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Chapter 3: Problem 78

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

Short Answer

Expert verified
The bond energy of A₂ is 49 kJ/mol.

Step by step solution

01

Write down the given information

Here are the information given in the problem: - A₂ + B₂ ⟶ 2AB, ∆E = -285 kJ - Bond energy of B₂ = 432 kJ/mol - Bond energy of A₂ = (1/2) × Bond energy of AB
02

Calculate the total bond energy of the products

Assuming that the bond energy of AB is x kJ/mol, the total bond energy of products, considering the stoichiometric coefficients, will be 2x kJ.
03

Calculate the total bond energy of the reactants

The bond energy of A₂ is (1/2) x, and the bond energy of B₂ is 432 kJ/mol. Therefore, the total bond energy of reactants is (1/2)x + 432 kJ.
04

Apply Hess's Law

Hess's law states that the energy change for the reaction (∆E) is equal to the total bond energy of products minus the total bond energy of reactants. In this case, we have: -285 kJ = (2x kJ) - [(1/2)x + 432 kJ]
05

Solve for x (bond energy of AB)

Rearrange the equation to solve for x: -285 kJ + 432 kJ = (2x kJ) - (1/2)x 147 kJ = (3/2)x x = 98 kJ/mol The bond energy of the AB molecule is 98 kJ/mol.
06

Find the bond energy of A₂

Using the relationship given, we can now find the bond energy of A₂: Bond energy of A₂ = (1/2) × Bond energy of AB Bond energy of A₂ = (1/2) × 98 kJ/mol Bond energy of A₂ = 49 kJ/mol So, the bond energy of A₂ is 49 kJ/mol.

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Most popular questions from this chapter

Write Lewis structures for the following. Show all resonancestructures where applicable.a. \(\mathrm{NO}_{2}^{-}, \mathrm{NO}_{3}^{-}, \mathrm{N}_{2} \mathrm{O}_{4}\left(\mathrm{N}_{2} \mathrm{O}_{4} \text { exists as } \mathrm{O}_{2} \mathrm{N}-\mathrm{NO}_{2} .\right)\) b. \(\mathrm{OCN}^{-}, \mathrm{SCN}^{-}, \mathrm{N}_{3}^{-}\) (Carbon is the central atom in \(\mathrm{OCN}^{-}\) and \(\mathrm{SCN}^{-} .\) )

Name each of the following compounds. Assume the acids are dissolved in water. a. \(\mathrm{HC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}\) b. \(\mathrm{NH}_{4} \mathrm{NO}_{2}\) c. \(\mathrm{Co}_{2} \mathrm{S}_{3}\) d. ICl e. \(\mathrm{Pb}_{3}\left(\mathrm{PO}_{4}\right)_{2}\) f. \(\mathrm{KClO}_{3}\) g. \(\mathrm{H}_{2} \mathrm{SO}_{4}\) \(\mathbf{h} . \mathrm{Sr}_{3} \mathrm{N}_{2}\) i. \(\quad \mathrm{Al}_{2}\left(\mathrm{SO}_{3}\right)_{3}\) J. \(\mathrm{SnO}_{2}\) \(\mathbf{k} . \mathrm{Na}_{2} \mathrm{CrO}_{4}\) I. \(\mathrm{HClO}\)

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