Gibbs Free Energy and Equlibrium Constant
Q is supposed to be calculated in terms of partial pressures, not moles.  $\Delta G^0$ is based on a reversible process you have devised to take the pure reactants in stoichiometric proportions and 1 atm (actually, 1 bar) and 298 K and convert them to pure products in stoichiometric proportions, also at 1 atm. and 298 K.