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The dependence of chemical composition on the average sizes of subnanometer-scale intrinsic structural open spaces surrounded by glass random networks in two-component silica-based glasses was investigated systematically using positronium (Ps) confined in the open spaces. The average sizes of the open spaces for SiO2-B2O3 and SiO2-GeO2 glasses are only slightly dependent on the chemical compositions because the B2O3 and GeO2 are glass network formers that are incorporated into the glass network of the base SiO2. However, the open space sizes for all SiO2-R2O (R=Li, Na, K) glasses, where R2O is a glass network modifier that occupies the open spaces, decrease rapidly with an increase in the R2O concentration. Despite the large difference in the ionic radii of the alkali metal (R) atoms, the open space sizes decrease similarly for all the alkali metal atoms studied. This dependence of the chemical composition on the open space sizes in SiO2-R2O observed by Ps shows that the alkali metal atoms do not randomly occupy the structural open spaces, but filling of the open spaces by R2O proceeds selectively from the larger to the smaller open spaces as the R2O concentrations are increased. [ABSTRACT FROM AUTHOR]