The heat of atomization is the heat required to convert a molecule in the gas phase into its constituent atoms in the gas phase. The heat of atomization is used to calculate average bond energies. Without using any tabulated bond energies, calculate the average C–Cl bond energy from the following data: the heat of atomization of CH₄ is 1660 kJ/mol, and the heat of atomization of CH₂Cl₂ is 1495 kJ/mol.

Verified step by step guidance

1. Identify the total number of bonds and types of bonds in each molecule. CH4 has four C-H bonds, and CH2Cl2 has two C-H bonds and two C-Cl bonds.
2. Calculate the total bond energy for all bonds in CH4 using the given heat of atomization. Since the heat of atomization of CH4 is 1660 kJ/mol, this is the total energy required to break all four C-H bonds in one mole of CH4.
3. Calculate the total bond energy for all bonds in CH2Cl2 using the given heat of atomization. Since the heat of atomization of CH2Cl2 is 1495 kJ/mol, this is the total energy required to break two C-H bonds and two C-Cl bonds in one mole of CH2Cl2.
4. Subtract the total energy of the two C-H bonds in CH2Cl2 (obtained from the energy per C-H bond in CH4) from the total bond energy of CH2Cl2 to find the total energy for the two C-Cl bonds.
5. Divide the total energy of the two C-Cl bonds by two to find the average energy per C-Cl bond, which is the average C-Cl bond energy.

Key Concepts

Heat of Atomization

The heat of atomization is the amount of energy required to break a molecule into its individual atoms in the gas phase. It reflects the strength of the bonds within the molecule; higher values indicate stronger bonds. This concept is crucial for understanding how energy changes during chemical reactions and for calculating bond energies.

Bond Energy

Bond energy is the amount of energy required to break one mole of a specific type of bond in a molecule, resulting in the formation of separate atoms. It is a measure of bond strength and is typically expressed in kJ/mol. Understanding bond energies is essential for predicting the stability of molecules and the energy changes during chemical reactions.

Average Bond Energy Calculation

Calculating average bond energy involves using the heat of atomization values of different molecules to derive the energy associated with specific bonds. In this case, the average C-Cl bond energy can be determined by analyzing the differences in heat of atomization between CH4 and CH2Cl2, allowing for the estimation of bond strengths without relying on tabulated values.