Consider the following data
Heat of combustion of H₂(g) =-241.8 kJ mol⁻¹
Heat of combustion of C(s) =-393.5 kJ mol⁻¹
Heat of combustion of C₂ H₅ OH(l) =-1234.7 kJ mol⁻¹
The heat of formation of C₂ H₅ OH(l) is (-) ___________ kJ mol⁻¹ (Nearest integer).

Solution

Chemistry ma’am · 4 steps

Burn the elements, then subtract the burning of ethanol: combustion data turns into formation data that way.

1. Target reaction. Ethanol is formed from its elements: 2C(s) + 3H₂(g) + 1/2 O₂(g) → C₂H₅OH(l). Two carbons need 2 mol C, and six hydrogens need 3 mol H₂.
2. Build it by Hess. Burn 2 mol C and 3 mol H₂ to CO₂ and H₂O. Then run the combustion of ethanol in reverse to turn those products back into C₂H₅OH. Reversing a reaction flips the sign of its enthalpy.

   Δ_f H = 2Δ_c H(C) + 3Δ_c H(H₂) - Δ_c H(C₂H₅OH)

3. Put in numbers. Δ_f H = 2(-393.5) + 3(-241.8) - (-1234.7) = -787 - 725.4 + 1234.7 = -277.7 kJ mol⁻¹.
4. So. The heat of formation of ethanol is about -278 kJ mol⁻¹, so the blank is 278.

The common slip: 2747. Adding the combustion enthalpy of ethanol instead of subtracting it gives -2747.1, so 2747 instead of 278. Its reaction must be reversed, which flips its sign.

The idea to keep. Heat of formation from combustion data: sum of combustion enthalpies of the reactants minus that of the product. Balance the atoms first so each element gets its correct coefficient.

Answer from the NTA final answer key. Solution by PrepWiser.