Predicted log₁₀(N_l/g_l) values for various isotopologs of acetylene, calculated as a function of the lower rotational quantum number, J_l at four temperatures, T = 100 (solid), 300 (dashed), 500 (dotted), and 1000 (dot-dashed lines) K. The left column corresponds to ¹³C₂H₂ (Isotopolog “3”), with separate plots for even (top) and odd (bottom) rotational states. The middle column shows results for D¹²C¹³ CH (Isotopolog “4”) and D¹³C¹²CH (Isotopolog “5”), both of which are asymmetric molecules. The right column corresponds to C₂D₂ (Isotopolog “6”), with separate plots for even (top) and odd (bottom) rotational states. The curves are based on partition functions and energy spectra derived from quantum chemical calculations. Even states start at J_l = 0, while odd states start at J_l = 1, reflecting the symmetry properties of the isotopologs. These plots illustrate the expected population distributions across a range of temperatures, providing insights into the ro-vibrational characteristics of these acetylene isotopologs.