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Chapter 8: Problem 72

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

Expert verified
The bond energy of A鈧� is \(49\ \mathrm{kJ/mol}\).

Step by step solution

01

Write down the equation relating bond energies and enthalpy change

To calculate the overall enthalpy change of a given reaction, we can sum the bond energy of products and subtract the bond energy of reactants. So in this case, we can write the equation in terms of the bond energies of A鈧�, B鈧�, and AB as: \(\Delta H = \text{Bond energy of products} - \text{Bond energy of reactants}\)
02

Substitute the given values

We are given the following information: \(\Delta H = -285\ \mathrm{kJ}\) Bond energy of A鈧� = \(x\ \mathrm{kJ/mol}\) Bond energy of AB = \(2x\ \mathrm{kJ/mol}\) Bond energy of B鈧� = \(432\ \mathrm{kJ/mol}\) Substitute the given values into the equation from Step 1: \(-285\ \mathrm{kJ} = (2 \times 2x\ \mathrm{kJ/mol}) - (x\ \mathrm{kJ/mol} + 432\ \mathrm{kJ/mol})\)
03

Solve the equation for the bond energy of A鈧�

Simplify the equation and solve for x: \(-285\ \mathrm{kJ} = 4x\ \mathrm{kJ/mol} - (x\ \mathrm{kJ/mol} + 432\ \mathrm{kJ/mol})\) \(-285\ \mathrm{kJ} = 3x\ \mathrm{kJ/mol} - 432\ \mathrm{kJ/mol}\) Add 432 kJ to both sides of the equation: \(147\ \mathrm{kJ} = 3x\ \mathrm{kJ/mol}\) Now, divide both sides of the equation by 3: \(x = 49\ \mathrm{kJ/mol}\) Therefore, the bond energy of A鈧� is 49 kJ/mol.

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Most popular questions from this chapter

Oxidation of the cyanide ion produces the stable cyanate ion, \(\mathrm{OCN}^{-}\). The fulminate ion, \(\mathrm{CNO}^{-}\), on the other hand, is very unstable. Fulminate salts explode when struck; \(\mathrm{Hg}(\mathrm{CNO})_{2}\) is used in blasting caps. Write the Lewis structures and assign formal charges for the cyanate and fulminate ions. Why is the fulminate ion so unstable? (C is the central atom in \(\mathrm{OCN}^{-}\) and \(\mathrm{N}\) is the central atom in \(\mathrm{CNO}^{-} .\).)

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