Final answer:
The enthalpy change for the reaction CH₄(g) + 4Cl₂(g) → CCl₄(g) + 4HCl(g) is calculated by summing the changes given for intermediate reactions, resulting in an enthalpy change of 1902.0 kJ.
Step-by-step explanation:
The enthalpy change for the overall chemical reaction is calculated using Hess's Law, which states that the total enthalpy change for a reaction is the sum of the enthalpy changes for the individual steps of the reaction. Therefore, we must manipulate the given reactions to derive the overall reaction:
CH₄(g) + 4Cl₂(g) → CCl₄(g) + 4HCl(g).
The steps involve breaking the bonds of CH₄ and creating C(s) and H₂(g), then breaking bonds in CCl₂(g) to create C(s) and Cl₂(g), and finally forming HCl from H₂(g) and Cl₂(g). By summing up the given enthalpies changes for the reactions (ΔH₁ = 74.6 kJ, ΔH₂ = 2012 kJ, and ΔH₃ = -92.3 kJ for each 2 moles of HCl) and considering the stoichiometry, we get:
ΔH = ΔH₁ + ΔH₂ + (2 * ΔH₃)
Plugging in the values:
ΔH = 74.6 kJ + 2012 kJ + (2 * (-92.3 kJ))
ΔH = 74.6 kJ + 2012 kJ - 184.6 kJ
ΔH = 1902.0 kJ
Therefore, the enthalpy change for the overall reaction is 1902.0 kJ.