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Chapter 7: Problem 12

How is average bond strength related to relative potential energies of the reactants and the products?

Short Answer

Expert verified
The relationship between average bond strength and relative potential energies of reactants and products can be expressed as \(\Delta E_{p} = -\Delta E_{b}\). The change in potential energy, \(\Delta E_{p}\), depends on the difference in average bond strength, \(\Delta E_{b}\), between the products and reactants. If the average bond strength of the products is higher than the reactants (\(\Delta E_{b} < 0\)), the potential energy will be lower (\(\Delta E_{p} > 0\)). Conversely, if the average bond strength of the products is lower than the reactants (\(\Delta E_{b} > 0\)), the potential energy will be higher (\(\Delta E_{p} < 0\)).

Step by step solution

01

1. Understand potential energy and average bond strength in a chemical reaction

Potential energy refers to the stored energy within molecules in a chemical reaction. During a chemical reaction, bonds between atoms are broken and new bonds are formed. The energy required to break these bonds is known as bond dissociation energy, and the energy released when new bonds are formed is called bond energy. The average bond strength is the average amount of energy required to break the bonds in a molecule.
02

2. Determine the difference in potential energy between reactants and products

In a chemical reaction, the potential energy of the system changes as bonds are broken and formed. This difference in potential energy can be represented as \(\Delta E_{p} = E_{p,products} - E_{p,reactants}\), where \(\Delta E_{p}\) is the change in potential energy, \(E_{p,products}\) is the potential energy of the products, and \(E_{p,reactants}\) is the potential energy of the reactants. This change in potential energy is also related to the difference in average bond strength between the reactants and products.
03

3. Calculate the change in average bond strength

For each molecule involved in the reaction, determine the average bond strength by taking the sum of the bond dissociation energies and divide by the number of bonds in the molecule. Now, calculate the change in average bond strength as \(\Delta E_{b} = E_{b,products} - E_{b,reactants}\), where \(\Delta E_{b}\) is the change in average bond strength, \(E_{b,products}\) is the average bond strength of the products, and \(E_{b,reactants}\) is the average bond strength of the reactants.
04

4. Relate the change in average bond strength to the change in potential energy

The relationship between the change in potential energy and the change in average bond strength can be expressed as \(\Delta E_{p} = -\Delta E_{b}\). This indicates that when the average bond strength of the products is higher than the reactants (\(\Delta E_{b} < 0\)), the potential energy will be lower (\(\Delta E_{p} > 0\)). Conversely, when the average bond strength of the products is lower than the reactants (\(\Delta E_{b} > 0\)), the potential energy will be higher (\(\Delta E_{p} < 0\)). In summary, the average bond strength can be used to understand the relative potential energies of the reactants and products. A higher average bond strength in the products means lower potential energy and vice versa.

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Most popular questions from this chapter

The reaction $$\mathrm{SO}_{3}(g)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{H}_{2} \mathrm{SO}_{4}(a q) $$ is the last step in the commercial production of sulfuric acid. The enthalpy change for this reaction is \(-227 \mathrm{kJ}\). In designing a sulfuric acid plant, is it necessary to provide for heating or cooling of the reaction mixture? Explain.

Consider the following reaction: $$2 \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(l) \quad \Delta H=-572 \mathrm{kJ}$$ a. How much heat is evolved for the production of 1.00 mole of \(\mathrm{H}_{2} \mathrm{O}(l) ?\) b. How much heat is evolved when 4.03 g hydrogen are reacted with excess oxygen? c. How much heat is evolved when \(186 \mathrm{g}\) oxygen are reacted with excess hydrogen?

A fire is started in a fireplace by striking a match and lighting crumpled paper under some logs. Explain all the energy transfers in this scenario using the terms exothermic, endothermic, system, surroundings, potential energy, and kinetic energy in the discussion.

It takes \(585 \mathrm{J}\) of energy to raise the temperature of \(125.6 \mathrm{g}\) mercury from \(20.0^{\circ} \mathrm{C}\) to \(53.5^{\circ} \mathrm{C}\). Calculate the specific heat capacity and the molar heat capacity of mercury.

You have a 1.00 -mole sample of water at \(-30 .^{\circ} \mathrm{C}\) and you heat it until you have gaseous water at \(140 .^{\circ} \mathrm{C}\). Calculate \(q\) for the entire process. Use the following data. Specific heat capacity of ice \(=2.03 \mathrm{J} /^{\circ} \mathrm{C} \cdot \mathrm{g}\) Specific heat capacity of water \(=4.18 \mathrm{J} /^{\circ} \mathrm{C} \cdot \mathrm{g}\) Specific heat capacity of steam \(=2.02 \mathrm{J} /^{\circ} \mathrm{C} \cdot \mathrm{g}\) $$\begin{array}{ll}\mathrm{H}_{2} \mathrm{O}(s) \longrightarrow \mathrm{H}_{2} \mathrm{O}(l) & \Delta H_{\text {fusion }}=6.02 \mathrm{kJ} / \mathrm{mol}\left(\mathrm{at} 0^{\circ} \mathrm{C}\right) \\\\\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{H}_{2} \mathrm{O}(g) & \Delta H_{\text {vaporization }}=40.7 \mathrm{kJ} / \mathrm{mol}\left(\text { at } 100 .^{\circ} \mathrm{C}\right)\end{array}$$
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