We develop the thermodynamic underpinnings of a two-dimensional volatility basis set (2D-VBS) employing saturation mass concentration (Co) and the oxygen content (O:C) to describe volatility, mixing thermodynamics, and chemical evolution of organic aerosol. The work addresses a simple question: "Can we reasonably constrain organic-aerosol composition in the atmosphere based on only two measurable organic properties, volatility and the extent of oxygenation?" This is an extension of our earlier one-dimensional approach employing volatility only (C* = γ Co, where γ is an activity coefficient). Using available constraints on bulk organic-aerosol composition, we argue that one can reasonably predict the composition of organics (carbon, oxygen and hydrogen numbers) given a location in the Co – O:C space. Further, we argue that we can constrain the activity coefficients at various locations in this space based on the O:C of the organic aerosol.