In an attempt to explore how electrolyte ions influence the friction experienced by solutes with different functional groups, rotational diffusion of two structurally similar coumarins, coumarin 343 (C343) and coumarin 334 (C334), has been studied in dimethyl sulfoxide (DMSO) at several concentrations of LiNO3. The two coumarins are almost identical except for the different functional groups in the 3-position; C343 has -COOH whereas C334 has -COCH3. Because of the presence of the -COOH functional group, C343 exists as both anionic and neutral species in DMSO. Although both anionic and neutral forms of C343 exist in the ground state, C343 predominantly exists as neutral species in the excited state. The measured reorientation time of C343 in DMSO is slower by a factor of 2 compared to that of C334 due to the hydrogen bonding between the -COOH group of the probe and sulfoxide group of the solvent. However, the viscosity normalized reorientation times (tau(r)/eta) of C343 in LiNO3/DMSO solutions increase by 60% to 70% compared to that in pure DMSO. Addition of electrolyte ions shifts the equilibrium toward the anionic form of C343, which in turn forms ion pairs with Li+, and the large increase in tau(r)/eta values is due to the association of DMSO solvent molecules with these ion pairs. On the other hand, tau(r)/eta values of the neutral solute, C334, remain invariant in the entire range of the electrolyte concentration. The C343-Li+ ion pairs have been characterized using ab initio molecular orbital methods. Two approaches have been employed to model the friction experienced by the C343-Li+ ion pairs. In the first approach, the complex formed between C343-Li+ and the solvent molecules is treated as a rigid entity and the increase in the viscosity normalized reorientation time has been accounted for solely as an enhancement in the mechanical friction. Alternatively, the solvent association with the C343-Li+ ion pairs has been modeled as dielectric friction using the extended charge distribution theory.