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Tro, Principles of Chemistry: A Molecular Approach Chapter 1 Matter, Measurement, and Problem Solving 1.

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1 Tro, Principles of Chemistry: A Molecular Approach Chapter 1 Matter, Measurement, and Problem Solving 1

2 Tro, Principles of Chemistry: A Molecular Approach Composition of Matter Atoms and Molecules Scientific Method 2 Lecture One Objectives: Define atoms, molecules, and chemistry Draw & identify simple molecules Define and distinguish between hypothesis, theory, and scientific law Define matter, states of matter, gases, liquids, solids Classify the properties that differentiate the states of matter Define & interpret differences in chemical properties & changes Define energy, work, kinetic, potential, thermal LECTURE 1

3 Tro, Principles of Chemistry: A Molecular Approach Structure Determines Properties The properties of matter are determined by the atoms and molecules that compose it. 1.composed of one carbon atom and one oxygen atom 2.colorless, odorless gas 3.burns with a blue flame 4.binds to hemoglobin carbon monoxide 1.composed of one carbon atom and two oxygen atoms 2.colorless, odorless gas 3.incombustible 4.does not bind to hemoglobin carbon dioxide 3

4 Tro, Principles of Chemistry: A Molecular Approach Atoms and Molecules atoms are submicroscopic particles are the fundamental building blocks of all matter molecules two or more atoms attached together in a specific geometric arrangement  attachments are called bonds  attachments come in different strengths come in different shapes and patterns Chemistry is the science that seeks to understand the behavior of matter by studying the behavior of atoms and molecules. 4

5 Tro, Principles of Chemistry: A Molecular Approach Gathering Empirical Knowledge─Observation Some observations are simple descriptions about the characteristics or behavior of nature─qualitative. “ The soda pop is a liquid with a brown color and a sweet taste. Bubbles are seen floating up through it. ” Some observations compare a characteristic to a standard numerical scale─quantitative. “ A 240-mL serving of soda pop contains 27 g of sugar. ” 5

6 Tro, Principles of Chemistry: A Molecular Approach From Observation to Understanding hypothesis─a tentative interpretation or explanation for an observation “ The sweet taste of soda pop is due to the presence of sugar. ” A good hypothesis is one that can be tested to be proved wrong! falsifiable One test may invalidate your hypothesis. 6

7 Tro, Principles of Chemistry: A Molecular Approach From Specific to General Understanding A hypothesis is a potential explanation for a single or small number of observations. A theory is a general explanation for the manifestation and behavior of all nature. models pinnacle of scientific knowledge validated or invalidated by experiment and observation 7

8 Tro, Principles of Chemistry: A Molecular Approach Scientific Method the careful noting and recording of natural phenomena a procedure designed to test an idea a tentative explanation of a single or small number of natural phenomena a general explanation of natural phenomena a generally observed natural phenomenon 8

9 Tro, Principles of Chemistry: A Molecular Approach Relationships between Pieces of the Scientific Method 9

10 Tro, Principles of Chemistry: A Molecular Approach Classification of Matter Matter is anything that has mass and occupies space. We can classify matter based on whether it ’ s solid, liquid, or gas. 10

11 Tro, Principles of Chemistry: A Molecular Approach Classifying Matter by Physical State Matter can be classified as solid, liquid, or gas based on the characteristics it exhibits. fixed = keeps shape when placed in a container indefinite = takes the shape of the container 11

12 Tro, Principles of Chemistry: A Molecular Approach12

13 Tro, Principles of Chemistry: A Molecular Approach Classification of Matter by Composition 1)made of one type of particle 2)All samples show the same intensive properties. 1)made of multiple types of particles 2)Samples may show different intensive properties. 13

14 Tro, Principles of Chemistry: A Molecular Approach Classification of Pure Substances  Elements Pure substances that cannot be decomposed into simpler substances by chemical reactions are called elements. decomposed = broken down basic building blocks of matter composed of single type of atom  though those atoms may or may not be combined into molecules 14

