Here we're going to say that Gibbs free energy, which is ΔG0 so. We're talking about standard Gibbs free energy is the bridge to the standard cell potential, which here that is Ecell and the equilibrium constant K. Now this connection can be seen in the following way.

So on the left side we have the connection between our standard cell potential and Gibbs free energy. Here we're talking about standard Gibbs free energy. It is equal to -N⋅F⋅Ecell. Here we'd say that our standard gives free energy is in units of kilojoules, and it's just the number of moles transferred within our redox reaction. F is Faraday's constant which remember is 96,485 coulombs per moles of electrons and then our standard cell potential here will be in units of volts abbreviated V.

On the right side we have the connection between our equilibrium constant K and our standard gift free energy. Here we say that standard Gibbs free energy the change in it is equal to -RT⋅lnK. So here R is our gas constant which is 8.314 joules over moles times T here equals temperature in Kelvin. K here is just R equilibrium constant. So we say that Gibbs free energy equals this equation.

We say that gives free energy equals this equation. Since Gibbs free energy equals both equations, they must be equal to one another. So in the middle here we can say that the connection between our standard cell potential and our equilibrium constant K is -N⋅F⋅Ecell=-RT⋅lnK. Now here from this middle equation we can isolate our standard cell potential.

So here we want to isolate this variable here. To do that, you divide out -N⋅F from both sides so they can slot here on the left side. The negative signs cancel out. So at the end we'd get here that our standard cell potential equals RTNF⋅lnK. This represents the connection between our standard sub potential, your equilibrium constant in its simplified form.