We present a methodology for the quantitative use of laser-induced breakdown spectroscopy (LIBS) for the compositional characterization of nanoaerosols, using an internal standard. The approach involves finding the optimal laser delay time to collect spectra for each of the elemental species of interest, and measuring the plasma temperature, and background gas density under the same conditions. This enabled us to eliminate effects due to different experimental conditions, species excitation from different energy states, temporal evolution of the plasma volume itself and instrumental collection efficiencies and biases. We apply the method to the problem of determining the extent of oxidation or coating thickness of aluminum nanoparticles. The specific choice of system is based on a need to understand the nature of energetic properties of nano-materials and in particular the reactivity and stability of passivation coatings, such as metal oxides. The present work establishes LIBS as an effective analytical tool for quantitative estimation of the extent of oxidation in Al nanoparticles from time-resolved atomic emission spectra. More generically this approach of using the background gas as the internal standard mitigates the need for the use of materials standards and should be extendable to the characterization of other multi-component aerosol systems.