We present a computational method to calculate the electronic states of a molecule in an electrochemical environment. The method is based on our recently developed finite-temperature density functional theory approach to calculate the electronic structures at a constant chemical potential. A solvent effect is treated at the level of the extended self-consistent reaction field model, which allows considering it nonequilibrium solvation effect. An exchange-correlation functional with a long-range correction is employed in this calculation, because the functional is adjusted so that the derivative discontinuity of energy with respect to a number of electrons could be satisfied. It has been found that the derivative discontinuity condition plays it crucial role in an electrochemical system. The Computational results are presented for a reaction of NO+ + e(-) reversible arrow NO in chemical equilibrium. Owing to the improvement in the solvation effect and the exchange-correlation functional, the calculated activation free energy is in good agreement with experimental results.