Here the example says a certain reaction takes place at 25°C and has an equilibrium constant of 2.8 * 104 determinant Gibbs free energy of the reaction. All right, so we need to find Gibbs free energy, so ΔG0. They're giving us the equilibrium constant.
So the formula that connects them together is -RT ln K. We plug in our R value which is 8.314 Joules over moles times K. Temperature needs to be in Kelvin so add 273.15 to this degree Celsius which gives us 298.15 K and then we have ln of our equilibrium constant which is 2.8 * 104.
When we multiply everything across the board, we see that Kelvin will cancel out. We'll get at the end -2.5 * 104 joules per mole. So here this will be our final answer for Gibbs free energy of this reaction.