## What are basic chemical calculations?

Chemical calculations involve material and energy balance calculations which enable engineers to calculate material and energy requirements in various chemical processes. In addition to this, chemical calculations help to study the behavior and properties of gases, liquids, and their mixtures.

## Unit operations and unit processes

The chemical processes in industry can be broadly divided into *unit operations* and *unit processes*. Unit operations involve only physical change like adding or removing energy, transfer of a solute from one phase to another, size reduction of materials, etc. The main unit operations are mass transfer, heat transfer, size reduction, filtration, fluid flow, etc. The process involving the chemical conversion of materials is called the unit process. For example, oxidation, biochemical reactions, pyrolysis, hydrolysis, etc.

## Types of processes

- Steady state and unsteady state process
- Batch and continuous process

### Steady state and Unsteady state process

In a steady state process, the properties of the system like pressure, temperature, composition, etc. at a given point in the system do not change with time. On the other hand, when the properties at a given point in the system change with time it is an unsteady state process.

### Batch and Continuous process

Here the given material is charged in a vessel and allowed to stay some time so that changes can occur by physical or chemical means. Such processes are called batch processes. It is an unsteady state operation. An example of a batch process is a Batch Reactor.

In a continuous process, the feed is given to the process or vessel continuously and the product is withdrawn continuously. Here the accumulation of material is zero. An example of a continuous process is a continuous stirred tank reactor.

## Material balance calculations

Material balance calculation is essential in the design of processes and equipment, economic evaluation of processes, and controlling and optimizing the processes. According to the law of conservation of mass, it can neither be created nor destroyed. The material balance for processes with or without chemical reaction can be written as

*Material input to the system - Material output to the system + Material generation in the system- Material consumption within the system = Accumulation of material within the system*

Material balance calculations help to find the material required for a given process. Material balance can be written on a mass basis or a mole basis. It can be done for the total material or each component in the process. Finally, all the balance equations are solved simultaneously to find the unknown quantities.

Identification of the *basis *and *tie* element is the main step in material balance calculation. In the process, a certain quantity of one of the components is chosen as Basis. For example, “1 kg of dried wood in the feed to the dryer” is the basis for a particular dryer. The tie element or key component is the component that enters and leaves the process without change. In the absorption of ammonia from the air- ammonia mixture by contact with water, the amount of air will be the same in the entering stream and leaving the stream. Hence air is the key element here and the balance of such components will help to solve the problem easily.

## Material balance without reaction

Unit operations are processes without reactions encountered in the chemical industry. The material balance of such unit operations is important in the design of processes. Some of them are:

- Evaporation
- Distillation

### Evaporation

In industries, evaporation is used to concentrate an aqueous solution by vaporizing the solvent water in an evaporator. Evaporation is used in a concentration of sugar solution. The concentration of spent soap lye to produce glycerin in the soap industry, etc. The most important evaporators used are short tubes, falling films, long tubes, climbing film evaporators, etc.

The overall material balance can be given as F = L + V

Solute balance can be given as $F{x}_{F}=L{x}_{L}$

Simultaneous solution of these equations helps to find the unknown quantities.

### Distillation

Distillation is the separation of a liquid mixture by boiling the feed. Separation mainly depends on the volatilities of the components in the mixture. The vapor will be richer in more volatile components and it is condensed and the product obtained is called the distillate. The residue or bottom product is leaner in volatile components. In industry, distillation is carried out in a fractionation column where a part of the distillate (reflux) is recycled back to the column to increase the purity of the distillate. The fractionation can be done in multistage operation in a plate or packed column.

Consider distillation of a binary mixture containing components A & B. If A is a more volatile component, then the xF, xD, and xW are the mass fractions of A.

Overall balance is given by

F= D+ W

Component balance of A is,

$F{x}_{F}=D{x}_{D}+W{x}_{W}$

Solving these equations will give the unknown quantities of components in the process.

## Energy balances

When designing a chemical process/ chemical plant, one must account for the energy that flows into and out of each unit of the system and the overall energy requirement of the process. This can be done by wringing energy balance for each unit. The basis for energy balance is the first law of thermodynamics which states that energy can neither be created nor destroyed. The total energy of a system can be divided into kinetic energy, potential energy, and internal energy.

A system can be termed open or close according to whether or not mass can cross the system boundary during the process.

Energy balance for a closed system can be given by

*Final system energy - Initial system energy = Net energy transferred to the system*

$\left({U}_{f}+{E}_{kf}+{E}_{pf}\right)-\left({U}_{i}+{E}_{ki}+{E}_{pi}\right)=Q$

Where i and f refer to the initial and final state and U, E_{k}, E_{p}, Q and W represent internal energy, kinetic energy, potential energy, heat transferred to the system, and work done by the system on surrounding respectively.

## Context and Applications

Basic chemical calculation is a major course studied in a bachelor in chemical engineering. It is one of the main prerequisites in the design of various equipment and overall chemical plants. The material and energy balance calculation helps in determining the composition and energy requirement of various components in the process. Efficient and economic utilization of energy will help the chemical engineer to conserve energy. Chemical process calculation is a major concept required in competitive exams like GATE. It is also studied in the following graduate and postgraduate programs:

- Bachelor in Chemical Engineering
- Master in Chemical Engineering

## Practice Problems

1. Which of the following is a unit operation?

- Pyrolysis
- Biochemical reaction
- Nitration
- Size reduction

Answer: Option d

Explanation: Size reduction is a unit operation.When we reduce the material size by crushing, milling, etc. the physical properties of the material change, not the chemical properties. hence size reduction is a unit operation.

2. Which is a steady state process?

- Process where all properties at a given point change with time
- Process where all properties at a given point do not change with time
- Process with recycling
- Batch process

Answer: Option b

Explanation: In a steady state process the properties of the system at any given point do not change with time. For example in a stirred tank reactor, the reactants are continuously fed and products are taken out. The tank is uniformly mixed. Hence the concentration of various reactants or products will be the same inside the reactor and at the exit. Hence it is a steady state system.

3. An evaporator is fed with 4000 kg/h of feed containing 15% of NaOH and is concentrated to get 40% Thick liquor. Calculate the amount of thick liquor obtained?

- 1500 kg/hr.
- 1200 kg/hr.
- 2000 kg/hr.
- 2500 kg/hr.

Answer: Option a

Explanation: We know that F X_{F}=L X_{L}, substituting $4000\times 0.15=L\times 0.4$

L, amount of thick liquor = 1500 kg/hr.

4. In distillation x_{F}, x_{D}, x_{W} are -

- the mass fractions of the less volatile component.
- the mass fractions of the more volatile component.
- flow rates of feed, distillate, and residue.
- none of the above.

Answer: Option b

Explanation: In distillation x_{F}, x_{D}, x_{W} are the mass fractions of the more volatile component. x_{F}, x_{D }and x_{W}_{ }are the mass fraction of more volatile component in the feed, distillate and residue respectively.

5. What is a closed system?

- Where mass and energy can cross the system boundary.
- Where mass cannot cross the system boundary but it can exchange energy.
- Where both mass and energy cannot cross the system boundary.
- None of the above.

Answer: Option b

Explanation: A closed system cannot transfer mass to its surroundings but can exchange energy. Here mass is conserved but energy exchange between the system and surroundings occurs in the form of heat or work.

## Related Concepts

- Mass transfer
- Heat transfer
- Design of process equipment
- Thermophysics

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