While pulsed field gradient stimulated echo nuclear magnetic resonance (PFGSTE NMR) spectroscopy has found widespread use in the quantification of self-diffusivity for many NMR-active nuclei, extending this technique to uncommon nuclei with unfavorable NMR properties remains an active area of research. Potassium-39 (39K) is an archetypical NMR nucleus exhibiting an unfavorable gyromagnetic ratio combined with a very low Larmor frequency. Despite these unfavorable properties, this work demonstrates that 39K PFGSTE NMR experiments are possible in aqueous solutions of concentrated potassium nitrite. Analysis of the results indicates that 39K NMR diffusometry is feasible when the nuclei exhibit spin–lattice and spin–spin relaxation coefficients on the order of 60–100 ms and 50–100 ms, respectively. The diffusivity of 39K followed Arrhenius behavior, and comparative 23Na, 7Li, and 1H PFGSTE NMR studies of equimolal sodium nitrite and lithium nitrite solutions led to correlations between the enthalpy of hydration with the activation energy governing self-diffusion of the cations and also of water. Realizing the feasibility of 39K PFGSTE NMR spectroscopy has a widespread impact across energy sciences because potassium is a common alkali element in energy storage materials and other applications.