Question

Consider the following reaction: $$ \mathrm{A}_{2}+\mathrm{B}_{2} \longrightarrow 2 \mathrm{AB} \quad \Delta H=-285 \mathrm{~kJ} $$ The bond energy for \(\mathrm{A}_{2}\) is one-half the amount of the \(\mathrm{AB}\) 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 -239 kJ/mol.

Step-by-step solution

Write down the enthalpy change formula

We can calculate the enthalpy change of the reaction using the following equation: \[ \Delta H = \text{Energy of bonds broken} - \text{Energy of bonds formed} \]

Identify the bonds broken and formed

In the given reaction, one A2 bond and one B2 bond are broken, and two AB bonds are formed.

Write the enthalpy change equation for this reaction

Substitute values in the enthalpy change equation: \[ -285\,\text{kJ} = (1 \times \text{A}_{2} \text{ bond energy}) + (1 \times 432\,\text{kJ}) - (2 \times \text{AB bond energy}) \]

Express the A2 bond energy in terms of the AB bond energy

We are given that the bond energy of A2 is half of the AB bond energy. So, we can express the A2 bond energy as: \[ \text{A}_{2} \text{ bond energy} = \frac{1}{2} \times \text{AB bond energy} \]

Substitute the A2 bond energy expression into the enthalpy change equation

Replace the A2 bond energy term with the expression in terms of AB bond energy: \[ -285\,\text{kJ} = \left(\frac{1}{2} \times \text{AB bond energy}\right) + 432\,\text{kJ} - (2 \times \text{AB bond energy}) \]

Solve for the AB bond energy

Rearrange the equation to solve for the AB bond energy: \[ -285\,\text{kJ} = \left(\frac{1}{2} - 2\right) \times \text{AB bond energy} + 432\,\text{kJ} \] \[ -717\,\text{kJ} = -\frac{3}{2} \times \text{AB bond energy} \] \[ \text{AB bond energy} = \frac{2}{3}\times (-717\,\text{kJ}) = -478\,\text{kJ} \]

Calculate the A2 bond energy using the AB bond energy

Now, we can find the A2 bond energy using the relationship we found in Step 4: \[ \text{A}_{2} \text{ bond energy} = \frac{1}{2} \times -478\,\text{kJ} = -239\,\text{kJ} \] The bond energy of A2 is -239 kJ/mol.

Key concepts

Enthalpy Change

Enthalpy change, denoted as \( \Delta H \), is a measure of the heat energy released or absorbed during a chemical reaction at constant pressure. It's an essential aspect of thermodynamics and helps to understand how energy changes in a reaction. If the enthalpy change is negative (\(-\Delta H\)), the reaction releases heat and is exothermic, whereas a positive enthalpy change (\(+\Delta H\)) means the reaction absorbs heat and is endothermic.

Calculating the enthalpy change involves finding the difference between the energy required to break the reactant bonds and the energy released upon forming the product bonds. The enthalpy of a reaction can be influenced by factors like temperature, pressure, and the nature of reactants and products. It is important for predicting the feasibility and spontaneity of reactions, as well as designing chemical processes efficiently.

Chemical Reactions

Chemical reactions are processes where reactants transform into products through the breaking and forming of chemical bonds. They can be represented by balanced chemical equations that illustrate the conservation of mass, showing that atoms are neither created nor destroyed.

A chemical reaction's progress can be monitored by changes in energy, color, formation of a precipitate, gas production, or temperature change. Understanding how chemical reactions occur and the changes involved helps to explain phenomena in our everyday lives, from combustion engines to the biochemistry within our bodies. Key to predicting the outcome of reactions is appreciating the role of factors such as concentration, pressure, and catalysts which can all influence the rate and direction of a reaction.

Stoichiometry

Stoichiometry is the calculation of reactants and products in chemical reactions based on the balanced equations. It underpins the quantitative aspect of chemical science by providing the proportions in which substances react and are produced.

In practice, stoichiometry allows for the prediction of yields, the amounts of reactants required for a desired product quantity, and the conversion of mass to moles or vice versa by using the molar mass. Stoichiometric coefficients from a balanced equation are the roadmap to understanding the exact ratio of substances involved in the reaction, making it possible to perform calculations reflected in exercises like the one given involving bond energy.

Bond Dissociation Energy

Bond dissociation energy is the measure of the strength of a chemical bond. It represents the amount of energy required to break one mole of bonds in a substance in the gas phase, converting molecules into individual atoms. This quantity is vital for understanding the stability of compounds and predicting the outcome of chemical reactions.

Specifically, bond dissociation energies help to explain why certain reactions occur more readily than others by comparing the energy needed to break different types of bonds. Variations in this energy can result from factors such as bond length, the electronegativity of the atoms involved, and the molecular environment. In the given exercise, the bond dissociation energy was crucial in determining the enthalpy change of the reaction.