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Single molecule conductance measurements on 1,8-octanedithiol were performed using the scanning tunneling microscope break junction method with an externally controlled modulation of the bias voltage. Application of an AC voltage is shown to improve the signal to noise ratio of low current (low conductance) measurements as compared to the DC bias method. The experimental results show that the current response of the molecule(s) trapped in the junction and the solvent media to the bias modulation can be qualitatively different. A model RC circuit which accommodates both the molecule and the solvent is proposed to analyze the data and extract a conductance for the molecule.