# Question b62d7

Dec 2, 2015

$\Delta G = - 817 k J$

#### Explanation:

To solve this question we will use Hess's Law:

We need to rearrange the individual steps in order for the sum to give the desired equation:
CH_4(g) + 2O_2(g) → CO_2(g) + 2H_2O(l)

For that we will do the following:
Step 1:
Since $C {H}_{4}$ is needed to be in the reactant side, we will flip the reaction and in this case, we reverse the sign of $\Delta G$:
$C {H}_{4} \left(g\right) \to 2 {H}_{2} \left(g\right) + C \left(s\right) \text{ " " } - \Delta G = 51 k J$

Step 2:
2H_2(g) + O_2(g) → 2H_2O(l) " " " "Delta G = -474 kJ
This equation will be left the way it is.

Step 3:
C(s) + O_2(g) → CO_2(g)" " " "Delta G = -394kJ
This equation will be left the way it is.

Now we sum these three steps:
$C {H}_{4} \left(g\right) \to \cancel{2 {H}_{2} \left(g\right)} + \cancel{C \left(s\right)} \text{ " " } - \Delta G = 51 k J$
cancel(2H_2(g)) + O_2(g) → 2H_2O(l) " " " "Delta G = -474 kJ
cancel(C(s)) + O_2(g) → CO_2(g)" " " "Delta G = -394kJ
$- - - - - - - - - - - - - - - - - - -$
CH_4(g) + 2O_2(g) → CO_2(g) + 2H_2O(l)" " " "Delta G = -817kJ#

Here is a video about Hess's Law:
Thermochemistry | Hess's Law, Enthalpy and Heating/Cooling Curve.