The impact of the density dependence of symmetry energy and effective mass on the properties of the liquid-gas phase transition in hot asymmetric nuclear matter is investigated in the relativistic mean field model using Hornick-Tolos-Zacchi-Christian-Schaffner (HTZCS) parameter sets. The HTZCS parameter sets adhere to recent constraints on the symmetry energy $J$ and the slope parameter $L$ for pure neutron matter. The density dependence of the symmetry energy is governed by the slope parameter $L$. In the present study, two values of effective mass $m^{*}/m=0.65$ and 0.75 with fixed values of $L=50$ and 60 MeV for $J=32$ MeV were used. The present study indicates that compared to the effective mass, the density dependence of symmetry energy exerts a significant influence on various aspects of the liquid-gas phase, including the boundaries and area of the liquid-gas coexistence region, the maximum isospin asymmetry, and the critical values of pressure and isospin asymmetry. The critical pressure and the area of the phase-coexistence region systematically increase with the softening of the symmetry energy. The critical temperature of hot asymmetric nuclear matter, which marks the boundary between the single-phase region and two-phase regions, is influenced by the symmetry energy. Nevertheless, the critical temperature of hot asymmetric nuclear matter consistently exhibits a pattern of higher (lower) values up to a certain isospin asymmetry ($\alpha$) value for $m^{*}/m=0.65\left(0.75\right)$, then shifts to lower (higher) values for $m^{*}/m=0.65\left(0.75\right)$ for both $L=50$ and 60 MeV.

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• Asymmetric nuclear matter
• Equations of state of nuclear matter
• Nuclear matter
• Symmetry energy