The equation traditionally used to interpret temperature programmed desorption (TPD) spectra, the Polanyi-Wigner equation, does not contain explicitly the coverage and temperature dependence necessary to predict TPD spectra in several important systems including CO-Ni(lll). Herein, the statistical rate theory (SRT) approach is used to formulate equations for temperature programmed desorption which are then used to examine TPD spectra reported in the literature for CO-Ni(lll). The molecular and material properties for the CO-N1(111) system have been previously established. One experimental spectrum has been chosen to determine the apparatus constants. The material properties and the apparatus constants are then used in the SRT equations to predict the eight additional TPD spectra for different initial coverages. A critical comparison can then be made between the theory and these eight experimental spectra, since no fitting constants were used in these eight cases. The results show that there is clearly qualitative agreement. The SRT equations are then used along with the heat of adsorption to derive an equation for the pre-exponential factor appearing in the Polanyi-Wigner equation. A prediction is made for the pre-exponential factor that is in agreement with that found empirically. The agreement found between the SRT predictions and the measured spectra indicates that all of the coverage and temperature dependence necessary to predict TPD spectra is given explicitly by the SRT approach. Hence, the experimental support for the SRT approach is enhanced. The SRT equations are then used to predict CO-Ni(lll) spectra that would occur if the heating rate were varied.