Context : For a fraction of single white dwarfs with debris disks , an additional gaseous disk was discovered . Both dust and gas are thought to be created by the disruption of planetary bodies . Aims : The composition of the extrasolar planetary material can directly be analyzed in the gaseous disk component , and the disk dynamics might be accessible by investigating the temporal behavior of the Ca ii \xspace infrared emission triplet , hallmark of the gas disk . Methods : We obtained new optical spectra for the first helium-dominated white dwarf for which a gas disk was discovered ( Ton 345 ) and modeled the non-LTE spectra of viscous gas disks composed of carbon , oxygen , magnesium , silicon , sulfur , and calcium with chemical abundances typical for solar system asteroids . Iron and its possible line-blanketing effects on the model structure and spectral energy distribution was still neglected . A set of models with different radii , effective temperatures , and surface densities as well as chondritic and bulk-Earth abundances was computed and compared with the observed line profiles of the Ca ii \xspace infrared triplet . Results : Our models suggest that the Ca ii \xspace emission stems from a rather narrow gas ring with a radial extent of R = 0.44 \text { - - } 0.94 R _ { \sun } , a uniform surface density \varSigma = 0.3 \mathrm { g } \mathrm { cm } ^ { -2 } , and an effective temperature of T _ { \mathrm { eff } } \approx 6000 \mathrm { K } . The often assumed chemical mixtures derived from photospheric abundances in polluted white dwarfs – similar to a chondritic or bulk-Earth composition – produce unobserved emission lines in the model and therefore have to be altered . We do not detect any line-profile variability on timescales of hours , but we confirm the long-term trend over the past decade for the red-blue asymmetry of the double-peaked lines . Conclusions :