Problem 8 - Introductory Chemistry Atoms First

Question

Consider the reaction \(\Lambda_{2}+\mathrm{B}_{2} \rightarrow 2 \Lambda \mathrm{B}\). Breaking \(1 \mathrm{molc}\) of \(\Lambda-\Lambda\) bonds and \(1 \mathrm{molc}\) of \(\mathrm{B}-\mathrm{B}\) bonds requires \(2200 \mathrm{~kJ}\). Forming 1 mole of \(\mathrm{A}-\mathrm{B}\) bonds releases \(1000 \mathrm{~kJ}\). (a) Is this reaction exothermic or endothermic? Explain. (b) What is the value of \(\Delta E_{\mathrm{rxn}} ?\) (Get the sign right.) How is it to be interpreted?

Step-by-Step Solution

Answer

(a) The reaction is endothermic because the energy required for bond breaking (2200 kJ) is greater than the energy released during bond formation (2000 kJ). (b) The value of \(\Delta E_{\mathrm{rxn}}\) is -200 kJ, indicating that the reaction is endothermic and absorbs 200 kJ of energy from its surroundings.

Step 1: (a) Determining whether the reaction is exothermic or endothermic

We are given that breaking 1 mole of \(\Lambda-\Lambda\) bonds and 1 mole of \(\mathrm{B}-\mathrm{B}\) bonds requires 2200 kJ. Forming 1 mole of \(\Lambda\mathrm{B}\) bonds releases 1000 kJ. Since 2 moles of \(\Lambda\mathrm{B}\) are formed in the reaction, the total energy released during bond formation is 2 x 1000 kJ = 2000 kJ. Now, compare the energy required for bond breaking and energy released during bond formation: - If the energy required for bond breaking is greater than the energy released during bond formation, the reaction will be endothermic (absorbing energy). - If the energy required for bond breaking is less than the energy released during bond formation, the reaction will be exothermic (releasing energy). In this case, 2200 kJ (energy required for bond breaking) is greater than 2000 kJ (energy released during bond formation), so the reaction is endothermic.

Step 2: (b) Calculating ΔErxn and its interpretation

ΔErxn (change in energy during the reaction) can be calculated using the following formula: ΔErxn = energy released during bond formation - energy required for bond breaking ΔErxn = 2000 kJ - 2200 kJ = -200 kJ Since the value of ΔErxn is negative, it indicates that the reaction is endothermic. This means that the reaction absorbs 200 kJ of energy from its surroundings.

Key Concepts

Bond Energy

Bond energy refers to the amount of energy required to break a chemical bond. It is a crucial concept in thermochemistry, as it helps us understand the energetic requirements of breaking bonds and forming new ones during a chemical reaction. Each type of bond has a specific bond energy value, which indicates how much energy is needed to break it. For instance, in the provided exercise, breaking 1 mole of \( \Lambda-\Lambda \) and \( \mathrm{B}-\mathrm{B} \) bonds requires 2200 kJ.

• Higher bond energies mean stronger bonds that require more energy to break.
• Lower bond energies indicate weaker bonds, needing less energy to be disrupted.

Bond energy is vital for calculating the energetic changes in reactions, as it allows us to compare the input and output energy.

Exothermic Reaction

In thermochemistry, an exothermic reaction is one that releases energy, usually in the form of heat, to its surroundings. This release occurs because the total energy required to break bonds in the reactants is less than the energy released when new bonds form in the products.

• Exothermic reactions often feel warm or hot to the touch because they emit heat.
• Combustion reactions, like burning wood or gasoline, are typical examples of exothermic processes.

For the reaction given in the exercise, we check if the energy released in forming the bonds (2000 kJ for two moles of \( \Lambda\mathrm{B} \) bonds) exceeds the energy needed to break the initial bonds (2200 kJ for \( \Lambda-\Lambda \) and \( \mathrm{B}-\mathrm{B} \) bonds). Here, because less energy was released than required for breaking bonds, the reaction is actually endothermic, not exothermic.

Endothermic Reaction

An endothermic reaction absorbs energy from its surroundings, often leading to a cooling effect in the immediate environment. In such reactions, the energy required to break the initial bonds in the reactants exceeds the energy released by forming new bonds in the products.

• This absorption of energy often results in a temperature drop in the surroundings.
• Photosynthesis in plants is an example of an endothermic reaction.

For the reaction discussed in the exercise, since 2200 kJ are necessary to break existing bonds, and only 2000 kJ are released when new bonds form, it results in a net absorption of energy. Thus, it is classified as an endothermic process, with the environment supplying the balance of energy needed to facilitate the reaction.

Energy Change in Reactions

The energy change in reactions, often denoted as \( \Delta E_{\text{rxn}} \), can tell us whether a reaction is endothermic or exothermic. This value is determined by subtracting the energy required to break bonds from the energy released in bond formation: \( \Delta E_{\text{rxn}} = \text{energy released} - \text{energy required} \).

• If \( \Delta E_{\text{rxn}} \) is positive, the reaction is exothermic, indicating a net release of energy.
• If \( \Delta E_{\text{rxn}} \) is negative, the reaction is endothermic, reflecting a net absorption of energy.

In our given example, the calculated \( \Delta E_{\text{rxn}} \) is \(-200 \text{kJ}\), demonstrating an endothermic reaction where the system absorbs 200 kJ from its surroundings.