The General Balance Equation
Accumulation = In − Out + Generation − Consumption
Every equation you will encounter in chemical engineering — from the energy balance on a heat exchanger to the design equation for a plug flow reactor — is a special case of a single statement. If you learn to read that statement, you can read every equation in the field.
The statement
Chemical engineering is the study of systems where things move, transform, and accumulate. At the most fundamental level, every such system obeys a single accounting principle: what goes in, minus what comes out, plus what is generated, minus what is consumed, equals what accumulates.
Applied to mass, energy, momentum, or moles — this generates every governing equation in the field.
This is not a formula to memorize. It is a way of thinking. Every time you encounter a new system — a reactor, a distillation column, a membrane, a heat exchanger — your first move should be to ask: what is being balanced? What crosses the boundary? What is generated or consumed inside?
Applying it to mass
Consider a tank with an inlet and outlet stream. If we balance total mass:
No generation or consumption term — total mass is conserved. It can move, but it cannot be created or destroyed.
Applying it to moles
Now consider balancing moles of species A in a reactor. Unlike total mass, individual species can be generated or consumed by chemical reaction:
The generation term r_A·V is what makes reaction engineering different from simple mass transfer. When r_A = 0, you recover the simple mass balance.
The pattern
Notice the structure. In every case, we have:
- 1.A quantity being tracked (mass, moles, energy, momentum)
- 2.A boundary that defines the system
- 3.Transport terms for what crosses the boundary (in and out)
- 4.Source terms for what is created or destroyed inside (generation and consumption)
- 5.An accumulation term for what changes with time
Every equation you will see in this course is this pattern, instantiated for a specific quantity and a specific system. Thermodynamics balances energy. Transport phenomena balance momentum, heat, and mass fluxes. Reaction engineering adds the generation term. Process design couples them together.
Mass balance on a mixing tank
A tank initially contains 100 kg of water. An inlet stream delivers 5 kg/min of a salt solution. An outlet stream removes 3 kg/min. Assuming perfect mixing, what is the total mass in the tank after 10 minutes?
- ×Writing a balance without defining the system boundary first. If you don’t know the boundary, you don’t know what “in” and “out” mean.
- ×Forgetting that total mass has no generation term. Only individual species can be generated or consumed by reaction.
- ×Treating steady-state as the default. Accumulation is zero only when you can justify it — it is not a starting assumption.
Key takeaways
- •Every equation in ChemE is a balance: accumulation = in − out + gen − con
- •The first step is always: define the system, define the boundary, identify the quantity being balanced
- •Steady-state (\u2202/\u2202t = 0) is a special case, not the default
- •Total mass is always conserved. Individual species are not.
Practice prompt
Write the general balance for energy on an open system (a system with inlet and outlet streams). What plays the role of “generation” for energy? What about “consumption”? Compare your answer to the first law of thermodynamics for an open system.