Essential Chemistry

Clarke EarleyKent State University Stark Campus

Chemistry in Our World

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Copyright c© 2018 by Clarke Earley

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Author contact information:

Clarke W. Earley, Ph.D.Kent State University at Stark6000 Frank Avenue, N.W.North Canton, OH 44720http://delta.stark.kent.edu

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CONTENTS 3

Contents

Contents 3

1 What is Science? 51.1 THE SCIENTIFIC METHOD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.1.1 Importance of Scientific Theories and Laws . . . . . . . . . . . . . . . . . . 71.1.2 Applying the scientific method . . . . . . . . . . . . . . . . . . . . . . . . . 8

1.2 Measurements and Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91.2.1 The metric system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91.2.2 Conversions between units . . . . . . . . . . . . . . . . . . . . . . . . . . . 111.2.3 Sample Conversion Problems . . . . . . . . . . . . . . . . . . . . . . . . . 121.2.4 Scientific notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141.2.5 Temperature conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

1.3 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

Chapter 1

What is Science?

All of us have a natural curiosity about the world around us. Young children are constantly asking"Why?". A rather simplistic definition of science, but one that is useful for our purposes, is thatscience is the study of the physical world around us. While we often have the idea that science canonly be studied after years of formal training, in a very practical sense, anyone can study aspects oftheir world. Put more bluntly, science can be, and is, practiced by almost everyone.

1.1 THE SCIENTIFIC METHOD

The term "scientific method" is used to attempt to more precisely define the process by which modernscience is formally practiced. Unfortunately, the scientific method has very many different definitions.Worse, most scientists don’t conscientiously attempt to follow the scientific method when they areattacking scientific problems. While trying to give a definition of the scientific method may appear tobe a rather pointless exercise, it does provides a useful starting point to describe the process used inexperimental science.

In all cases, whether explicitly recognized or not, the first step of the scientific method is a desireto answer a question. This is typically the result of an observation. For example, we might want toknow "Does this milk smell OK?", "Why is grass green?", Why does popcorn ’pop’?". Although noneof these may sound like scientific questions, they are perfectly valid questions to begin a scientificinquiry, and could lead to very scientific results and practical applications. For our first example, ifwe know what products are formed when milk (or any other food) goes bad, that could lead to anunderstanding of how spoilage occurs, which could lead to improved methods for increasing the shelflife of food. It is quite common in in the course of scientific investigation that the results of one studylead to additional questions. While the tools required to study problems in detail may increase incomplexity, all that is required to begin a scientific inquiry is our natural sense of curiosity.

Once we have a question, the second step of the scientific method is to formulate a possibleanswer that explains our observation. This tentative explanation is called a HYPOTHESIS. The onlyrequirements for a hypothesis is that it must be able to explain all known facts. It is typically the case

Figure 1.1: Scientific Method

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6 CHAPTER 1. WHAT IS SCIENCE?

Teflon: Importance of ObservationYou are probably familiar with Teflon as a non-stick coating for cookware. In addition tothis common application, Teflon has a number of other practical uses due to the fact that is arather unreactive molecule. However, the discovery of Teflon was an ’accident’. The reasonthat Teflon became the product it is today is because scientists were interested in ’whathappened’ and took the steps necessary to discover the chemistry behind this molecule. In1938, Roy Plunkett and fellow researchers at DuPont were investigating the properties oftetrafluoroethylene, which is a gas that they hoped could have application as a refrigerant.After preparing this gas, it was stored in heavy metal cylinders under high pressure andfitted with a valve to control the flow of gas out of the cylinder. When the valve on one ofthese cylinders was opened, no gas was released. However, from the weight of the tank, itappeared that the cylinder was full. Curious to know what was happening, these workersdecided to saw the cylinder open and see what was inside. By studying the properties ofthe material inside and from knowing where this solid had apparently come from, theseresearchers where able to hypothesize an explanation. Eventually, this hypothesis not onlylead to an explanation of what the solid was (Teflon), but also how it had formed inside thecylinder and provided a potential route for the chemical production of this molecule in amore controlled manner.

that several different explanations could be proposed, all of which are consistent with the known facts.Obviously, for well-studied problems, a large number of facts will be known, and our hypothesis mustexplain all of these. This limits the range of potential explanations. For other problems, very littlemay be known, and a much broader set of explanations will be possible. At this stage, it is notimportant that our hypothesis is correct (although it might be).

