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To find the enthalpy change (∆H) for the overall process A → 2C + E, you need to manipulate the given reactions to match the desired reaction. Here's how:
1. Double reaction II: Since you need 2C in the final reaction, double reaction II. This gives:
2B → 2C + 2D (∆H = 2
∆H2)
2. Reverse reaction III: To get E on the product side, reverse reaction III:
2D → E (∆H = -∆H3)
3. Combine the reactions: Now add the three manipulated reactions together. Notice that 2B cancels out on both sides, and 2D also cancels out:
A → 2B + 2B → 2C + 2D + 2D → E
A → 2C + E
4. Add the enthalpy changes: The enthalpy change for the overall reaction is the sum of the enthalpy changes for the individual steps:
∆H = ∆H1 + 2
∆H2 - ∆H3