Substance ΔG°f(kJ/mol) M3O4(s) −8.80 M(s) 0 O2(g) 0 Consider the decomposition of a metal oxide to its elements, where M represents a generic metal. M3O4(s)↽−−⇀ 3M(s)+2O2(g) What is the standard change in Gibbs energy for the reaction, as written, in the forward direction? ΔG∘rxn= kJ/mol What is the equilibrium constant of this reaction, as written, in the forward direction at 298 K? K= What is the equilibrium pressure of O2(g) over M(s) at 298 K?

The equilibrium constant is  

The equilibrium pressure for oxygen gas is  

Explanation:

  From the question we are told that

       The equation of the chemical reaction is

   The Gibbs free energy for is  

  The Gibbs free energy for is  

    The Gibbs free energy for is  

The Gibbs free energy of the reaction is mathematically represented as

Substituting values

From the balanced equation

The Gibbs free energy of the reaction can also be represented mathematically as

Where R is the gas constant with a value of  

             T is the temperature with a given value  of  

             K is the equilibrium constant

Now equilibrium constant for a reaction that contain gas is usually expressed in term of the partial pressure of the reactant and products that a gaseous in state

The equilibrium constant for this chemical reaction  is mathematically represented as

Where   is the equilibrium pressure of oxygen

         The p subscript shows that we are obtaining the equilibrium constant using the partial pressure of gas in the reaction

Now equilibrium constant the subject on the  second equation of the Gibbs free energy of the reaction

Substituting values

Now substituting this into the equation above to obtain the equilibrium of oxygen

multiplying through by