While a hypothesis must explain all known observations, it will generally be possible to makenew predictions based on this hypothesis. For example, we might hypothesize that popcorn popsbecause the kernels contain water that expands by turning into steam at high temperature. Given thishypothesis, we might want to determine whether or not water is present inside popcorn. If water ispresent, we could expand this study by trying to determine how much water is present. The third stepof our scientific method is EXPERIMENTATION. Modern science requires that theories be tested.While the degree of sophistication that will be applied will vary depending on the question beingasked, experimentation must be done to test our hypothesis.

Qualitative measurement (“Big”) Quantitative measurement (“162 feet”)

Closely related to actually performing an experiment is the process of observing, and typicallyrecording, the results obtained. The final step of our scientific method is OBSERVATION. Observa-tion may be either be QUALITATIVE, which does not require a numerical result, or QUANTITA-TIVE, which does. For example, we might observe that that temperature outside on a summer day isQuantitative:

Descriptioninvolving anumericalmeasurement.

’hot’, which is a qualitative statement. Qualitative observations are useful because they are generallymuch easier to obtain. However, they do not tend to be as useful, in part because of possible dif-ferences in interpretation. To someone living in Canada, a hot summer day may be 75◦F, while this

1.1. THE SCIENTIFIC METHOD 7

Data vs. InterpretationJust as in almost every other field, disagreements can arise in all areas of science. Thesedisagreements generally have nothing to do with the actual data, but instead on the inter-pretation of this data (which is the scientific hypothesis or theory). One example of thiscommonly referred to in the media is global warming. The fact that carbon dioxide levelsin the atmosphere are increasing is almost universally accepted. What implications (if any)this has on future temperatures on our planet is much less certain.

would be considered quite cold for a summer temperature is more tropical climates. The practice ofmodern science almost always deals with quantitative measurements.

These are the only steps in the scientific method, but the original question will almost never beanswered at this point. The results of our experiment need to be compared with the prediction of ourhypothesis. If the experimental results are inconsistent with our original hypothesis, this hypothesisneeds to be modified. In some cases, the results are so different that there is no choice but to ’startover’ with a completely new hypothesis. In other cases, only slight modifications may be required.Given our ’new’ hypothesis, additional experiments can be designed, performed, and observationsrecorded. It may (or may not) come as a surprise that even if the results are consistent with ouroriginal hypothesis, additional experiments are usually required.

It can be seen from this that the scientific method is a iterative, or a cyclic process. A naturalquestion at this point is "how do we known when we are done?". In a theoretical sense, applicationof the scientific method will never be finished. The scientific method cannot ever prove that anexplanation is correct, it can only prove that an explanation is incorrect. It will always be possible todesign and perform additional experimental tests.

In a practical sense, once a hypothesis has undergone sufficient testing (which is not well de-fined), the hypothesis is raised to the level of a THEORY. A simple definition for a theory is a wellstudied, experimentally tested hypothesis. While a theory may be the result of a single individual’swork, more commonly it is the result of many different researchers studying the same problem fromdifferent angles. Once a theory has been well studied experimentally and is generally accepted bymost researchers in a field, the theory can be elevated to the level of a LAW.

1.1.1 Importance of Scientific Theories and Laws

While it may seem reasonable to conclude that a scientific law is (i) correct and (ii) the scientificmethod is finished, neither of these conclusions are actually correct. As a familiar example, Newton’sLaws of Motion have been extensively studied and are a well accepted explanation to account for the

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Historical vs. Observational ScienceThe scientific method is a very powerful technique that has greatly expanded our knowledgeof the world around us. However, not all problems can be studied using the scientificmethod outlined in this chapter. Operational science is a term that has sometimes been usedto indicate areas where the scientific method can be applied. This type of research requiresthat experiments be performed. Historical science is a term that is sometimes used to referto the study of events that have happened in the past and are irreproducible. Examples ofthese types of studies include study of the origins of the earth or trying do determine causesfor the extinction of dinosaurs. Because it is impossible to perform experiments involvingthe creation of the universe or killing off dinosaurs, the scientific method as outlined herecannot be applied. In historical science, the emphasis is on gathering, quantifying, andclassifying data and interpreting these results to reach a consistent theory. Because thedata is typically limited and no further experiments are possible, the theories of historicalscience are generally much more tentative than those obtained from operational science.

