy of AB) Bond energy of AB = 294 kJ/mol Finally, we can find the bond energy of A₂ using the given relationship: Bond energy of A₂ = (1/2) × (Bond energy of AB) Bond energy of A₂ = (1/2) × 294 kJ/mol Bond energy of A₂ = 147 kJ/mol The bond energy of A₂ is 147 kJ/mol.

Key concepts

Enthalpy Change

Enthalpy change, often represented by the symbol \( \Delta H \), is a crucial concept in thermochemistry and chemical reactions. It measures the heat absorbed or released during a chemical or physical process at constant pressure. This parameter helps us understand whether a reaction is exothermic or endothermic. - **Exothermic reactions** have a negative \( \Delta H \), meaning they release energy to the surroundings as they proceed.- **Endothermic reactions** have a positive \( \Delta H \), indicating they absorb energy from their environment.In the given exercise, the reaction has an enthalpy change \( \Delta H = -285 \) kJ, showing it releases energy and is exothermic. This piece of information is vital as it provides us with insights into the energy changes and stability of the reaction products compared to reactants.

Chemical Reaction

A chemical reaction involves the transformation of reactants into products via the breaking and formation of chemical bonds. Such processes are fundamental to chemistry, dictating how substances interact and change.- **Reactants** are substances that start a reaction. Here, they are \( A_2 \) and \( B_2 \).- **Products** are the end results of a reaction. For this reaction, it's \( 2 AB \).Understanding the chemical reaction equation \( A_2 + B_2 \rightarrow 2 AB \) helps in visualizing the rearrangement of atoms. Energy plays a critical part in breaking bonds of reactants and forming new bonds in products, which directly relates to enthalpy change. Recognizing this rearrangement allows students to see how materials interact to form new compounds.

Bond Energy Calculation

Bond energy is the measure of bond strength in a chemical bond. It is the average energy needed to break one mole of bonds in gaseous molecules. Calculating bond energies can help predict the enthalpy change for reactions, as energy is needed to break the original bonds, and energy is released when new bonds form.The step-by-step solution for this exercise involves calculating the bond energy of \( A_2 \) based on the given relationship that its bond energy is half that of \( AB \). Using the equation for enthalpy change: \[ \Delta H = \text{Bond energy of reactants} - \text{Bond energy of products} \] helps establish a relationship between reactants and products' energies. With the given bond energy of \( B_2 = 432 \) kJ/mol, the solution solves for the bond energy of \( AB \) and subsequently \( A_2 \), arriving at the answer: 147 kJ/mol.

Thermochemistry

Thermochemistry deals with the study of heat energy involved in chemical reactions and physical transformations. It explores how thermal energy is absorbed or evolved by chemical substances. - **Key focus:** how enthalpy changes during a reaction, connecting the movements of energy. The exercise discusses thermochemical evaluations by detailing how energy changes relate to bond formations and breakages. This is critical for understanding diverse applications, such as in industrial processes where energy management is essential. By calculating enthalpy changes and understanding bond energy calculations, students gain insight into how chemical reactions can be manipulated and controlled, aiding in the design and application of energy-efficient chemical processes.