The Nernst equation is an equation that relates the the total voltage, i.e. the electromotive force, of the full cell at any point in time to the standard electrode potential, temperature, activity, and reaction quotient of the underlying reactions and species used. I have been wondering why Universal gas constant (R) is included in Nernst and Goldmann equations while describing the steady state of membrane potential?
As in the ideal gas law, the universal gas constant allows for calculation of amount of energy associated with a certain group of molecules (see https://en.wikipedia.org/wiki/Gas_constant). As the Nernst equation compares the "osmotic pressure" to "electrical pressure", the universal gas constant is needed to convert amount of an ion on the two sides of a membrane ("osmotic concentrations") to the amount of energy associated with that concentration differential ("osmotic pressure").
Carefully looking at the units of all of the constituents of the equation can help clear things up. R is in units of J / (mol * degree), and V is J/coulomb. zF in the denominator gets you your coulombs.
In short, both the left and right sides of the equation are more or less measures of energy. R converts amounts of ions to the energy associated with their osmotic pressure so that it can be compared with the electrical energy associated with their charge.