We included vertical turbulent mixing and diffusion in ProDiMo thermo-chemical models for protoplanetary disks. The models are carefully checked for convergence toward the time-independent solution of the reaction-diffusion equations, as e.g. used in exoplanet atmosphere models. A series of five T Tauri disk models is presented where we vary the mixing parameter α from 0 to 0.01 and take into account (a) the radiative transfer feedback of the opacities of icy grains that are mixed upward and (b) the feedback of the changing molecular abundances on the gas temperature structure caused by exothermic reactions and increased line heating/cooling. We see considerable changes of the molecular and ice concentrations in the disk. The most abundant species (H2, CH4, CO, the neutral atoms in higher layers, and the ices in the midplane) are transported both up and down, and at the locations where these abundant chemicals finally decompose, for example by photo processes, the release of reaction products has important consequences for all other molecules. This generally creates a more active chemistry, with a richer mixture of ionized, atomic, molecular and ice species and new chemical pathways that are not relevant in the unmixed case. We discuss the impact on three spectral observations caused by mixing and find that (i) icy grains can reach the observable disk surface where they cause ice absorption and emission features at IR to far-IR wavelengths, (ii) mixing increases the concentrations of certain neutral molecules observable by mid-IR spectroscopy, in particular OH, H2O, HCN and C2H2, and (iii) mixing can change the optical appearance of CO in ALMA line images and channel maps, where strong mixing would cause the CO molecules to populate the distant midplane.