properties of moving objects. These laws have proven to be very reliable and have been used exten-sively in automotive and rocket design, ballistics, and a wide range of other applications. However,it was discovered these laws do not properly account for the motion of particles moving at velocitiesapproaching the speed of light. A portion of the theory of relativity deals with the corrections nec-essary to properly account for these types of motion. Because these effects are only significant forobjects traveling at incredibly high speed, the experiments of Newton and his colleagues could notdetect these discrepancies. In most practical applications, relativistic effects are insignificant and canbe ignored, so Newton’s Laws are ’good enough’.

While it is always nice to be right, science does not require that theories and laws be absolutelycorrect. One of the goals of science is to develop working explanations that will allowed problemsto be understood and, ideally, ’solved’. The fact that Newton’s Laws are incomplete (and that betterequations are known) does not stop a scientist from using these equations to design a better air bag orrocket. As long as the range of applications and limitations of a law or theory are known, the resultsof this law or theory can be used.

1.1.2 Applying the scientific method

As a very simple example of the application of the scientific method, lets pretend that we notice acontainer of water. We might want to know if the water is hot (step one - question). We could guessthat this water is hot (step two - hypothesis), and decide that if we put our hand in the water we couldfind out (step three - experiment). When we actually do put our hand in the water, we might findout that the water is not hot (step four - observation). At this point, we recognize that our hypothesiswas wrong, so we come up with a new hypothesis. We now have a hypothesis that is consistent withone piece of experimental evidence. Simply repeating the same experiment (putting our hand backinto the water) will generally not give us any additional information. However, we might recognizethat the terms hot and cold are somewhat ambiguous, so we could decide that we might want toquantitatively determine how hot (or cold) the water is. To answer this, we need a more sophisticatedexperiment, such as putting a thermometer in the water.

This simple study could easily be extended in a number of different ways depending on theinterests or needs of the investigator. Scientists commonly use the scientific method to develop newstrategies for solving a problem or improving upon an existing technology. To extend this example,

1.2. MEASUREMENTS AND UNITS 9

the amount of energy required to raise the temperature of a given amount of water could be used toexplain why temperatures are cooler near large bodies of water in summer months, which could beimportant for weather forecasts and gardening. How different liquids respond to adding or removingheat is important in the development of coolants and anti-freeze.

1.2 Measurements and Units

One of the features of scientific experiments is that they should be reproducible. If two differentpeople perform the same experiment exactly the same way, then the results should be the same.Implicit in this is the assumption that it is possible to determine whether or not the same result isobtained. For qualitative observations, complete details of the experimental procedure may not benecessary. For example, mixing baking soda and vinegar together makes bubbles, and the quantitiesused don’t change this result. However, for quantitative experiments, these missing details becomeimportant. If we want to know how much gas was formed (bubbles), this will depends on the ratio ofvinegar and baking soda and how much was used.

Cooking is a familiar example of an experimental procedure where details make a difference.Recipes generally start by listing all of the ingredients required (butter, chocolate chips, milk, ...) andthe amounts of each (2 sticks butter, 1 cup chocolate chips, ...). Following this is the experimentalprocedure. (Preheat oven to 350, melt butter in a saucepan until melted, then add chocolate chips andvanilla). While the “ingredients” are generally quite different1 and the procedures not as familiar,descriptions of chemical reactions carried out in a laboratory are typically done in a very similarmanner. Most scientific papers include an experimental section that describes the procedures used sothat other workers can reproduce their results.

If you have ever tried to use an original recipe from another country, it is common for the quan-tities to be given in somewhat unfamiliar units, such as grams or milliliters. To avoid this problem,scientists around the world generally report their work using a standard system of measurements.This system (S.I. for System International) is essentially the same as the metric system. Note that themetric (or S.I.) system is no better or worse than any other system of measurements, it is simply thestandard that everyone agrees to use.

