3C(s)+ 4H2(g) -> C3H8(g) Use the following reactions with known delta G values:

Question

3C(s)+ 4H2(g) -> C3H8(g) Use the following reactions with known delta G values: C3H8(g)+5O2(g) -> 3CO2(g)+4H2O; deltaG=-2074 kJ C(s)+O2(g) -> CO2(g); delta G=-394.4kJ 2H2(g)+O2(g) -> 2H2O(g); delta G=-457.1 kJ
With the answer being -23kJ. I'm just not sure how to solve for delta G from a series, and not just a single given reaction and given delta H, delta S, and T using Gibbs equations. I am having particular problem figuring out how to do these types of problems you could please show all the steps.

Explanation / Answer

It's just a mathematical problem with simple logic from thermodynamics.

3C(s)+ 4H2(g) -> C3H8(g)     (Reaction 1)

C3H8(g)+5O2(g) -> 3CO2(g)+4H2O; deltaG=-2074 kJ     (Reaction 2)

C(s)+O2(g) -> CO2(g); delta G=-394.4kJ     (Reaction 3)

2H2(g)+O2(g) -> 2H2O(g); delta G=-457.1 kJ     (Reaction 4)

First concentrate on the given reaction to which you have to find DeltaG.

There are three C and four H2 on left side of the arrow and there is a C3H8 on right side. Always consider arrows as equal symbol.

Take reaction 2:

We have C3H8 on left side, which is directly opposite to the reaction 1. So, reverse the reaction 2, then atomatically DeltaG sign will change to positive.

3CO2(g) + 4H2O ---> C3H8(g) + 5O2(g); deltaG= + 2074 kJ

Take reaction 3:

In reaction 3, one should have three C so multiply the whole reaction with 3.

3C(s) + 3O2(g) ---> 3 CO2(g);   delta G= - 1183.2 kJ

Take reaction 4:

In reaction 4, one should have four H2 so multiply the whole reaction with 2 to get 4H2.

4H2(g) + 2O2(g) ---> 4H2O(g);    delta G= - 914.2 kJ

Add all the three (2,3 & 4) reactions:

3CO2(g) + 4H2O + 3C(s) + 5O2(g) + 4H2(g) ----> C3H8(g) + 5O2(g) + 3 CO2(g) + 4H2O(g)

Similarly, DeltaG values = - 1183.2 - 914.2 + 2074 = -23 kJ

Cross out the common terms (both sides of the arrows). Carefully strike out the term against the one present in opposite side of the arrow.

3C(s) + 4H2(g) ---> C3H8(g); DeltaG= -23 kJ

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