Concept:Hess's Law states that the overall enthalpy change of a reaction is equal to the algebraic sum of the enthalpy changes of individual steps in a thermodynamic cycle, provided the initial and final states are identical.
Formula:$$ \Delta H_{A \rightarrow B} = \Delta H_{A \rightarrow C} + \Delta H_{C \rightarrow D} + \Delta H_{D \rightarrow B} $$
Solution:- We want to find the direct route enthalpy from state A to state B.
- The indirect route provides three sequential steps:
- Step 1 (A to C): \( -540 \text{ kJ/mol} \)
- Step 2 (C to D): \( +200 \text{ kJ/mol} \)
- Step 3 (D to B): \( -100 \text{ kJ/mol} \)
- Summing the steps: \( (-540) + 200 + (-100) = -640 + 200 = -440 \text{ kJ/mol} \).
Why other options are incorrect:The other options are mathematically incorrect sums, resulting from incorrectly flipping signs or ignoring one of the sequence steps.
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