1.2.1 The metric system

A tape measure showing inches and centimeters

Table 1.1 gives common base units for the metric system2 and their approximate American equiv-alents. A common misconception is that the metric system is harder to use than our system becausethe conversions are so hard. In reality, converting between two different systems of measurement willalmost always require mathematical conversions, but changing units within a system of measurementsmay not be difficult at all. In fact, conversions between units within the metric system is often mucheasier than conversions within the metric system because the units all differ by powers of ten. As a

1And usually not as tasty.2While there are some technical differences between the metric and S.I. systems, they are similar enough that we can

consider them to be the same.

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Table 1.1: Standard base units

Type of quantity Base unit Approximate American equivalentlength meter 1 meter ≈ 1 yardvolume liter 1 liter ≈ 1 quartmass gram 1 ounce ≈ 28 grams

temperature Celsius (◦C) (No simple conversion)time second (Identical)

Table 1.2: Metric Prefixes

Abbreviation Name Size (relative to base unit)k kilo- 1000- - -d deci- 0.1 = 1

10c centi- 0.01 = 1

100m mill- 0.001 = 1

1000µ micro 0.000 001 = 1

1,000,000

simple example, since there are 12 inches in a foot, a person who is 5’ 3" tall is 5x12 + 3 = 63 inchestall. As a somewhat more difficult cases, how many feet are in 1

3 mile or how many tablespoons ina pint? In contrast, conversions within the metric system only involving changing by powers of 10(moving the decimal point). For example, since there are 10 dm in one meter, a person who is 1.61meters tall is 16.1 dm tall.The metric

system is nobetter than anyother system ofmeasurements.Scientists usethe metricsystem becauseit is a single,commonsystem that isusedworldwide.

For many applications, exact conversions between units is not necessary and a rough approxima-tion will do. For example, gasoline may cost $1.52/Liter in Canada. How does this compare withgas prices here (assuming this is given in U.S. dollars)? If we note that a liter is roughly the sameas a quart and remember that there are four quarts in a gallon, this means that it will take four litersof gasoline at a cost of $1.52 x 4 to equal one gallon. Therefore, the cost of this gasoline is roughly$6/gallon.

As another example, a meter is just over a yard. If an athlete can sprint a 100 yard dash in under10 seconds, he or she will take approximately the same amount of time to run 100 meters. If we wantto be a little more accurate, we could note that since a meter is just over a yard, 100 meters is slightlylonger than a yard. Therefore, times for a 100 yard dash are expected to be slightly better than timesfor a 100 meter dash.

In addition to the fact that units within the metric system all differ by powers of 10, a single setof naming rules is used for all types of metric units. The base name, including those in Table 1.1and other derived units, defines the type of quantity the unit measures. For example, meters are usedto measure length or distance, and grams are used to measure mass. These base units can then bemodified by addition of a prefix to give units of a more convenient scale. The same prefixes are usedfor all base units. In the American system, we typically choose the units depending on the size of theobject being measured. For example, we never ask a person how many miles tall he or she is, nor dowe measure the gallons of vanilla to put in recipe. In the same manner, metric base units are modifiedto give more convenient numbers. The most common metric prefixes are listed in Table 1.2.

1.2. MEASUREMENTS AND UNITS 11

1.2.2 Conversions between units

To perform accurate conversions between two different systems of units, it is necessary to have aconversion factor. As an example of this, consider the fact that there are exactly 12 inches in 1 foot.Since 12 inches and 1 foot represent the same amount of distance, we can write:

12 inches = 1 foot

It is crucial that the units be written in these equations. Without units, the about equation statesthat 12 equals 1 (which is obviously not correct). Units will be included in all of the followingcalculations, and will actually make some steps less prone to error. If we divide both sides of thisequation by 12 inches, we obtain:

12 inches12 inches = 1 foot

12 inches

Since any non-zero quantity divided by itself is one (for example, 6.13 / 6.13 = 1), the left side ofthis equation is one. Therefore, since both sides of this equation are equal:

1 = 1 foot12 inches

Since any value multiplied by one remains unchanged, we can multiply any number by 1 foot12 inches

and not change the value of that quantity. For example, if we multiply 18 inches by 1 we get 18inches. If we multiply 18 inches by 1 foot

12 inches , we get:

18 inches * ( 1 foot12 inches ) = 18

12inch ·foot

inch = 1.5 feet

Note that both the numbers changed (18 −→ 1.5) AND the units changed (inches −→ feet). Theunits of our final answer (feet) is a result of the fact the the inches ’canceled’.

