The ionic liquid propylammonium nitrate (PAN) was elaborated in the present study applying NMR. Temperature dependences of 1H and 13C spin–lattice relaxation rates and diffusion coefficients were measured to describe molecular mobility in PAN. It was discovered that the temperature dependences of the relaxation rates do not have a maximum. An approach to solve the problem of finding a “hypothetical” maximum was applied. Verification of the correctness of the approach on the examples of temperature dependences with a pronounced real maximum was performed. As a result, the correlation times for selected molecular groups of PAN were calculated. Analyzing the data obtained one can conclude that the translational and rotational degrees of freedom in PAN are weakly correlated. The translational motion “slows down” more strongly with the decrease in temperature.