Quality and Quantity of Mixture Problems

Am classic type of mathematical word problem is the mixture problem. v But mixture problems go beyond just mixing up antifreeze with water or chocolate syrup with milk. Mixture problems involve all sorts of situations where you combine so much of one thing that has a certain amount of worth or density with so much of something else that has more worth or more density. 

In this chapter, you find problems that multiply numbers of coins times their monetary value, pints of coolant with their concentrations and cartons of goodies with their product count. All these make for some interesting and, yes, even useful problems. So you can put your spoon away and find out what mixture problems are all about. 

---

Chapter 14 Improving the Quality and Quantity of Mixture Problems 189... 

In the arrangement discussed, the feed is introduced continuously to the column and two product streams are obtained, one at the top much richer than the feed in the MVC and the second from the base of the column weaker in the MVC. For the separation of small quantities of mixtures, a batch still may be used. Here the column rises directly from a large drum which acts as the still and reboiler and holds the charge of feed. The trays in the column form a rectifying column and distillation is continued until it is no longer possible to obtain the desired product quality from the column. The concentration of the MVC steadily falls in the liquid remaining in the still so that enrichment to the desired level of the MVC is not possible. This problem is discussed in more detail in Section 11.6. 

The common theme in all mixture problems is that you take two or more different amounts (quantities) of two different concentrations (or qualities) and mix them together to get an amount (quantity) that s the sum of the two ingredient quantities and a concentration (quality) that s somewhere between the concentration of the two ingredients that you started with. Figure 14-1 illustrates this property or theme with containers. 

The basic structure for the mixture problem will have one more term in it. You ll have a quality x quantity term that s subtracted from the original amount. Let x represent the number of quarts taken out and put back into the radiator. The end quantity will have to be the original 16 quarts. 

Chemical transformations involve the application of reagents and reaction conditions to transform target species. Such processes involve a string of events that are usually well defined and can often be controlled to maximize efficiency. However, chemical processes often require the presence of excess quantities of reagents to accomplish the transformation to the desired extent. In addition, particularly harsh conditions (e.g., high temperature or extremes of pH) are sometimes required to facilitate the chemical transformations. This can present a problem once the desired transformation has taken place because the resulting stream may be a low-quality mixture that cannot be disposed into the environment or reused without... 

Bleaching Earth. The quantity of earth used is primarily a function of crude oil quality and press efficiency. In both cases, there is already a high degree of problem recognition because of the process and economic implications. Therefore, there will generally not be substantial opportunities to reduce waste earth through process control simply for environmental purposes. Certain brands and types of filter media are better for various crude mixtures and presses however, this is also dictated by process conditions out of necessity. This subject is addressed in more detail elsewhere in other articles. 

---