Answer to Question #327643 in Chemistry for hazim

Question

Find the total enthalpy for rection   

 2C (g) +   3H₂ (g)         C₂H₆ (g)

                Given the thermochemical equations.

           2C(g) + 2 O₂ (g)                   2CO₂ (g)                 ∆H = -786 kJ/mol

           3H₂ (g) +  O₂ (g)            3H₂O (l)                           ∆H = -858 kJ/mol

2CO₂ (g) + 3H₂O (l)           C₂H₆ (g) +  O₂ (g)            ∆H = +1560 kJ/mol  

Answer 1

eq - equation

(1^st eq): 2C(g) + 2O₂(g) → 2CO₂(g), ∆H₁ = −786 kJ/mol

(2^nd eq): 3H₂(g) + 1.5O₂(g) → 3H₂O(l), ∆H₂ = −858 kJ/mol

(3^d eq): 2CO₂(g) + 3H₂O(l) → C₂H₆(g) + 3.5O₂(g), ∆H₃ = +1560 kJ/mol

Target equation: 2C(g) +  3H₂(g) → C₂H₆(g), ∆H_x = ???

 

Solution:

According to Hess's law, the heat of reaction depends upon initial and final conditions of reactants and does not depend of the intermediate path of the reaction.

 

1) Modify the three given equations to get the target equation:

(1^st eq): do nothing. We need 2C(g) on the reactant side and that's what we have.

(2^nd eq): do nothing. We need 3H₂(g) on the reactant side and that's what we have.

(3^d eq): do nothing. We need C₂H₆(g) on the product side and that's what we have.

2) Rewrite all three equations with the changes made (including changes in their enthalpy):

(1^st eq): 2C(g) + 2O₂(g) → 2CO₂(g), ∆H₁ = −786 kJ/mol

(2^nd eq): 3H₂(g) + 1.5O₂(g) → 3H₂O(l), ∆H₂ = −858 kJ/mol

(3^d eq): 2CO₂(g) + 3H₂O(l) → C₂H₆(g) + 3.5O₂(g), ∆H₃ = +1560 kJ/mol

3) Cancel out the common species on both sides:

3.5O₂(g) ⇒ (sum of 1^st eq and 2^nd eq) & (3^d eq)

3H₂O(g) ⇒ (3^d eq) & (2^nd eq)

2CO₂(g) ⇒ (3^d eq) & (1^st eq)

Thus, adding modified equations and canceling out the common species on both sides, we get:

2C(g) +  3H₂(g) → C₂H₆(g)

Add the ΔH values of (1^st), (2^nd) and (3^d) equations to get your answer:

∆H_x = ∆H₁ + ∆H₂ + ∆H₃ = (−786 kJ/mol) + (−858 kJ/mol) + (+1560 kJ/mol) = −84 kJ/mol

Therefore, the enthalpy of reaction is −84 kJ/mol

Answer: The total enthalpy for rection is −84 kJ/mol