Please help me with this chemistry question!

Question

Use Hess's Law to complete

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2 C (s) + 2 H2 (g) = C2H4 (g)

1) C (s) + O2 (g) -------> CO2 (g) Delta H= -393.5 kJ

2) H2 (g) + 1/2 O2 (g) -------> H2O (i) Delta H= -285.8 kJ

3) C2H4 (g) + 3 O2 (g) -----> 2 CO2 (g) +2 H2O (i) Delta H=-1,411.2 kJ

Answer 1

2 C (s) + 2 H2 (g) = C2H4 (g) ... TARGET EQUATION

1) C (s) + O2 (g) -------> CO2 (g) Delta H= -393.5 kJ

2) H2 (g) + 1/2 O2 (g) -------> H2O (i) Delta H= -285.8 kJ

3) C2H4 (g) + 3 O2 (g) -----> 2 CO2 (g) +2 H2O (i) Delta H=-1,411.2 kJ

Procedure:

eq. 1) x 2: 2C(s) + 2O2(g) ==> 2CO2(g) ∆H = 2 x -393.5 = -787 kJ

eq.2) x 2: 2H2(g) + O2(g) ==> 2H2O(l) ∆H = 2 x -285.8 = -571.6 kJ

eq.3) reversed: 2CO2(g) + 2H2O(l) ==> C2H4(g) + 3O2(g) ∆G = +1411.2 kJ

Add eq 1,2 and 3 to get...

2C(s) + 2O2(g) + 2H2(g) + O2(g) + 2CO2(g) + 2H2O(l) => 2CO2(g) + 2H2O(l) + C2H4(g) + 3O2(g)

Combine and cancel like terms to get...

2C(s) + 2H2(g) ==> C2H4(g) ... TARGET EQUATION

Add the ∆H values to get...

-787 kJ + -571.6 kJ + 1411.2 kJ = 52.6 kJ

Answer 2

Hello, Lala,

The total enthalpy change for the reaction is the sum of all changes of the individual reactions. I placed each of the individual reactions as a separate line and manipulated the direction and coefficients so that their sum yields the desired reaction on top. Line 2 is multiplied by two so that we'd have 2 carbons, and thus also multiplied the enthalpy by 2. Same for line 2. Line 3 reverses the reaction provided, and thus the enthalpy is also reversed. Add the equations and the net reaction is the one desired, as well as the total enthalpy change.

Rearrange the given reactions by adding coefficients and reversing them so that the target reaction is formed. The first two reactions need to be multiplied by 2 to get the correct coefficient numbers of molecules. The enthalpy numbers also have to be increased by the same amount. The third reaction needs to be reversed so that C2H is formed. That enthalpy changes sign (from -1411.2kj to 1411.2kJ.

Then add all the enthalpies to arrive at the heat of formation of C2H4 (52.6kJ).

I hope this helps,

Bob