In a similar manner, it can be shown that:

12 inches1 foot = 1 foot

1 foot = 1

We now have two different ways to represent ’1’ in terms of feet and inches ( 12 inches1 foot and 1 foot

12 inches ),which we will call conversion factors. In order to make use of these conversion factors, we need toknow which conversion factor to use. Our choice will be determined by which of these equation willgive an answer in the desired units. For example, both of the following equations are ’correct’, butonly the first equation gives the answer is convenient units.

18 inches * ( 1 foot12 inches ) = 1.5 inch ·foot

inch = 1.5 ft (Meaningful units)

18 inches * ( 12 inches1 foot ) = 216 inch·inch

foot = 216 in2

ft (Units make no sense)

The procedure outlined in Box 1.1 is a general method for conversion of between any two typesof units. These may both be in the same ’system’, such as inches to feet, or this may be betweendifferent systems, such as miles to kilometers. The only requirement of this method is that suitableconversion factors can be obtained. Table 1.3 gives a list of common equalities that can be used toobtain conversion factors. Box 1.1 gives a few examples of conversions between different units ofmeasurement.

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Box 1.1: Converting between units

The following rules give a simple procedure for converting a known quantity between anytwo units for which a suitable conversion factor can be obtained. Whenever possible, it is agood idea to try to get a crude estimate of the approximate value expected before doing thecalculation to determine whether the answer obtained is reasonable.

1. Write the value and the units for the known, measured quantity. (Some people findit easier to perform the multiplications that come later if this value is written as afraction over ’1’).

2. Multiply this value by a fraction. The units for the numerator (top quantity) will bethe desired units for your answer. The units for the denominator (bottom quantity)will be the units of the original, measured quantity that you are trying to ’get rid of’.

3. Find the appropriate equality from a table similar to Table 1.3. Be sure that thenumber from this table ’stays with’ its units.

4. Perform the multiplication. The original units should cancel and your answer shouldbe in the desired units.

1.2.3 Sample Conversion Problems

In this section, several examples of converting between units are worked out according to the proce-dure outlined in Box 1.1.

Example #1: How many inches are there in 1.73 feet?

We know that 12 inches = 1 foot. Simply by looking at the number, we know that our answer shouldbe a little under 24 inches. To get a more exact answer, we follow our procedure.

(1) We are given a measurement of 1.73 feet. 1.73 feet or 1.73 ft1

(2)Multiply by a fraction so that the ’old’ unitscancel and the answer will be in the ’new’ units.(Don’t actually put in any numbers yet).

1.73 ft1 * ? inches

? ft

(3)

Find the appropriate equality in Table 1.3 thatrelates feet and inches. Plug these numbers intoour equation, being sure to keep the propernumber associated with its unit.

1.73 ft1 * 12 in

1 ft

(4)Multiply the original quantity by the conversionfactor. The answer must include all units that didnot cancel in the multiplication.

1.73 ft1 ∗ 12 in

1 ft = 20.76in

Note: Feet (ft)cancel in thelast step.

As anticipated, our value is a little less than 24 inches. Whenever possible, it is a good idea topredict the approximate size of the answer before doing the calculation. If the answer obtained isvery different from this answer, it is likely that a mistake was made in setting up the problem.

1.2. MEASUREMENTS AND UNITS 13

Table 1.3: Equalities for Converting Between Units

In this table, ≡ indicates and exact equality, while ≈ indicates an approximate relationship.Length Volume Mass

1 inch ≡ 2.54 cm 1 gallon ≡4 quart (qt) 1 pound (lb) ≡ 16 ounces (oz)1 foot (ft) ≡ 12 in 1 L ≈ 1.06 qt 1 kg ≈ 2.2 lb1 mile ≈ 1.609 km 1 qt ≡ 4 cups 1 oz ≈ 28.35 g1 mile ≡ 5280 ft 1 cup ≡ 16 Tablespoons

Example #2: How many centimeters are there in 2.53 meters?

