The transverse momentum spectra of the well-identified produced particles, π + ,and Ξ + are analyzed in a statistical approach. From the partition function of grand-canonical ensemble, we propose a generic expression for the dependence of the generic chemical potential µ on the rapidity y. Then, by fitting this expression to the experimental results on the most central p ⊥ and d 2 N/2πp ⊥ dp ⊥ dy, at energies ranging from 7.7 to 200 GeV, we have introduced a generic expression for the rapidity dependence of µ, at different energies, namely µ = a+by 2 , where a and b is constants. We find that the resulting energy dependence √ s NN = c[(µ − a)/b] d/2 agrees well with the statistical thermal models. We also present precise estimations of various types of chemical potentials, µ B , µ S , and µ Q , the baryon, the strangeness, and the charge chemical potential, respectively.