Problems Metric system

Click Coached Problems for a self-study module on metric system prefixes. 

Basic study skills needed to study chemistry Macroscopic and microscopic properties of matter The SI (Metric) system Basic problem solving techniques Unit Conversion Method Significant figures... 

Chemistry is full of calculations. Our basic goal is to help you develop the knowledge and strategies you need to solve these problems. In this chapter, you will review the Metric system and basic problem solving techniques, such as the Unit Conversion Method. Your textbook or instructor may call this problem solving method by a different name, such as the Factor-Label Method and Dimensional Analysis. Check with your instructor or textbook as to for which SI (Metric) prefixes and SI-English relationships will you be responsible. Finally, be familiar with the operation of your calculator. (A scientific calculator will be the best for chemistry purposes.) Be sure that you can correctly enter a number in scientific notation. It would also help if you set your calculator to display in scientific notation. Refer to your calculator s manual for information about your specific brand and model. Chemistry is not a spectator sport, so you will need to Practice, Practice, Practice. 

When solving gas law problems using the combined gas law, the pressure and volume units do not have to be as indicated by the authors of the laws and by the ideal gas law they don t even have to be in the metric system. However, temperature must be in the Kelvin scale. Explain. 

The SI (metric) system of units is the primary one for the text. Because the Btu-ft-pound system is still in wide use, answers and intermediate steps to examples are occasionally stated in these units. A few examples and problems are completely in English units. Some figures have dual coordinates that show both systems of units. These displays will enable the student to develop a bilingual capability during the period before full metric conversion is achieved. 

The metric system problem, part (a), can be solved without paper and pencil— by moving the decimal point in 5.200 three places to the right. The English system conversion, part (b), requires that we remember the number of yards per mile (harder than the 1000 m/km metric conversion factor) and that we use pencil and paper or a calculator to do the arithmetic. The conversion factor 1000 is used for kilograms, kilohters, kilowatts, and any other factor involving the prefix kilo-. The English conversion factor 1760 yd/mile is not used in any other conversion. 

Practice Problem 2.22 Calculate the number of (a) meters in 6.66 km, (b) liters in 6.66 kL, and (c) grams in 6.66 kg. (d) Highlight the differences among these three problems and comment on the ease of the metric system. ... 

The problem of changing over a highly industrialized nation such as the United States to a new system of measurements is a substantial one. Once the metric system is in general use in the United States, its simplicity and convenience will be enjoyed, but the transition period, when both systems are in use, can be difficult. Nevertheless, it will be easier than it seems. While the complete SI is intimidating because it covers every conceivable kind of scientific measurement over an enormous range of magnitudes, there are only a small number of units and prefixes that are used in everyday life. 

Process safety performance should be reviewed by the manager who authorizes and supports the process safety and metrics systems. As mentioned above, management s commitment to act on problems identified by the metrics is as important, if not more important, than the metrics themselves. Unless leaders respond to weaknesses identified by the metrics, collecting the data is virtually useless. 

The metric system is an alternative way to measure distances, volumes, and masses. Once you understand what the prefixes mean and what the basic terms used for measurement are, you will have no problem dealing with these units. For example, meters (m) are used to measure length. 

As you saw in Chapter 1, one of the convenient features of the metric system is that the relationships between metric units can be derived from the metric prefixes. These relationships can easily be translated into conversion factors. For example, milli- means 10 (or 0.001 or 1/1000), so a milliliter (mL) is 10 liters (L). Thus there are 1000 or 10 milliliters in a liter. (A complete list of the prefixes that you need to know to solve the problems in this text is in Table 1.2.) Two possible sets of conversion factors for relating milliliters to liters can be obtained from these relationships. 

Then if we make the mistake of canceling the Ibm on top and the Ibf on the bottom right-hand side, we will conclude that l=32.2ft/s. This is clearly wrong, and if we do it in a problem, we will find that the dimensions do not check and the numerical value of the answer will be wrong by a factor of 32.2 (if we use English units) or 9.8 (if we use metric units). Similarly, in the traditional metric system, we have... 

The question mark stands for the number we want to find. To solve this problem, we must know the relationship between inches and centimeters. In Table 2.7, which gives several equivalents between the English and metric systems, we find the relationship... 

Himbert, M. E. A Brief History of Measurement. European Physical Journal Special Topics 172 (2009) 25-35. Describes measurement in a historical context. Shoemaker, Robert W. Metric For Me A Layperson s Guide to the Metric System for Everyday Use vnth Exercises, Problems and Estimations. 2d ed. South Beloit, 111. Blackhawk Metric Supply, 1998. A basic guide for the average person wanting to learn and understand the use of metric units. 

The first measurements were probably based on the human body (the length of the foot, for example). In time, fixed standards developed, but these varied from place to place. Each country or government (and often each trade) adopted its own units. As science became more quantitative in the seventeenth and eighteenth centuries, scientists found that the lack of standard units was a problem. They began to seek a simple, international system of measurement. In 1791 a study committee of the French Academy of Sciences devised such a system. Called the metric system, it became the official system of measurement for France and was soon used by scientists throughout the world. Most nations have since adopted the metric system or, at least, have set a schedule for changing to it. 

The closest U.S. unit to the centimeter is the inch, and the closest U.S. unit to the meter is the yard. You can compare unit conversions in the metric system with similar conversions in the U.S. system by calculating the number of yards in 2608 inches. Again, it is a dimensional analysis problem ... 

If you are sufficiently familiar with the metric system, you can solve this problem in one step. However, at this point we recommend that you convert from the given unit to the base unit, and then from the base unit to the wanted unit. Write the Given, Wanted, and Per/Path, set it up, and calculate the answer. Be sure to check the answer. 

Go to http //now.brookscole.com/ cracoliceSe and click Coached Problems for a step-by-step tutorial on Metric System Prefixes. 

H Appendix The Appendix of Introductory Chemistry includes a section on how to use a calculator in solving chemistry problems a general review of arithmetic, exponential notation, algebra, and logarithms as they are used in this book and a section on SI units and the metric system. 

Attention has been also paid to make formalisms as easy as possible to readers from different scientific areas. I tried my best to make the book accurate. Of course, inaccuracies are always possible and I will be grateful to any reader and colleague pointing out possible problems. Whenever possible, the International System has been used as metric system (for units and for shaping equations), with a few exceptions however when different units of measurements are definitely established in a given literature field. Each physical quantity has been described by a dedicated symbol or character throughout the book. Symbols are listed in a Table at the end of the book, where the reader also finds the reference of the first Section where each symbol is introduced. 

We are going to work this problem in lb s, ft- and lb-moles rather than g, mol, and m in order to give the reader more practice in working in both the English and metric systems. Many planes still use the English system of units. 

Another reason for the success of CIO is that these methods are based on very little assumptions (or none at all) on the problem at hand. These methods are, in fact, black-box, so that virtually any input/output system (i.e. a system where inputs-the problem design variables-are mapped to one or more outputs-the problem metrics to minimize or maximize, or fitness in the evolutionary jargon) can be optimized by using them. This property is especially useful for example in many engineering, networking, or logistic problems where an explicit, closed-form mapping between inputs and outputs is not available but is often the output of a domain-specific simulator. 

Chapter 2. Chemistry and Measurements, looks at measurement and emphasizes the need to understand numerical relationships of the metric system. Significant numbers are discussed in the determination of final answers. Prefixes from the metric system are used to write equalities and conversion factors for problem-solving strategies. Density is discussed and used as a conversion factor. 

There are many systems of measurement in use throughout the world, but primarily two that have been in use for years— the English system and the metric system. These systems suffer from many variations and problems. 

---