<u>Answer:</u> The
for the reaction is -806.86 kJ
<u>Explanation:</u>
We are given:
(Conversion factor: 1 kJ = 1000)

Temperature of the reaction = 293 K
To calculate the standard Gibbs's free energy of the reaction, we use the equation:

Putting values in above equation, we get:
![\Delta G^o_{rxn}=-803000J-[(293K)\times (-4.05J/K)]=-801813.35J](https://tex.z-dn.net/?f=%5CDelta%20G%5Eo_%7Brxn%7D%3D-803000J-%5B%28293K%29%5Ctimes%20%28-4.05J%2FK%29%5D%3D-801813.35J)
For the given chemical equation:

The expression for
is given as:
![K_{c}=\frac{[H_2O]^2[CO_2]}{[CH_4][O_2]^2}](https://tex.z-dn.net/?f=K_%7Bc%7D%3D%5Cfrac%7B%5BH_2O%5D%5E2%5BCO_2%5D%7D%7B%5BCH_4%5D%5BO_2%5D%5E2%7D)
We are given:
![[H_2O]=6.41M](https://tex.z-dn.net/?f=%5BH_2O%5D%3D6.41M)
![[CO_2]=3.83M](https://tex.z-dn.net/?f=%5BCO_2%5D%3D3.83M)
![[CH_4]=14.51M](https://tex.z-dn.net/?f=%5BCH_4%5D%3D14.51M)
![[O_2]=9.27M](https://tex.z-dn.net/?f=%5BO_2%5D%3D9.27M)
Putting values in above equation, we get:


To calculate the Gibbs free energy of the reaction, we use the equation:

where,
= Gibbs' free energy of the reaction = ?
= Standard gibbs' free energy change of the reaction = -801813.35 J
R = Gas constant = 
T = Temperature = 293 K
= equilibrium constant in terms of concentration = 0.126
Putting values in above equation, we get:


Hence, the
for the reaction is -806.86 kJ