The General Balance Equation
The single equation that governs every material and energy balance in chemical engineering.
Every material balance you will ever write — from a simple mixer to a multi-unit refinery — boils down to one equation. What is it?
The General Balance Equation
Every material balance in chemical engineering starts from one master equation. For any system boundary and any balanced quantity (total mass, species mass, energy), the general balance equation is:
Accumulation = In − Out + Generation − Consumption
The accumulation term is the rate of change of the quantity inside the system. In and Out are flow rates crossing the boundary. Generation and Consumption apply only when chemical reactions create or destroy the balanced species within the system.
Steady-State vs Unsteady-State & Conservative Quantities
At steady state, nothing inside the system changes with time, so the accumulation term is zero and the equation simplifies to In = Out (+ Generation − Consumption if reaction occurs). At unsteady state (transient operation, startup, shutdown, tank filling), accumulation is non-zero.
A conservative quantity is one that is neither created nor destroyed: total mass and total energy are always conservative (Generation = Consumption = 0). Individual species mass or moles are conservative only when no reaction occurs. In a reactor, a species can be generated or consumed, so its balance retains those terms.
For total mass with no nuclear reactions: Generation = Consumption = 0, always. For species mass with no chemical reaction: Generation = Consumption = 0. At steady state: Accumulation = 0. Most introductory balances are steady-state and non-reactive, so all four terms collapse to In = Out.
- Write the general balance (total mass, no reaction): Accumulation = In - Out
- Accumulation rate = 120 - 100 = 20 kg/min
- Over 10 min: Δm = 20 kg/min × 10 min = 200 kg
- m_final = m_initial + Δm = 500 + 200 = 700 kg
- Accumulation rate = 50 - 30 = 20 kg/min
- m(5) = 200 + 20 × 5 = 200 + 100 = 300 kg
Check your understanding
- General balance: Accumulation = In - Out + Generation - Consumption
- Steady state: accumulation = 0, simplifying to In = Out (+ reaction terms if applicable)
- Total mass and energy are always conservative; species are conservative only without reaction
- Most introductory problems are steady-state and non-reactive: In = Out