Problem 9 - Introductory Chemistry Atoms First

Question

Consider the reaction \(\mathrm{A}_{2}+\mathrm{B}_{2} \rightarrow 2 \mathrm{AB}\), for which \(\Delta E_{\mathrm{rxn}}=-100 \mathrm{~kJ}\). Forming 1 mole of A \(-B\) bonds releases \(150 \mathrm{~kJ}\). How much energy does it take to break the reactant bonds?

Step-by-Step Solution

Answer

It takes 200 kJ of energy to break the reactant bonds in the reaction \(A_{2}+B_{2} \rightarrow 2AB\), where \(\Delta E_{rxn} = -100 \text{kJ}\) and forming 1 mole of AB bonds releases 150 kJ of energy.

Step 1: Identify the given information

We are given: - ΔErxn = -100 kJ - Energy released to form 1 mole of AB bonds = 150 kJ

Step 2: Write the energy balance equation

Using the given information, write the energy balance equation for this reaction: ΔErxn = Energy required to break reactant bonds - Energy released to form product bonds

Step 3: Calculate the energy released to form product bonds

Since 1 mole of A2 and B2 yields to 2 moles of AB, we need to multiply the energy released to form 1 mole of AB bonds by 2 to find the energy released to form 2 moles of AB bonds: Energy released to form 2 moles of AB bonds = 150 kJ/mol × 2 = 300 kJ

Step 4: Calculate the energy required to break reactant bonds

Now, substitute the values of ΔErxn and the energy released to form product bonds into the energy balance equation: -100 kJ = Energy required to break reactant bonds - 300 kJ To find the energy required to break reactant bonds, add 300 kJ to both sides of the equation: Energy required to break reactant bonds = -100 kJ + 300 kJ = 200 kJ So, it takes 200 kJ of energy to break the reactant bonds.

Key Concepts

Energy Balance Equation

Understanding the energy balance equation is key when studying chemical reactions. The equation allows us to comprehend how energy is conserved as reactants transform into products. Here's the basic idea: - Energy balance equation: \[ \Delta E_{\text{rxn}} = \text{Energy required to break reactant bonds} - \text{Energy released to form product bonds} \] In any chemical reaction, some bonds are broken, requiring energy input, and new bonds are formed, which often releases energy. By organizing given values into this equation, we can solve for unknowns, like the energy required to break reactant bonds or the overall energy change of the reaction. This helps us gain a better understanding of the reaction's energy dynamics.

Bond Energy

In simple terms, bond energy is the amount of energy required to break one mole of bonds in gaseous molecules. This concept is very useful when analyzing chemical reactions, as it allows us to quantify the energy changes involved. - Bond energy is always positive because breaking bonds requires energy input. - Conversely, energy released when bonds form is negative. Let's take the example from the exercise: forming one mole of AB bonds releases 150 kJ of energy. When we apply this to the energy balance equation, we can see how bond energies influence whether a reaction is endothermic or exothermic. Knowing the bond energies involved, we can predict how much energy is needed or released, allowing for a deeper appreciation of the reaction process.

Chemical Reactions

Chemical reactions involve the transformation of one or more substances into new substances. This occurs through the making and breaking of chemical bonds. A basic understanding of chemical reactions involves knowing:- Reactants are the starting materials in a chemical reaction, while products are the substances formed.- Breaking bonds in reactants requires energy, and forming bonds in products releases energy. In our reaction example, the transformation of \( \text{A}_2 + \text{B}_2 \to 2 \text{AB} \) involves breaking the bonds of A2 and B2, needing 200 kJ, as solved, and forming AB bonds, releasing energy. Tracking the energy flow in chemical reactions is guided by the energy balance equation. It helps chemists and students alike to see the complexity and beauty involved in chemical transformations.