In this case, we know that a centimeter (≈1/2 inch) is much less than a meter (≈1 yard). It will takea lot of these small units (cm) to equal the larger unit (meter), so our answer in centimeters should bemuch more than 2.53. Following the same procedure:

(1) We are given a measurement of 2.53 meters. 2.53 m1

(2)Multiply by a fraction so that the meters cancel(on the bottom) and only cm remain. (Don’tactually put in any numbers yet).

2.53 m1 * ? cm

? m

(3)For this problem, our conversion factor comesfrom the table of metric prefixes (Table 1.2).

2.53 m1 * 100 cm

1 m

(4)Perform the multiplication. The meters willcancel, and our answer is in units of cm.

2.53 m1 * 100 cm

1 m = 253 cm

Checking our answer, 253 (ignoring units) is indeed much larger than 2.53, so our answer lookscorrect.

Example #3: How many inches are there in 18.0 cm?

To get an idea of the expected answer, we note that a centimeter is < 12 inch. Since we are going from

a smaller unit (cm) to a larger unit (inches), it shouldn’t take as many inches to equal 18 cm. Ouranswer should be roughly 1

2 of 18, or 9 inches. Using the same procedure to obtain a more exactvalue:

(1) The given quantity is 18.0 cm. 18.0 cm1

(2)Multiply by a fraction to properly convert theunits from cm to inches.

18.0 cm1 * ? in

? cm

(3)Since we are converting between different typesof units, our conversion factor comes from Table1.3.

18.0 cm1 * 1 in

2.54 cm

(4)Perform the multiplication. The centimeters willcancel, and our answer is in units of inches.

18.0 cm1 * 1 in

2.54 cm = 7.09 in

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Again, this value is about what we expected. The actual quantity is a little smaller than ouroriginal guess because one centimeter is actually significantly less than 0.5 inches.

1.2.4 Scientific notation

The building blocks of all matter are incredibly small particles called atoms. A single teaspoon ofwater contains approximate 600,000,000,000,000,000,000,000 atoms. The distance between theseatoms must be quite small, and may be on the order of 0.0000000001 meters. Numbers that are verylarge or very small are difficult to work with: They have too many zeros. In some cases, metricprefixes can be used to solve this problem. For example, the distance between some of the atomsin water is approximately 140 picometers. An alternative to this is to use exponential or scientificnotation.

Scientific notation is very similar in concept to the prefixes used in the metric system. In sci-entific notation, all quantities are converted into numbers between 1 and 10, and then scaled to theappropriate size by multiplying by some power of ten. For example, we might represent numbers as3.52 x 10+6 or 7.22 x 10−5. The size of the number is determined primarily by the power of ten.The exponent indicates how many positions the decimal point has been shifted. If the exponent is apositive number, the overall quantity is greater than one (a large number). If the exponent is negative,the overall quantity is less than one (a small number).

It is important to remember that small changes in exponents give rise to very large changes insize. Changing a number by a factor of 10 is often called one order of magnitude. The line drawingabove shows a change of only two orders of magnitude (100 to 102).

For the first value listed above (3.52 x 10+6), the positive 6 indicates that we are representing alarge quantity and that the decimal point has been shifted 6 places. Starting from 3.52, we move thedecimal point six places to the right, adding zeros as necessary to obtain the following result.

3.52 x 10+6 = (3.520000 x 10+6) −→ 3,520,000

In our final answer, it is not usually necessary or desirable to show the decimal point.For our second example, the negative 5 indicates a small quantity with the decimal point shifted

5 spaces to the left.

