Chapter 5, Problem 44Q

Bond energies such as those in Table 5.1 are sometimes found by “working backward” from heats of reaction. A reaction is carried out, and the heat absorbed or evolved is measured. From this value and known bond energies, other bond energies can be calculated. For example, the energy change associated with the combustion of formaldehyde (H₂CO) is −465 kJ/mol.

${\text{H}}_2\text{CO(g)}+\text{O(g)}\to {\text{CO}}_2\text{(g)}+{\text{H}}_2\text{O(g)}$

Use this information and the values found in Table 5.1 to calculate the energy of the C═O double bond in formaldehyde. Compare your answer with the C═O bond energy in CO₂ and speculate on why there is a difference.

Interpretation Introduction

Interpretation:

The carbon – oxygen double energy has to be calculated and compare with the bond energy in ${\text{CO}}_{\text{2}}$.

Concept introduction:

Endothermic reaction: When the heat energy was absorbed by the system from the surrounding is called endothermic reaction

Exothermic reaction: When heat energy or light energy was unconfined to the surrounding from the system is called exothermic reaction.

Net energy change is calculated from the difference between the total energy absorbed in breaking bonds and total energy released in forming bonds.

Explanation of Solution

The given is shown below,

Bonds broken in the reactants are given below:

$\text{1 mol C–H bonds = 416 kJ}$

$\text{1 mol C=O}\text{double bonds = 1}\times \text{ x kJ}$

$\text{1 mol O=O}\text{double bonds = 498 kJ}$

Therefore,

$\text{2 mol C–H bonds = 2(416 kJ) = 832 kJ}$

$\text{Total energy absorbed in bond breaking = 832 kJ+ x kJ}$

Bonds formed in the products are given below:

$\begin{array}{l}\text{1 mol O–H single bonds = 467 kJ}\\ \text{1 mol C=O}\text{double bonds = 803 kJ}\end{array}$

Therefore,

$\text{2 mol O–H single bonds = 2(467 kJ) = 934 kJ}$

$\text{2 mol C=O}\text{double bonds = 2}\left(\text{803 kJ}\right)\text{ = 1606 kJ}$

$\text{Total energy released in bond breaking = 2540 kJ}$

$\begin{array}{l}\text{Net energy change}\text{=}\text{total}\text{energy}\text{absorbed}\text{in}\text{the}\text{bond}\text{breaking}\text{-}\text{total}\text{energy}\text{released in}\text{the}\text{bond}\text{forming}\\ \text{Net energy change is 832 kJ+ x kJ + 498 kJ - (2540 kJ})\text{= - 465 kJ}\\ \text{x kJ}\text{=}\text{- 465 kJ}\text{- 1330kJ}\text{+ 2540kJ}\\ \text{x kJ}\text{=}745\text{ kJ}\end{array}$

The value for $\text{C=O}$ double bonds in carbon dioxide is $\text{803 kJ}$, therefore, the $\text{C=O}$ double bonds in carbon dioxide are stronger than the $\text{C=O}$ double bond in formaldehyde.