 # Mass Balance Equation

The mass balance equation forms basis to a number of process engineering calculations. Mass balance equation simply states that total mass in any system is always conserved. That is,
Total mass in = Total mass out + Total mass accumulated in the system

The mass balance can be performed for different components of the inlet and outlet streams. When considering individual component instead of the total mass of a stream, it has to be kept in mind that for a reacting system, one or more components can be converted to one or more different components. Hence for individual component mass balance for a reacting system, we get a generation term and a consumption term. The basic mass balance for a reacting system becomes,
MN in + MN generation = MN out + MN consumption + MN accumulation
M indicates mass and subscript N is second equation denotes the Nth component of the system. Hence for a system comprised N components, there are N such mass balance equations.

When equation is differentiated with respect to time, we get a mass balance equation in terms of rates. Let F denote mass flowrate, let R denote reaction rate to generate or consume a component and let A denote accumulation rate.
FN in + RN generation = FN out + RN consumption + AN

For steady state systems accumulation rate is zero and the mass balance equation is,
FN in + RN generation = FN out + RN consumption

The equations presented here are very basic mass balance equations. For specific systems each term in these equations can be detailed and solved for compositions and component mass flows in the inlet and outlet streams as well as in the system under consideration.