Mass and Energy Balances

In one line: Draw a boundary around the system, then account for everything crossing it. In equals out plus accumulation, adjusted for anything generated or consumed. It is the first check on any process claim.

Core idea

Mass and energy are conserved. For any system you choose to draw, a whole plant, a single reactor or a mixing point, the general balance is:

$\text{accumulation}=\text{in}-\text{out}+\text{generation}-\text{consumption}$

Generation and consumption apply to individual species in a reaction. Total mass is never created or destroyed. At steady state, nothing inside the boundary changes with time, so accumulation is zero and in equals out.

How it works

1. Draw and label a diagram: every stream, with known flows and compositions, and unknowns as variables.

2. Classify the process:

   • batch: nothing crosses the boundary during operation
   • continuous: streams flow in and out the whole time
   • semi-batch: a mix of the two

3. Choose a basis: a convenient amount, such as 100 mol of feed or one hour of operation.

4. Count the degrees of freedom: unknowns minus independent equations.

   • Zero: the problem is solvable.
   • Positive: more information is needed.
   • Negative: the problem is over-specified, and the data may conflict.

   Equations come from balances, process specifications, the requirement that fractions sum to one, reaction stoichiometry, and physical laws or properties.

5. Solve, often unit by unit for multi-unit processes, or for the whole process at once.

6. Check: does the overall balance close?

Watch the units. Mole fractions and mass fractions differ. Example: a gas that is 50 mol% nitrogen (molar mass 28) and 50 mol% carbon dioxide (molar mass 44) is only about 39% nitrogen by mass.

Energy balances follow the same pattern with enthalpy. Energy in with the streams, plus heat and work added, equals energy out, plus any accumulation. They size heaters, coolers and boilers, and they show where energy can be recovered.

In practice

Balances are the chemical engineer’s equivalent of a financial audit, and leaders can use the same logic on any operation. If a supplier claims 99% yield, ask where the other 1% goes. If a factory’s material purchases don’t match its output plus scrap, something is unaccounted for. The degrees-of-freedom habit is also useful outside engineering: before arguing about an answer, check whether there is enough information to determine one.

Questions to ask the experts

• Where is the boundary drawn, and does the overall balance close?
• What basis and which assumptions, such as steady state or no side reactions, were used?
• How many degrees of freedom remain, and which specification fixes each one?

Connections

• The discipline: Chemical Engineering. Loops in a process: Recycle and Purge. The energy side: Thermodynamic Cycles.
• The same accounting for operations: Value Stream Mapping. Stocks and flows: Thinking in Systems.
• Capabilities exercised: Inquiry, Decision Making, Connecting Across Disciplines.

Sources

• Course lectures on process representation and material balances; no public source.