The electrical conductance of single n-alkanethiol and alpha,omega-alkanedithiol molecules was measured via in situ distance tunneling spectroscopy in aqueous 0.1 M KOH solution. The statistical analysis of the conductance values show that the alpha,omega-alkanedithiol molecule trapped in the STM break junction can adopt two distinct geometries that result in "lower" and "higher" conductivity values. In contrast, n-alkanethiol molecules trapped in the junction show only a single conductivity value characteristic for a particular molecule. Furthermore, the "lower" conductivity value determined for alpha,omega-alkanedithiol is virtually identical to the electrical conductivity of the n-alkanethiol containing the same number of atoms in the backbone. Moreover when the STM tip is polarized to electrochemical potential preventing a chemical reaction between the terminal -SH group and Au, only "lower" conductivity values are observed for alpha,omega-alkaneditiols.