15 Tro, Principles of Chemistry: A Molecular Approach Classification of Matter by Composition Matter whose composition does not change from one sample to another is called a pure substance. made of a single type of atom or molecule Because the composition of a pure substance is always the same, all samples have the same characteristics. Matter whose composition may vary from one sample to another is called a mixture. two or more types of atoms or molecules combined in variable proportions Because composition varies, different samples have different characteristics. 15

16 Tro, Principles of Chemistry: A Molecular Approach Classification of Pure Substances  Compounds Substances that can be decomposed are called compounds. chemical combinations of elements composed of molecules that contain two or more different kinds of atoms All molecules of a compound are identical, so all samples of a compound behave the same way. Most natural pure substances are compounds. 16

17 Tro, Principles of Chemistry: A Molecular Approach Classification of Pure Substances 1)made of one type of atom (some elements found as multi- atom molecules in nature) 2)combine together to make compounds 1)made of one type of molecule, or array of ions 2)units contain two or more different kinds of atoms 17

18 Tro, Principles of Chemistry: A Molecular Approach Classification of Mixtures homogeneous = mixture that has uniform composition throughout Every piece of a sample has identical characteristics, though another sample with the same components may have different characteristics. atoms or molecules mixed uniformly heterogeneous = mixture that does not have uniform composition throughout contains regions within the sample with different characteristics atoms or molecules not mixed uniformly 18

19 Tro, Principles of Chemistry: A Molecular Approach Classification of Mixtures 1)made of multiple substances, but appears to be one substance 2)All portions of an individual sample have the same composition and properties. 1)made of multiple substances, whose presence can be seen 2)Portions of a sample have different composition and properties. 19

20 Tro, Principles of Chemistry: A Molecular Approach Changes in Matter Changes that alter the state or appearance of the matter without altering the composition are called physical changes. Changes that alter the composition of the matter are called chemical changes. During the chemical change, the atoms that are present rearrange into new molecules, but all of the original atoms are still present. 20

21 Tro, Principles of Chemistry: A Molecular Approach Properties of Matter Physical properties are the characteristics of matter that can be changed without changing its composition. characteristics that are directly observable Chemical properties are the characteristics that determine how the composition of matter changes as a result of contact with other matter or the influence of energy. characteristics that describe the behavior of matter 21

22 Tro, Principles of Chemistry: A Molecular Approach CO 2 (s) CO 2 (g) Dry Ice Subliming of Dry Ice Common Physical Changes processes that cause changes in the matter that do not change its composition state changes boiling/condensing melting/freezing subliming Dissolving of Sugar C 12 H 22 O 11 (s) C 12 H 22 O 11 (aq) dissolving 22

23 Tro, Principles of Chemistry: A Molecular Approach Common Chemical Changes processes that cause changes in the matter that change its composition rusting processes that release lots of energy burning C 3 H 8 (g) + 5 O 2 (g) → 3 CO 2 (g) + 4 H 2 O(l) 23

24 Tro, Principles of Chemistry: A Molecular Approach Energy 24

25 Tro, Principles of Chemistry: A Molecular Approach Energy of Matter All matter possesses energy. Energy is classified as either kinetic or potential. Energy can be converted from one form to another. When matter undergoes a chemical or physical change, the amount of energy in the matter changes as well. 25

26 Tro, Principles of Chemistry: A Molecular Approach Energy of Matter  Kinetic Kinetic Energy is energy of motion. motion of the atoms, molecules, and subatomic particles Thermal (heat) energy is a form of kinetic energy because it is caused by molecular motion. 26

27 Tro, Principles of Chemistry: A Molecular Approach Energy of Matter  Potential Potential Energy is energy that is stored in the matter. due to the composition of the matter and its position in the universe Chemical potential energy arises from electrostatic attractive forces between atoms, molecules, and subatomic particles. 27

28 Tro, Principles of Chemistry: A Molecular Approach Conversion of Energy You can interconvert kinetic energy and potential energy. Whatever process you do that converts energy from one type or form to another, the total amount of energy remains the same. Law of Conservation of Energy 28

29 Tro, Principles of Chemistry: A Molecular Approach LECTURE 2 29 OBJECTIVES: Define systems of measurements List temperature scales Calculate conversions

