In this paper, the energy spectra of the general molecular potential are obtained using the asymptotic iteration method within the framework of non-relativistic quantum mechanics.With the energy spectrum obtained, the vibrational partition function is calculated in a closed form and is used to obtain an expression for other thermodynamic functions such as vibrational mean energy $U$, vibrational mean free energy $F$, vibrational entropy $S$ and vibrational specific heat capacity $C$. These thermodynamic functions are studied for the electronic state $\rm{X}^{1} \Sigma^{+}_{g}$ of $K_2$ diatomic molecules.
