what is the numerical value of the equilibrium constant Kgoal for the reaction CO2(g) C(s) +O2(g)

I don't believe you have provided enough information unless you make sense of Kgoal and that might tell me something.

To find the numerical value of the equilibrium constant (Kgoal) for the reaction CO2(g) -> C(s) + O2(g), we need to know the equilibrium expression for the reaction and the corresponding equilibrium concentrations (or partial pressures) of the reactants and products.

The equilibrium expression for the reaction is written as follows:

Kgoal = [C(s)] * [O2(g)] / [CO2(g)]

In this expression, the square brackets denote the concentration (or partial pressure) of each species at equilibrium. However, we cannot determine the exact numerical value of Kgoal without additional information, such as the equilibrium concentrations or partial pressures.

To determine the value of Kgoal, you would need to provide the actual concentration (or partial pressure) values of CO2(g), C(s), and O2(g), which can be obtained through experimental data or given in the problem statement.

Once you have the equilibrium concentrations (or partial pressures), substitute these values into the equilibrium expression and then perform the necessary calculations to find the numerical value of Kgoal.