Converting between units

As explained in Section A, to convert between units, we use a conversion factor of the form... 

The unit analysis method of problem solving is extremely versatile. You can use it to convert between units or to solve some formula problems. If you forget a formula during a test, you may still be able to solve the problem using unit analysis. 

Embracing the International System of Units Relating base units and derived units Converting between units... 

You may encounter questions that ask you to convert between units of measurement in length, weight, or time. To convert from a smaller unit (such as inches) to a larger unit (such as feet), divide the smaller unit by the number of those units necessary to equal the larger unit. To convert from a larger unit to a smaller unit, multiply the larger unit by the conversion number. 

Many scientific activities involve numerical calculations—measuring, weighing, preparing solutions, and so forth—and it s often necessary to convert a quantity from one unit to another. Converting between units isn t difficult we all do it every day. If you run 7.5 laps around a 200 meter track, for instance, you have to convert between the distance unit lap and the distance unit meter to find that you have run 1500 m (7.5 laps times 200 meters/lap). Converting from one scientific unit to another is just as easy. 

If you are asked to convert between units of the same quantity, simply pay attention to what the prefixes stand for. If asked Figure 2-lc to convert 3.45 kilograms... 

Factor-label method A method used to convert between units of different quantities. 

Factor to convert between units and to convert from lifetime risk to annual risk... 

Use conversion factors derived from percentages to convert between units of a part and units of the whole. 

Careful measurements and the proper use of significant figures, along with correct calculations, will yield accurate numerical results. But to be meaningful, the answers also must be expressed in the desired units. The procedure we will use to convert between units in solving chemistry problems is called the factor-label method, or dimensional analysis. A simple technique requiring little memorization, the factor-label method is based on the relationship between different units that express the same physical qnan-tity. 

I Convert between units using dimensional analysis. 

To convert between units of radon-222 radioactivity (Ci or Bq) and the potential alpha energy concentration (WL or J/m the equilibrium between radon gas and radon daughters must be known (See Chapter 9 for conversion formula). When radon is in equilibrium with its progeny, that is, when each of the short-lived radon daughters is present at the same activity concentration in air as radon-222, then 1 WL equals 100 pCi radon-222/L of air. However, when removal processes other than radioactive decay are operative, such as with ventilation, the concentration of short- lived daughters will be less than the equilibrium amount. In such cases an equilibrium factor (F) is applied. For example, if the equilibrium factor is 0.5, then 200 pCi radon-222/L of air is equivalent to 1.0 WL if the equilibrium factor is 0.3, then 1 WL corresponds to 333 pCi radon-222/L of air. 

The first thing you need in order to convert between units is the equivalence between the units you want and the units you have. To do this use a conversion table. See w Conversion of units for a fairly extensive (but not exhaustive) list of common units and their equivalences. 

We use ratios in a variety of common calculations in chemistry. One that you will undoubtedly also encounter in engineering is the need to convert between units of different sizes. Example Problem 1.5 introduces this type of manipulation. 

The key to converting between units is to write a conversion factor such as 10 C/pC, carry out the multiplication, cancel the same units that appear in the numerator and denominator, and show that the answer has the correct units. The number of electrons in 0.27 pC is... 

Gas solubility has been measured by a variety of means, for a wide variety of purposes. As a consequence of this, there exist at least ten expressions for the solubility of a gas in a liquid [5]. This is problematic as it is not always simple to convert between units. The units that are most relevant to expressing the influence of electrolytes on gas solubility are the Bunsen Coefficient (a), the mole fraction ( 2), and the Henry s law constant (Kh,). 

Converting Between Unit Systems We use the same procedure to convert between systems of units, for example, between the English (or American) nnit system and the International System (a revised metric system Section 1.4). Suppose we know that the height of Angel Falls in Venezuela (the world s highest) is 3212 ft, and we find its height in miles as... 

Converting Between Units When Multiple Steps Are Required... 

Identify energy as potential or kinetic convert between units of energy. 

By this time, you are probably experienced in working with units. Most science and engineering texts have a section in the first chapter on this topic. In this text, we will mainly use the Systeme International, or SI units. The SI unit system uses the primary dimensions m, s, kg, mol, and K. Details of different unit systems can be found in Appendix D. One of the easiest ways to tell that an equation is wrong is that the units on one side do not match the units on the other side. Probably the most common errors in solving problems result from dimensional inconsistencies. The upshot is Pay close attention to units Try not to write a number down without the associated units. You should be able to convert between unit systems. It is often easiest to put all variables into the same unit system before solving a problem. 

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