# General balance equation

The **general balance equation** is a fundamental concept of chemical engineering which is based on the principles of conservation of mass and conservation of energy. The general balance equation states that the total or component mass or energy of any system can be modeled by:

- In - Out + Generation - Consumption = Accumulation

The equation is used to describe and design almost every process unit within chemical engineering.

## Contents

## Mass Balance

When the general balance equation is applied to the mass of a component or of the entire system, it is called a *mass balance*. Mass balances are the simplest forms of the general balance equation and one of the first forms a chemical engineer learns. One of the ways chemical engineers ensure their calculations on linked process units have been performed correctly is to perform a mass balance over the entire system.

### Using Mass Balances

Below is a general description of how to use mass balances for different situations.

#### Steady State

If the system is at steady state then there are no terms which vary over time. This means that the *in*, *out*, *generation*, and *consumption* terms are constants, and the *accumulation* term is 0. Steady state can only be applied to flow systems, or batch systems in which no changes are taking place. The mass balance for a steady state system is:

- In - Out + Generation - Consumption = 0

#### Batch Systems

A batch system is one in which all of the materials of the system are placed into a fixed vessel and left to react for an amount of time. Since there is no flow in or out, the *in* and *out* terms are both 0. Thus the general balance equation applied to a batch system is:

- -Consumption + Generation = Accumulation

If the system is at steady state, then the accumulation term is 0. The balance equation then becomes

- Consumption = Generation

This type of situation is also known as chemical equilibrium.

#### Overall Mass Balance

An *overall mass balance* is a mass balance which models the entire mass of the system, as opposed to the mass of one component of the system. Since mass can not be created or destroyed, the *consumption* and *generation* terms for an overall mass balance are 0. Thus the overall balance is shown by:

- In - Out = Accumulation

If the system is also at steady state, then the equation reduces to:

- In = Out

Note that an overall mass balance can not be performed on a batch system, as all terms would equal 0.

## Mole Balance

Another way the general balance equation is used is the *mole balance*, that is, a balance on the number of moles of one component of the system. Since each mole of any given chemical must weigh the same, a mole balance is simply a direct product of the mass balance. However, mole balances still have advantages over mass balances in some situations (for example, if the flow rates are given in moles per time). The same principles used to form mass balances can be used to form mole balances.