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Search Ebook here:. Brown and H. Book Preface To the Instructor Philosophy We authors of Chemistry: The Central Science are delighted and honored that you have chosen us as your instructional partners for your general chemistry class. Designed by readallbooks. Download here Download Now here. She measures her body temperature with a surements? Significant Figures in Calculations When carrying measured quantities through calculations, the least certain measure- ment limits the certainty of the calculated quantity and thereby determines the number of significant figures in the final answer.
The final answer should be reported with only one uncertain digit. To keep track of significant figures in calculations, we will make frequent use of two rules: one for addition and subtraction, and another for multiplica- tion and division.
For addition and subtraction, the result has the same number of decimal places as the measurement with the fewest decimal places. When the result contains more than the correct number of significant figures, it must be rounded off. Consider the following example in which the uncertain digits appear in color:. This number limits We report the result as For multiplication and division, the result contains the same number of sig- nificant figures as the measurement with the fewest significant figures.
For example, the area of a rectangle whose measured edge lengths are 6. Notice that for addition and subtraction, decimal places are counted in determining how many digits to report in an answer, whereas for multiplication and division, significant figures are counted in determining how many digits to report. In determining the final answer for a calculated quantity, exact numbers are as- sumed to have an infinite number of significant figures.
Thus, rounding off 7. Rounding off 4. Give It Some Thought a rectangular garden plot is measured to be Which of these dimensions needs to be measured to greater accuracy to provide a more accurate estimate of the area of the plot?
One common practice is to round up to the next higher number if that number will be even and down to the next lower number otherwise. Thus, 4. Calculate the volume of the box, using the correct number of significant figures in your answer.
SOLUTION In reporting the volume, we can show only as many significant figures Practice Exercise 1 as given in the dimension with the fewest significant figures, which is Ellen recently purchased a new hybrid car and wants to check her that for the height two significant figures : gas mileage. At an odometer setting of At Calculate her average round off to two significant figures. Because the resulting number is speed in meters per second and express the result to the correct , it is best reported in exponential notation, 2.
Thus, the mass of the gas, of the gas. The mass of the gas is just the difference in the masses of 1. There are three significant figures in our answer, corresponding to the number of significant figures in the two numbers that form the ratio.
Notice that in this example, following the rules for determining significant figures gives an answer containing only three significant figures, even though the measured masses con- tain five significant figures.
Practice Exercise 1 Which of the following numbers is correctly rounded to three. Practice Exercise 2 Volume: 1. When a calculation involves two or more steps and you write answers for intermedi- ate steps, retain at least one nonsignificant digit for the intermediate answers. This pro- cedure ensures that small errors from rounding at each step do not combine to affect the final result. Accumulated rounding-off errors may account for small differences among results you obtain and answers given in the text for numerical problems.
Throughout the text we use dimensional analysis in solving problems. In dimen- sional analysis, units are multiplied together or divided into each other along with the numerical values. Equivalent units cancel each other. Using dimensional analysis helps ensure that solutions to problems yield the proper units. Moreover, it provides a systematic way of solving many numerical problems and of checking solutions for possible errors. The key to using dimensional analysis is the correct use of conversion factors to change one unit into another.
A conversion factor is a fraction whose numerator and denominator are the same quantity expressed in different units. For example, 2. This relationship allows us to write two conversion factors: 2. For example, the length in centimeters of an object that is 8. Desired unit 2. Given unit. The unit inches in the denominator of the conversion factor cancels the unit inches in the given data 8. Because the numerator and denominator of a conversion factor are equal, multiplying any quantity by a conversion factor is equivalent to multiplying by the number 1 and so does not change the intrinsic value of the quantity.
The length 8. In general, we begin any conversion by examining the units of the given data and the units we desire. We then ask ourselves what conversion factors we have available to take us from the units of the given quantity to those of the desired one. Careful inspection of units often reveals the source of the error. If a woman has a mass of lb, what is her mass in grams?
Use the relationships between units given on the back inside cover of the text. To cancel pounds and leave grams, we write the conversion factor with grams in the numerator Given: lb and pounds in the denominator:. The process we have used is diagrammed in the margin. Find: g Practice Exercise 1 At a particular instant in time the Earth is judged to be 92,, miles from the Sun. What is the distance in kilometers to four significant figures? See back inside cover for conversion factor.
Practice Exercise 2 By using a conversion factor from the back inside cover, determine the length in kilometers of a Estimating Answers done without a calculator. Even though this approach does not give an exact answer, it gives one that is roughly the correct size. By using di- Calculators are wonderful devices; they enable you to get to the mensional analysis and by estimating answers, you can readily check wrong answer very quickly.
You can take certain steps to avoid putting that wrong You can get better at making estimates by practicing in every- answer into your homework set or on an exam.
One is to keep track day life. How far is it from your dorm room to the chemistry lecture of the units in a calculation and use the correct conversion factors. How much do your parents pay for gasoline per year? How many Second, you can do a quick mental check to be sure that your an- bikes are there on campus? Give It Some Thought how do we determine how many digits to use in conversion factors, such as the one between pounds and grams in Sample exercise 1.
