The H trs –T trs Function of Phase Transition Enthalpy for Chemical Elements and Inorganic and Organic Compounds

The periodic table of chemical elements has undergone over a century of development and has made indelible contributions to the fields of physics and chemical science. Exploring the relationship between the structure and properties of elements and establishing mathematical models of their physical properties has always been a goal that scientists have pursued tirelessly. For example, can the relationships between melting points (Tf), boiling points (Tb), and enthalpies (Hv or Hf) of various elements be unified into a single mathematical function? Does the phase transition temperature of an element necessarily increase with its atomic number? Does the phase transition enthalpy also increase accordingly? The valence electron number of an element is a significant characteristic value in its periodicity, and elements with the same valence electron number form the same groups. Connecting the Htrs/Ttrs points of elements in the same group yields a Htrs–Ttrs curve and function. Research has revealed that the Htrs–Ttrs functions of elements in the same group can all be unified into a single quadratic trinomial: Htrs = aTtrs2 + bTtrs + c, with a correlation coefficient R2 ≈ 1. This quadratic trinomial is an increasing function; therefore, the phase transition enthalpy of elements in the same group increases with the rise in phase transition temperature. Based on this quadratic trinomial and the phase transition temperatures of elements, the phase transition enthalpy of homologous elements can be predicted, or the phase transition temperature can be retrodicted from known phase transition enthalpy. In addition, this method can also be used to correct the known phase transition temperatures or enthalpies of the elements. Further work has found that many inorganic and organic compounds also exhibit the characteristics of Htrs–Ttrs. The concept of Htrs–Ttrs function will provide new fundamental data and research approaches for thermodynamics, material structure, condensed matter physics, quantum mechanics, inorganic chemistry, and organic chemistry.