how is equilibrium constant related to standard electrode potential of the cell?give mathematical expression.

The Nernst Equation gives us the relation between EMF and Eqm. constant

E = Eº - (0.0591 / n ) x log (Q)

The Nernst equation shows how the cell potential depends on the concentration, or molarity, of what the components are in the cells.

Here, Q is equal to the product of the concentration of products divided by the product of the concentration of the reactants. In other words,

Q = ([product1]x[product2]) / ([reactant1]x[reactant2]

This equation is similar to rate equation in kinetics,

Also, n stands for the moles of electrons; Eº is the standard cell potential; E is the cell potential.
At equilibrium, E = 0 and Q = K.