the products). Although overall one term will account for the total balance on the system, if this balance equation is to be applied to an individual species and then the entire process, both terms are necessary. This modified equation can be used not only for reactive systems, but for population balances such as arise in particle mechanics problems. The equation is given below; note that it simplifies to the earlier equation in the case that the generation term is zero. In the absence of a nuclear reaction the number of atoms flowing in and out must remain the same, even in the presence of a chemical reaction. For a balance to be formed, the boundaries of the system must be clearly defined. Mass balances can be taken over physical systems at multiple scales. Mass balances can be simplified with the assumption of steady state, in which the accumulation term is zero. Illustrative example A simple example can illustrate the concept. Consider the situation in which a slurry is flowing into a settling tank to remove the solids in the tank. Solids are collected at the bottom by means of a conveyor belt partially submerged in the tank, and water exits via an overflow outlet. In this example, there are two substances: solids and water. The water overflow outlet carries an increased concentration of water relative to solids, as compared to the slurry inlet, and the exit of the conveyor belt carries an increased concentration of solids relative to water. Assumptions Steady state Non-reactive system Analysis Suppose that the slurry inlet composition (by mass) is 50% solid and 50% water, with a mass flow of . The tank is assumed to be operating at steady state, and as such accumulation is zero, so input and output must be equal for both the solids and water. If we know that the removal efficiency for the slurry tank is 60%, then the water outlet will contain of solids (40% times times 50% solids). If we measure the flow rate of the combined solids and water, and the water outlet is shown to be , then the amount of water exiting via the conveyor belt must be . This allows us to completely determine how the mass has been distributed in the system with only limited information and using the mass balance relations across the system boundaries. The mass balance for this system can