The Adam and Gibbs theory depicts the viscous flow of silicate melts as governed by the cooperative re-arrangement of molecular sub-systems. Considering that such subsystems involve the silicate Qn units (n = number of bridging oxygens), this study presents a model that links the Qn unit fractions to the melt configurational entropy at the glass transition temperature Tg, Sconf(Tg), and finally, to its viscosity η. With 13 adjustable parameters, the model reproduces η and Tg of melts in the Na2O-K2O-SiO2 system (60 ≤ [SiO2] ≤ 100 mol%) with 1σ standard deviations of 0.18 log unit and 10.6°, respectively. The model helps understanding the links between the melt chemical composition, structure, Sconf and η. For instance, small compositional changes in highly polymerized melts generate important changes in their Sconf(Tg) because of an excess of entropy generated by mixing Si between Q4 and Q3 units. Changing the melt silica concentration affects the Qn unit distribution, this resulting in non-linear changes in the topological contribution to Sconf(Tg). The model also indicates that, at [SiO2] ≥ 60 mol%, the mixed alkali effect has negligible impact on the silicate glass Qn unit distribution, as corroborated by Raman spectroscopy data on mixed Na-K tri- and tetrasilicate glasses. Such model may be critical to link the melt structure to its physical and thermodynamic properties, but its refinement requires further high-quality quantitative structural data on silicate and aluminosilicate melts.