Question

What will be \(\Delta H\) for the reaction, \(\mathrm{CH}_{2} \mathrm{Cl}_{2} \rightarrow \mathrm{C}+2 \mathrm{H}+2 \mathrm{Cl} ?\) \(\left(B \cdot E\right.\). of \(\mathrm{C}-\mathrm{H}\) and \(\mathrm{C}-\mathrm{Cl}\) bonds are \(416 \mathrm{~kJ} \mathrm{~mol}^{-1}\) and \(325 \mathrm{~kJ} \mathrm{~mol}^{-1}\) respectively) (a) \(832 \mathrm{~kJ}\) (b) \(1482 \mathrm{~kJ}\) (c) \(650 \mathrm{~kJ}\) (d) \(1855 \mathrm{~kJ}\)

Short answer

The change in enthalpy (\backslash Delta H) for the reaction is 1482 kJ.

Step-by-step solution

Calculate the Energy Required to Break Bonds

Determine the total energy required to break all of the bonds in CH2Cl2. This involves breaking 2 C-H bonds and 2 C-Cl bonds. The bond energy (B.E.) for each type of bond is given. To break 2 C-H bonds: 2 bonds * 416 kJ/mol = 832 kJ. To break 2 C-Cl bonds: 2 bonds * 325 kJ/mol = 650 kJ. Sum these energies to find the total energy required to break the bonds in one mole of CH2Cl2.

Calculate the Total Change in Enthalpy (ΔH)

Since the products are elemental carbon, hydrogen, and chlorine, they are in their standard states and their formation from the elements would require no energy change (ΔH = 0). Therefore, the total change in enthalpy for the reaction is just the energy required to break the original bonds in CH2Cl2. Add the energy required to break both types of bonds: ΔH = 832 kJ (for C-H bonds) + 650 kJ (for C-Cl bonds).

Determine the Correct Answer

Add the calculated bond energies to find the total enthalpy change: ΔH = 832 kJ + 650 kJ = 1482 kJ. The correct answer is thus (b) 1482 kJ.

Key concepts

Bond Energy

Bond energy refers to the amount of energy required to break one mole of a specific type of bond between atoms in a molecule. It is an essential concept in chemistry because it helps us understand the stability of a molecule and the energy involved in chemical reactions.

For instance, if we take a molecule of dichloromethane \(\mathrm{CH}_2\mathrm{Cl}_2\), it has bonds that hold carbon (C) to hydrogen (H) and carbon to chlorine (Cl). The bond energies for \(\mathrm{C}-\mathrm{H}\) and \(\mathrm{C}-\mathrm{Cl}\) bonds are given as 416 kJ/mol and 325 kJ/mol respectively. Therefore, to break two \(\mathrm{C}-\mathrm{H}\) bonds, as in our exercise, we need 2 \(\mathrm{bonds}\) \(\times\) 416 kJ/mol, resulting in 832 kJ. Similarly, breaking two \(\mathrm{C}-\mathrm{Cl}\) bonds requires 2 \(\times\) 325 kJ/mol, totaling 650 kJ.

To make bond energy concepts easier to understand for students, visual aids such as diagrams showing bonds and their respective energies can be very helpful, along with practical examples that link the abstract concept with familiar substances.

Chemical Reaction

A chemical reaction involves the transformation of one set of chemical substances to another through the breaking and making of chemical bonds. These processes are governed by the laws of thermodynamics, which include the conservation of energy.

Demonstrating a chemical reaction using the example of dichloromethane decomposing into its elemental components, we see the breaking of \(\mathrm{C}-\mathrm{H}\) and \(\mathrm{C}-\mathrm{Cl}\) bonds. In this particular chemical equation, no new bonds are formed as the products are elemental carbon, hydrogen, and chlorine, which occur naturally in their atomic or diatomic states. To aid students' comprehension, using balanced chemical equations, alongside step-by-step breakdowns of the bond-breaking process, can clarify the sequence and energy changes involved. Additionally, color-coding elements and the changes they undergo can make the process more visually accessible.

Thermochemistry

Thermochemistry is the study of energy changes, particularly heat, during chemical reactions. The key metric in thermochemistry is enthalpy (\(\Delta H\)), a measure of the total energy of a system. This includes the energy required to break bonds in the reactants and the energy released when new bonds form in the products.

In reactions where no new bonds form, such as the decomposition of dichloromethane, \(\Delta H\) is calculated by the energy required to break the bonds. Since there's no energy change associated with forming products (as they form from elements in their standard states), the \(\Delta H\) is straightforward to calculate. For educational purposes, breaking down the enthalpy change into its components and relating it to observable phenomena (such as temperature changes) can help students connect thermochemistry concepts with real-world experiences. Moreover, emphasizing that enthalpy is a state function and only depends on the initial and final states, not the path taken, is crucial for a thorough understanding.