Abstract: Based on the relationship between partition function and entropy in s tatistical thermodynamics for a distinguishable particle system, the atomic weig ht (A_r,i) and electronic shell number(n_i) of ground state atom i has an excellent correlativity with the standard entropies ［Ｓ^{0_m／(J·mol-1·K-1)］ of 70 cations in solid c ompounds: S0_m=-0.51＋3.59·(1.5ln A_r,i)_{1 .4}-0.31(ln n_i)2, R=0.9996. Based on the relationship between enthalpy and partition function for an indistinguishable parti cle system, the linear regression equation between ground state energies (ε_i) and hydrated enthalpies［-Δ_hH_m/(kJ·mol-1 )］ of 51 metal ions is drawn up: -Δ_hH_m=46.93＋525. 49ε_i, R=0.9920. The calculated values of Ｓ0_m ， Δ_hH_m basically tally with the experiment values.}

Key words: statistical thermodynamics, partition function, cation, standard en tropy, hydrated enthalpy