7.22 x 10−5 = (000007.22 x 10−5) −→ 0.0000722

1.2.5 Temperature conversions

Conversion between degrees Fahrenheit (◦F) and degrees Celsius (◦C) cannot be accomplished bysimple multiplication using a conversion factor. The reason for this is that zero is different on thesescales. For all of the equalities listed in Table 1.3, if the value of quantity was zero, the number wasthe same for all units. For example, 0 inches is the same as 0 feet is the same as 0 cm. For temperature,this is not true. On the Celsius scale, water freezes at 0◦C. However, on the Fahrenheit scale, waterfreezes at 32◦F. This means that 0◦C 6= 0◦F. To convert between ◦C and ◦F, it is necessary to findboth the relative size of a change in degrees on the two scales and to ’offset’ one of these temperaturescales.

1.2. MEASUREMENTS AND UNITS 15

The Celsius scale is based on the properties of water.Water freezes (and melts) at 0◦C and boils at 100◦C.Therefore, a change of 100 degrees on a Celsius scale(100 C◦) is required to go from freezing to boiling wa-ter. On a Fahrenheit scale, water freezes at 32◦F andboils at 212◦F. Therefore, a change of 180 degrees ona Fahrenheit scale (212◦F - 32◦F = 180 F◦) is requiredfor this process. Combining these results gives:

180 F◦ ≡ 100 C◦

or180 F◦100 C◦ = 9 F◦

5 C◦ = 1

Finally, it is necessary to shift the Fahrenheit scale by 32 degrees so that zero on the Celcius scale“lines up” with 32◦F. Our final results are:

◦F≡ ( ?◦C · 9F◦

5C◦)+32◦F (1.1)

◦C≡ 5C◦

9F◦· ( ?

◦F−32◦F) (1.2)

Note that thedegree sign (◦)is normallyplaced beforethe unit toindicate anactualtemperature(for example,78◦F). Placingthe degree signafter the unitsignifies achange intemperature.

The first of this equations (1.1) is used when the temperature in ◦C is known and the ◦F is desired.To verify that this is correct, we can use this equation to convert 100◦C into ◦F. Using this first

We know theanswer shouldbe 212◦F

equation:

◦F ≡ ? ◦C · ( 9 F◦5 C◦ ) + 32◦F = 100◦C · ( 9 F◦

5 C◦ ) + 32◦F = 180◦F + 32◦F = 212◦F

Equation 1.2 is an algebraic rearrangement of equation 1.1, and is used to convert from a knowntemperature in ◦F into a temperature in ◦C. For example, to convert 98.6◦F into ◦C, the second equa-tion should be used. The answer is:

◦C ≡ 5 C◦9 F◦ ·( ? ◦F – 32◦F) = 5 C◦

9 F◦ ·( 98.6◦F – 32◦F) = 5 C◦9 F◦ ·(66.6◦F) = 37.0◦C

Note that when the second equation is used, 32◦F is subtracted from the temperature beforemultiplication by the scale factor.

16 CHAPTER 1. WHAT IS SCIENCE?

1.3 Problems

1. Which of the following questions can be examined using the scientific method as used in oper-ational science?

a) How many calories are present in a candy bar?

b) Why does wood float?

c) What was the real reason for the Revolutionary War?

d) Is there life in other galaxies?

e) Are vitamins good for you?

2. Indicate whether each of the following statements are qualitative or quantitative.

a) He is really tall.

b) Today was very cold for this time of year.

c) He weighs about 175 pounds.

3. Perform each of the following metric conversions.

a) 315 mL = ? L

b) 2.54 cg = ? mg

c) 1.5 km = ? meters

d) 6.7 cm = ? dm

4. Perform each of the following conversions between English and metric units.

a) 8.50 in = ? cm

b) 8.50 cm = ? in

c) 354 mL = ? quarts

d) 65 miles = ? km

e) 150 lbs = ? kg

5. Perform each of the following temperature conversions.

a) 98.6◦F = ?◦C

b) 25.0◦C = ?◦F

c) -11.5◦C = ?◦F

Answers to Problems

Chapter 1

1. (a), (b), and (e) can be studied using operational science.

2. (a) and (b) are qualitative, while (c) is quantitative.

3. (a) 0.315 L, (b) 25.4 mg, (c) 1500 m, (d) 0.67 dm

4. (a) 21.6 cm, (b) 3.35 in, (c) 0.374 quarts, (d) 105 km, (e) 68.0 kg

5. (a) 37.0◦C, (b) 77.0◦F, (c) +11.3◦F

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