Answer:
final reaction to get is 2C(graphite) + H2(g) → C2H6(g)
First step: 2C(graphite) + 2O2(g) → 2CO2 (g) ΔH = (-393.5 x 2)
3H2(g) + 3/2O2(g) → 3H2O(l) ΔH = (-285.8 x 3)
2CO2(g) + 3H2O(l) → C2H6(g) + 7/2O2(g) ΔH = (-3119.6 X -1/2)
Second step: 2C(graphite) + 2O2(g) + 3H2(g) + 3/2O2 (g) + 2CO2(g) + 3H2O(l) → 2CO2(g) + 3H2O(l) + C2H6(g) + 7/2O2(g)
Third step: 2C(graphite) + O2(g) → C2H6(g)
ΔH final = (-393.5 x 2) + (-285.8 x 3) + (-3119.6 x -1/2) = -84.6 KJ/mol
Explanation: Using Hess Law
In the first step, rearrange the 3 given reactions in a way that they match the final reaction by multiplying or dividing (also the ΔH) by a given number and by reverse (if so the multiply by -1).
In the second step, add all 3 reactions with reactant on their side and product on theirs.
In 3rd step, cancel out similarity in the product and reactant(such as there are (2+3/2 = 7/2)O2 which cancels with 7/2O2 in the product) .
finally, add all 3 ΔH to find the final one which is -84.6 KJ/mol