This is an incomplete question, here is a complete question.
Consider the decomposition of a metal oxide to its elements, where M represents a generic metal.
Substance ΔG°f (kJ/mol)
M₃O₄ -9.50
M(s) 0
O₂(g) 0
What is the standard change in Gibbs energy for the reaction, as written, in the forward direction? delta G°rxn = kJ / mol.
What is the equilibrium constant of this reaction, as written, in the forward direction at 298 K?
What is the equilibrium pressure of O₂(g) over M(s) at 298 K?
Answer :
The Gibbs energy of reaction is, 9.50 kJ/mol
The equilibrium constant of this reaction is, 0.0216
The equilibrium pressure of O₂(g) is, 0.147 atm
Explanation :
The given chemical reaction is:
![PCl_3(l)\rightarrow PCl_3(g)](https://tex.z-dn.net/?f=PCl_3%28l%29%5Crightarrow%20PCl_3%28g%29)
First we have to calculate the Gibbs energy of reaction
.
![\Delta G^o=G_f_{product}-G_f_{reactant}](https://tex.z-dn.net/?f=%5CDelta%20G%5Eo%3DG_f_%7Bproduct%7D-G_f_%7Breactant%7D)
![\Delta G^o=[n_{M(s)}\times \Delta G^0_{(M(s))}+n_{O_2(g)}\times \Delta G^0_{(O_2(g))}]-[n_{M_3O_4(s)}\times \Delta G^0_{(M_3O_4(s))}]](https://tex.z-dn.net/?f=%5CDelta%20G%5Eo%3D%5Bn_%7BM%28s%29%7D%5Ctimes%20%5CDelta%20G%5E0_%7B%28M%28s%29%29%7D%2Bn_%7BO_2%28g%29%7D%5Ctimes%20%5CDelta%20G%5E0_%7B%28O_2%28g%29%29%7D%5D-%5Bn_%7BM_3O_4%28s%29%7D%5Ctimes%20%5CDelta%20G%5E0_%7B%28M_3O_4%28s%29%29%7D%5D)
where,
= Gibbs energy of reaction = ?
n = number of moles
Now put all the given values in this expression, we get:
![\Delta G^o=[3mole\times (0kJ/mol)+2mole\times (0kJ/mol)]-[1mole\times (-9.50kJ/K.mol)]](https://tex.z-dn.net/?f=%5CDelta%20G%5Eo%3D%5B3mole%5Ctimes%20%280kJ%2Fmol%29%2B2mole%5Ctimes%20%280kJ%2Fmol%29%5D-%5B1mole%5Ctimes%20%28-9.50kJ%2FK.mol%29%5D)
![\Delta G^o=9.50kJ/mol](https://tex.z-dn.net/?f=%5CDelta%20G%5Eo%3D9.50kJ%2Fmol)
The Gibbs energy of reaction is, 9.50 kJ/mol
Now we have to calculate the equilibrium constant of this reaction.
The relation between the equilibrium constant and standard Gibbs free energy is:
![\Delta G^o=-RT\times \ln K](https://tex.z-dn.net/?f=%5CDelta%20G%5Eo%3D-RT%5Ctimes%20%5Cln%20K)
where,
= standard Gibbs free energy = 9.50kJ/mol = 9500 J/mol
R = gas constant = 8.314 J/K.mol
T = temperature = 298 K
K = equilibrium constant = ?
![9500J/mol=-(8.314J/K.mol)\times (298K)\times \ln (K)](https://tex.z-dn.net/?f=9500J%2Fmol%3D-%288.314J%2FK.mol%29%5Ctimes%20%28298K%29%5Ctimes%20%5Cln%20%28K%29)
![K=0.0216](https://tex.z-dn.net/?f=K%3D0.0216)
The equilibrium constant of this reaction is, 0.0216
Now we have to calculate the equilibrium pressure of O₂(g).
The expression of equilibrium constant is:
![K=(P_{O_2})^2](https://tex.z-dn.net/?f=K%3D%28P_%7BO_2%7D%29%5E2)
![0.0216=(P_{O_2})^2](https://tex.z-dn.net/?f=0.0216%3D%28P_%7BO_2%7D%29%5E2)
![P_{O_2}=0.147atm](https://tex.z-dn.net/?f=P_%7BO_2%7D%3D0.147atm)
The equilibrium pressure of O₂(g) is, 0.147 atm