Question

We use Hess's law to calculate enthalpy changes that cannot be measured. One such reaction is the conversion of methane to ethylene: 2 CH4(g) → C2H4(g) + 2 H2(g) Calculate ΔHrxn for this reaction using the thermochemical data: CH4(g) + 2 O2(g) → CO2(g) + 2 H2O(g) ΔH = -802.5 kJ C2H4(g) + H2(g) → C2H6(g) ΔH = -136.4 kJ 2 H2(g) + O2(g) → 2 H2O(g) ΔH = -483.6 kJ 2 C2H6(g) + 7 O2(g) → 4 CO2(g) + 6 H2O(g) ΔH = -2856.8 kJ

Answer 1

Answer:

201.6  KJ

Explanation:

We order the equations as follows to obtain the globail equation we wants.

Everytime we multiply an equation, its enthaply (ΔH) is multiplied by the same number. And everytime we invert an equation, we multiply its ΔH by -1. The total equation is obtained by the addition of the equations, by cancelling the same chemical compounds that are in opposite places in the equation.

4 x (CH₄(g) + 2 O₂(g) → CO₂(g) + 2 H₂O (g) )           4 x ΔH₁

2 ( C₂H₆ (g) → C₂H₄ (g) + H₂(g) )                               -2 x ΔH₂

2 H₂O (g) → 2 H₂ (g) + O₂ (g)                                   -1 x ΔH₃

4 CO₂ (g) + 6 H₂O(g) → 2 C₂H₆(g) + 7 O₂(g)            -1 x ΔH₄

                                                                         

4 CH₄(g)  →  2 C₂H₄(g)  +  4 H₂(g)                               ΔHt

The total enthalpy for the reaction is:

ΔHt = 4 x ΔH₁  + (-2 x ΔH₂) + (-1 x ΔH₃) + (-1 x ΔH₄)

ΔHt = 4 (-802.5 KJ) -2 (-136.4 KJ) - (-483.6 KJ) - (-2856.8 KJ)

ΔHt = 403.2 KJ

As the obtained equation is equivalent to the equation we want but multiplied by 2, we have to divide into 2 to obtain the final equation:

4 CH₄(g)  →  2 C₂H₄(g)  +  4 H₂(g)   is equivalent to

2 ( 2 CH₄(g)  →  C₂H₄(g)  +  2 H₂(g) )

ΔH = ΔHt/2= 403.2 KJ/2 = 201.6 KJ