Using Two or More Conversion Factors It is often necessary to use several conversion factors in solving a problem. The table on the back inside. From our knowl- cover does not give the relationship between meters and inches. It does, however, give. Thus, we can convert step by step, first from meters to centimeters and then from centimeters to inches: Given: Find: Use Use m cm in. Combining the given quantity 8. Thus, meters are written in the denominator and centimeters in the numerator.
The second conversion factor is used to cancel centimeters and convert the length to inches, so it has centimeters in the denominator and inches, the desired unit, in the numerator. As long as you keep track of your given units and cancel them properly to obtain the desired units, you are likely to be successful in your calculations. Convert this speed to miles per hour. From our convert meters to miles and seconds to hours.
From the relationships given Thus, we can convert s to min and then convert min to hr. Applying first the conversions for distance and then those for time, we can set up one long equation in which unwanted units are canceled:. Our answer has the desired units. Dividing by Fabiola, who lives in Mexico City, fills her car with gas, paying converts m to km, giving 0.
Because 1 mi is about 1. What is her fuel cost in dollars per gallon, if 1 this speed corresponds to 0. The Practice Exercise 2 answer to the detailed solution has three significant figures, cor- A car travels 28 mi per gallon of gasoline. What is the mileage in responding to the number of significant figures in the given speed kilometers per liter? Conversions Involving Volume The conversion factors previously noted convert from one unit of a given measure to another unit of the same measure, such as from length to length.
We also have conver- sion factors that convert from one measure to a different one. The density of a sub-.
Suppose we want to know the mass in grams of 2 cubic inches The density gives us the conversion factors: The relationship between in. Cubing both sides of this equation gives 11 in. We have used four, one Notice that both the numbers and the units are cubed. Also, because 2. Applying our conversion factors, we can now solve the problem:. The procedure is diagrammed here. The final answer is reported to three significant figures, the same number of significant figures as in 2.
Given: Find: Use Use in. Calculate the volume in liters. Thus, converting from km3 to m3 to L, we have. Practice Exercise 1 A barrel of oil as measured on the oil market is equal to 1. The Importance of Practice sure to more fully master the content of the chapters by reading them through at least twice, even more for passages that present you with If you have ever played a musical instrument or participated in ath- difficulties in understanding.
Throughout the book, we have provided sample exercises in You cannot learn to play a piano merely by listening to music, and which the solutions are shown in detail.
For practice exercises, we sup- you cannot learn how to play basketball merely by watching games ply only the answer, at the back of the book. It is important that you on television. Likewise, you cannot learn chemistry by merely watch- use these exercises to test yourself. Simply reading this book, listening to The practice exercises in this text and the homework assignments lectures, or reviewing notes will not usually be sufficient when exam given by your instructor provide the minimal practice that you will time comes around.
Your task is to master chemical concepts and need to succeed in your chemistry course. Only by working all the as- practices to a degree that you can put them to use in solving problems signed problems will you face the full range of difficulty and coverage and answering questions.
Solving problems correctly takes practice— that your instructor expects you to master for exams. There is no sub- actually, a fair amount of it. You will do well in your chemistry course stitute for a determined and perhaps lengthy effort to work problems if you embrace the idea that you need to master the materials pre- on your own.
If you are stuck on a problem, however, ask for help sented, and then learn how to apply them in solving problems. Even from your instructor, a teaching assistant, a tutor, or a fellow student.
Almost no one fully absorbs new material on a first effective unless you know that it is particularly challenging and is ex- reading, especially when new concepts are being presented.
You are pected to require extensive thought and effort. The density of water is 1. We can further check our calculation by estimating. We can round 1. You should also use common sense to assess the reasonableness of your answer.
In this case we know that most people can lift a gallon of milk with one hand, although it would be tiring to carry it around all day. Milk is mostly water and will have a density not too different from that of water.
Therefore, we might estimate that a gallon of water has mass that is more than 5 lb but less than 50 lb. The mass we have calculated, 3.
Practice Exercise 1 Trex is a manufactured substitute for wood compounded from post-consumer plastic and wood. It is frequently used in outdoor decks. Practice Exercise 2 The density of the organic compound benzene is 0. Calculate the mass in grams of 1. In less the book to the odd-numbered exercises those with red exercise num- than two pages of reading you will encounter valuable advice on how bers. An exercise with a [bracket] around its number is designed to to navigate your way through this book and through the course.
Additional Exercises appear after the regular serious! This is advice you can use. We describe there also ters. The problems correlated to specific topics and sections of each chapter. The Merck Index is a stan- As previously mentioned, working exercises is very important— dard reference for the properties of many organic compounds, especially in fact, essential. You will find a large variety of exercises at the end ones of biological interest.
The first few exercises called of useful information on substances, numerical values, and other data. The that summarizes how nature behaves. A property is any characteristic that gives a sample of mat- istry are made using the metric system. Special emphasis is placed on ter its unique identity. A molecule is an entity composed of two or more SI units, which are based on the meter, the kilogram, and the second as atoms with the atoms attached to one another in a specific way. SI units use pre- fixes to indicate fractions or multiples of base units.
