Use hess's law to calculate the enthalpy change for the reaction: 3c(s) + 3h2(g) → c3h6(g) given the following thermochemical equations: 2c3h6(g) + 9o2(g) → 6co2(g) + 6h2o(l) δh = -4182.6 kj/mol c(s) + o2(g) → co2(g) δh = -393.51 kj/mol h2(g) + ½o2(g) → h2o(l) δh = -285.83 kj/mol

Explanation:

We have three equations:

(I)   2C₃H₆(g) + 9O₂(g) → 6CO₂(g) + 6H₂O(l); ΔH = -4182.6  kJ/mol  

(II)  C(s) + O₂(g) → CO₂(g);                               ΔH = -393.51 kJ/mol  

(III) H₂(g) + ½O₂(g) → H₂O(l);                           ΔH = -285.83 kJ/mol

From these, we must devise the target equation:

(IV) 3C(s) + 3H₂(g) → C₃H₆(g); ΔH = ?

The target equation has 3C on the left, so you triple Equation(II).

When you triple an equation, you triple its ΔH.

(V) 3C(s) + 3O₂(g) → 3CO₂(g); ΔH = -1180.53 kJ/mol  

Equation V has 3CO₂ on the right, and that is not in the target equation.

You need an equation with 3CO₂ on the left, so you reverse Equation I and divide by 2.  

When you reverse an equation, you reverse the sign of its ΔH.

When you divide an equation by 2, you divide its ΔH by 2.

(VI)  3CO₂(g) + 3H₂O(l) ⟶ C₃H₆(g) + ⁹/₂O₂(g); ΔH = 2091.3 kJ/mol

Equation VI has 3H₂O on the left, and that is not in the target equation.

You need an equation with 3H₂O on the right, so you multiply Equation III by 3.

(VII) 3H₂(g) + ³/₂O₂(g) → 3H₂O(l); ΔH = -857.49 kJ/mol

Now, you add equations V, VI, and VII, cancelling species that appear on opposite sides of the reaction arrows.

When you add equations, you add their ΔH values.

You get the target equation (III):

(V)   3C(s) + 3O₂(g) → 3CO₂(g);                          ΔH = -1180.53 kJ/mol  

(VI)  3CO₂(g) + 3H₂O(l) ⟶ C₃H₆(g) + ⁹/₂O₂(g); ΔH =  2091.3   kJ/mol

(VII) 3H₂(g) + ³/₂O₂(g) ⟶ 3H₂O(l);                     ΔH =  -857.49 kJ/mol

(III) 3C(s) + 3H₂(g) ⟶ C₃H₆(g)                        ΔH =    53.3    kJ/mol