The Nano Aerosol Mass Spectrometer (NAMS) was deployed to rural/coastal and urban sites to measure the composition of 20-25 nm diameter nanoparticles during new particle formation (NPF). NAMS provides a quantitative measure of the elemental composition of individual, size-selected nanoparticles. In both environments, particles analyzed during NPF were found to be enhanced in elements associated with inorganic species (nitrogen, sulfur) relative to that associated with organic species (carbon). A molecular apportionment algorithm was applied to the elemental data in order to place the elemental composition into a molecular context. These measurements show that sulfate constitutes a substantial fraction of total particle mass in both environments. The contribution of sulfuric acid to new particle growth was quantitatively determined and the gas-phase sulfuric acid concentration required to incorporate the measured sulfate fraction was calculated. The calculated values were compared to those calculated by a sulfuric acid proxy that considers solar radiation and SO(2) levels. The two values agree within experimental uncertainty. Sulfate accounts for 29-46% of the total mass growth of particles. Other species contributing to growth include ammonium, nitrate, and organics. For each location, the relative amounts of these species do not change significantly with growth rate. However, for the coastal location, sulfate contribution increases with increasing temperature whereas nitrate contribution decreases with increasing temperature.