## Introduction

Engineers and scientists frequently have the problem of separating a mixture into its components or need to purify a specific product. To solve the problem they usually apply a heuristic procedure, such as the following McMaster five-stage method:

1. Identify and define the problem.

2. Propose and develop several alternatives to solve the problem.

3. Based on available resources, choose one or two of the best alternatives.

4. Work on the chosen alternatives in greater detail and compare them before selecting the most appropriate solution.

5. Evaluate and decide if the problem has been solved.

Let us assume that, for step 1, the problem is identified as the recovery of one or more organic compounds from a mixture, or the purification of a specific chemical.

In order to apply the second step, the differences in physical properties are taken into account. Sometimes the physical properties of the components are very different, so that, if two phases already exist in the mixture, mechanical separations such as filtration or decanting may then be used. But more often the components of the mixture form a single phase and other differences in physical properties need to be found.

When a homogeneous mixture is formed with components of different vapour pressure or different boiling points, then distillation may be one of the several alternatives proposed in step 2. As will be seen later, the relative volatility (a) of a mixture is:

Ki j Kj yJXi yj|xj

where K and Kj are the equilibrium constant for components i and j respectively. These K values provide for each component a linear relationship for the mole fraction in the gas phase and the mole fraction of the same component in the liquid phase. Eqn [1] shows that the equilibrium constant and relative volatility depend on the ratios of vapour pressure, liquidphase activity coefficients (y) and vapour-phase fugacities (\$).

The relative volatility a is a measure of the ease of the separation.

• If a = 1.0 the separation is not possible by distillation.

• If a > 1.2, distillation will probably be a good alternative, and should be chosen as the next step.

In step 4, the distillation system should be designed. The design and analysis of these columns operating at high and low pressure form the core of this manuscript and are presented in the next sections.

Finally, in step 5, the scientist or engineer debates whether the problem have been solved satisfactorily. If this is the case, the problem is finished; if not, it is necessary to go back and start again.

## Solar Panel Basics

Global warming is a huge problem which will significantly affect every country in the world. Many people all over the world are trying to do whatever they can to help combat the effects of global warming. One of the ways that people can fight global warming is to reduce their dependence on non-renewable energy sources like oil and petroleum based products.

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