**Mass Balances (Sinnott, 1985)**

Material balances are the basis of process design. A material balance taken over the complete process will determine the quantities of raw materials required and products produced. Balances over individual process units set the process stream flows and compositions. A good understanding of material balance calculations is essential in process design. Here the fundamentals of the subject are covered, using simple examples to illustrate each topic. Practice is needed to develop expertise in handling what can often become very involved calculations. More examples and a more detailed discussion of the subject can be found in the numerous specialist books written on material and energy balance computations.

Material balances are also useful tools for the study of plant operation and trouble shooting. They can be used to check performance against design, to extend the often limited data available from the plant instrumentation, to check instrument calibrations, and to locate sources of material loss.

The general conservation equation for any process system can be written as:

Material out = Material in + Generation - Consumption - Accumulation

For a steady-state process the accumulation term will be zero. Except in nuclear processes, mass is neither generated nor consumed; but if a chemical reaction takes place a particular chemical species may be formed or consumed in the process. If there is no chemical reaction the steady-state balance reduces to

Material out = Material in

A balance equation can be written for each separately identifiable species present, elements, compounds or radicals; and for the total material.

**Example**

2000 kg of a 5 per cent slurry of calcium hydroxide in water is to be prepared by diluting a 20 per cent slurry. Calculate the quantities required. The percentages are by weight.

Let the unknown quantities of the 20% solution and water be X and Y respectively. Material balance on Ca(OH)2

eq. a

Balance on water:

eq. 2

From equation (a) X = 500 kg

Substituting into equation (b) gives Y = 1500 kg

Chech material balance on total quantity:

X + Y = 2000

500 + 1500 = 2000, correct

to be continued...

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