Calculate the ∆H° value for the following reaction:

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Step 1: Identify the bonds broken and formed in the reaction. In the given reaction, CH₄ reacts with Cl₂ under UV light to form CH₃Cl and HCl. Bonds broken: one C-H bond in CH₄ and one Cl-Cl bond in Cl₂. Bonds formed: one C-Cl bond in CH₃Cl and one H-Cl bond in HCl.

Step 2: Use bond dissociation energy (BDE) values to calculate the energy required to break the bonds. Look up the BDE values for the C-H bond in CH₄ and the Cl-Cl bond in Cl₂. For example, the BDE for a C-H bond in CH₄ is approximately 412 kJ/mol, and for a Cl-Cl bond, it is approximately 243 kJ/mol.

Step 3: Use bond dissociation energy values to calculate the energy released when bonds are formed. Look up the BDE values for the C-Cl bond in CH₃Cl and the H-Cl bond in HCl. For example, the BDE for a C-Cl bond is approximately 338 kJ/mol, and for an H-Cl bond, it is approximately 431 kJ/mol.

Step 4: Calculate the total energy change (∆H°) for the reaction using the formula: ∆H° = (Sum of BDEs of bonds broken) - (Sum of BDEs of bonds formed). Substitute the values from Steps 2 and 3 into this formula.

Step 5: Interpret the sign of ∆H°. If the value of ∆H° is negative, the reaction is exothermic, meaning it releases energy. If the value is positive, the reaction is endothermic, meaning it absorbs energy.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Enthalpy Change (∆H°)

Enthalpy change (∆H°) is a measure of the heat content of a system at constant pressure. It indicates whether a reaction is exothermic (releases heat, ∆H° < 0) or endothermic (absorbs heat, ∆H° > 0). Calculating ∆H° for a reaction involves using standard enthalpies of formation for the reactants and products, applying the formula ∆H° = Σ(∆H°f products) - Σ(∆H°f reactants).

Bond Dissociation Energy

Bond dissociation energy is the energy required to break a specific bond in a molecule, resulting in the formation of free radicals or atoms. In the context of the given reaction, understanding the bond energies of C-H and Cl-Cl bonds is crucial for calculating the overall energy change during the reaction. The difference in energy between the bonds broken and formed determines the reaction's enthalpy change.

Photochemical Reactions

Photochemical reactions are chemical reactions that are initiated by the absorption of light. In the provided reaction, the presence of light (hν) facilitates the breaking of the Cl-Cl bond, leading to the formation of chlorine radicals that react with methane (CH4). Understanding the role of light in these reactions is essential for analyzing the mechanism and energy changes involved.