Absolute zero is the lowest temperature attainable. It has the value states of matter. There are two kinds of pure substances: elements and 0 K. A derived unit is obtained by multiplication or division of SI base compounds. Each element has a single kind of atom and is represented units. Derived units are needed for defined quantities such as speed by a chemical symbol consisting of one or two letters, with the first or volume.
Density is an important defined quantity that equals mass letter capitalized. Compounds are composed of two or more elements divided by volume. Most matter consists of a mixture of quantities are inexact to some extent. The precision of a measurement substances. Mixtures have variable compositions and can be either indicates how closely different measurements of a quantity agree with homogeneous or heterogeneous; homogeneous mixtures are called one another. The accuracy of a measurement indicates how well a solutions.
The significant figures indicate the extent of unique set of physical properties and chemical properties that can be used the uncertainty of the measurement. Certain rules must be followed so to identify it. During a physical change, matter does not change its com- that a calculation involving measured quantities is reported with the position. Changes of state are physical changes.
In a chemical change appropriate number of significant figures. Extensive properties relate analysis approach to problem solving, we keep track of units as we to the amount of substance present. Differences in physical and chemi- carry measurements through calculations. The units are multiplied cal properties are used to separate substances. The scientific method is a dynamic process used to answer ques- Obtaining the proper units for the final result is an important means tions about the physical world.
Observations and experiments lead to of checking the method of calculation. When converting units and tentative explanations or hypotheses. As a hypothesis is tested and re- when carrying out several other types of problems, conversion factors fined, a theory may be developed that can predict the results of future can be used. These factors are ratios constructed from valid relations observations and experiments. When observations repeatedly lead to between equivalent quantities.
Section 1. Sections 1. Exercises Visualizing Concepts 1. More than one picture might fit each description. How do you know?
List the spheres from. List the cubes from smallest to largest. How many significant figures are there in this measurement? Jack, who kilometers per hour is shown. What speed is indicated, in picked up the stone on the Lake Superior shoreline and pol- both units? How many significant figures are in the measure- ished it, insists that agate is a chemical compound. Ellen ar- ments? Discuss the relative merits of their positions. Classification and Properties of Matter Sections 1.
If a mixture, indicate whether it is homogeneous or hetero- 1. If a mixture, indicate whether it is homogeneous or [Section 1. It decomposes to form a new white substance B and nominator? The gas has exactly the same properties as the prod- 1. To get an estimate A and B and gas C are elements or compounds? Explain your of the number of beans in the jar you weigh six beans and conclusions for each substance.
Then 1. The empty jar has a mass of g. Based on these data which is a nickname for iron pyrite, FeS2. What kinds of ex- estimate the number of beans in the jar. Justify the number of periments could be done to determine if the shiny nugget is significant figures you use in your estimate.
Convert this temperature to light. It reacts with chlorine to give a brittle white solid. Convert this temperature to degrees Fahrenheit and to into wires. It is a good conductor of electricity. Which of degrees Celsius. What is its density at this temperature? Will tetra-. Materials that are less dense. At a certain pressure, the density of supercritical CO2 is 0.
What is the mass of a When zinc granules are added to dilute ture? What mass of titanium displaces Zinc has a hardness on the Mohs scale of 2. Calculate of 7. It reacts slowly with oxygen gas at el- the mass of 0. Using a graduated cylinder, she measured out photo? Are these physical or chemical properties? She then measured the 1. What chemical process: a rusting of a metal can, b boiling a cup knew that the substance had to be either isopropyl alcohol of water, c pulverizing an aspirin, d digesting a candy bar, e exploding of nitroglyerin.
The col, a liquid whose density is 1. Rather than weigh following observations are made: a The match burns. What volume of the liquid d Soot carbon is deposited on the metal. Which of these should he use? If the metal is nickel, whose density is 8. One beaker 1. How can you tell which beaker is liquid to verify its identity. No tasting allowed! Is the calculated density in agreement with the tabulated value? What volume of cyclohexane should be used? What is.
Express this mass of 1. The density of silicon is 2. Silicon wafers for. The volume of a cylinder is given by according to the picture. How many significant figures are in pr2h, where r is the radius and h is its height. Diamond blade 0. Write the volume of the liquid, in milliliters, using the proper number of significant figures.
Dimensional Analysis Section 1. Round c mi to km, d ft3 to L. Cal- dard exponential notation. Round this number to four sig- whale is 5. Convert this volume into gallons. Calculate its height in 1. Convert this with the appropriate number of significant figures. Calculate its height in meters. Convert this volume to 1.
If the 1. What do you estimate to be the uncertainty in the calcu- c What is the engine piston displacement in liters of an engine lated volume? One barrel of petroleum is in a road atlas as miles. Describe some of the factors that equal to 42 gal. How many liters of petroleum were spilled? To make the num- 1. What is the mass, in kilograms, of the air in a 1. What mass of carbon monoxide in grams f 0.
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