Glyoxal-based electrolytes have been identified as promising for potassium-ion batteries (PIBs). Here we investigate the properties of electrolytes containing bis(fluorosulfonyl)imide (KFSI) in 1,1,2,2-tetra-ethoxy-ethane (tetra-ethyl-glyoxal, TEG) using density functional theory (DFT) calculations, Raman spectroscopy, and impedance spectroscopy. The coordination and configuration of the complexes possible to arise from coordination of the K+ ions by FSI and TEG were investigated both from an energetic point of view as well as qualitatively determined via comparing experimental and artificial Raman spectra. Overall, the K+ coordination depends heavily on the electrolyte composition with contributions both from FSI and TEG. Energetically the coordination by both the trans FSI anion conformer and the TEG solvent with four z-chain conformation is preferrable. From the spectroscopy we find that at lower concentrations, the predominant coordination is by TEG, whereas at higher concentrations, K+ is coordinated mostly by FSI. Concerning the diffusion of ions, investigated by impedance spectroscopy, show that the diffusion of the potassium salt is faster as compared to lithium and sodium salts in comparable electrolytes.