30 Tro, Principles of Chemistry: A Molecular Approach Standard Units of Measure 30

31 Tro, Principles of Chemistry: A Molecular Approach The Standard Units Scientists have agreed on a set of international standard units for comparing all our measurements called the SI units. Système International = International System QuantityUnitSymbol lengthmeterm masskilogramkg timeseconds temperaturekelvinK 31

32 Tro, Principles of Chemistry: A Molecular Approach Length measure of the two-dimensional distance an object covers often need to measure lengths that are very long (distances between stars) or very short (distances between atoms) SI unit = meter About 3.37 inches longer than a yard  1 meter = distance traveled by light in a specific period of time commonly use centimeters (cm) 1 m = 100 cm 1 cm = 0.01 m = 10 mm 1 inch = 2.54 cm (exactly) 32

33 Tro, Principles of Chemistry: A Molecular Approach Mass measure of the amount of matter present in an object Weight measures the gravitational pull on an object, which depends on its mass. SI unit = kilogram (kg) about 2 lb, 3 oz commonly measure mass in grams (g) or milligrams (mg) 1 kg = lb, 1 lb = g 1 kg = 1000 g = 10 3 g 1 g = 1000 mg = 10 3 mg 1 g = kg = 10 −3 kg 1 mg = g = 10 −3 g 33

34 Tro, Principles of Chemistry: A Molecular Approach Time measure of the duration of an event SI units = second (s) 1 s is defined as the period of time it takes for a specific number of radiation events of a specific transition from cesium

35 Tro, Principles of Chemistry: A Molecular Approach Temperature measure of the average amount of kinetic energy higher temperature = larger average kinetic energy Heat flows from the matter that has high thermal energy into matter that has low thermal energy. until they reach the same temperature Heat is exchanged through molecular collisions between the two materials. 35

36 Tro, Principles of Chemistry: A Molecular Approach Temperature Scales Fahrenheit scale, °F used in the U.S. Celsius scale, °C used in all other countries Kelvin scale, K absolute scale  no negative numbers directly proportional to average amount of kinetic energy 0 K = absolute zero 36

37 Tro, Principles of Chemistry: A Molecular Approach Fahrenheit vs. Celsius A Celsius degree is 1.8 times larger than a Fahrenheit degree. The standard used for 0 ° on the Fahrenheit scale is a lower temperature than the standard used for 0 ° on the Celsius scale. 37

38 Tro, Principles of Chemistry: A Molecular Approach Kelvin vs. Celsius The size of a “ degree ” on the Kelvin scale is the same as on the Celsius scale. Though, technically, we don ’ t call the divisions on the Kelvin scale degrees; we call them kelvins! So 1 kelvin is 1.8 times larger than 1 °F. The 0 standard on the Kelvin scale is a much lower temperature than on the Celsius scale. 38

39 Tro, Principles of Chemistry: A Molecular Approach Example 1.2 Convert °C into K and °F Substitute and compute. Solve the equation for the quantity you want to find °C °F Given: Find: Equation: Find the equation that relates the given quantity to the quantity you want to find. K = °C K = K = K Since the equation is solved for the quantity you want to find, substitute and compute °C K K = °C Given: Find: Equation: Find the equation that relates the given quantity to the quantity you want to find. 39

40 Tro, Principles of Chemistry: A Molecular Approach Practice  Convert 0.0 °F into Kelvin 40

41 Tro, Principles of Chemistry: A Molecular Approach Practice  Convert 0.0 °F into Kelvin Units and magnitude make sense. Check:Check K = 255 KRound:Sig. figs. and round Solution: Follow the conceptual plan to solve the problem. Conceptual Plan: Equations: Strategize 0.0 °F kelvin Given: Find: Sort information °F°CK 41

42 Tro, Principles of Chemistry: A Molecular Approach Related Units in the SI System All units in the SI system are related to the standard unit by a power of 10. The power of 10 is indicated by a prefix multiplier. The prefix multipliers are always the same, regardless of the standard unit. Report measurements with a unit that is close to the size of the quantity being measured. 42

43 Tro, Principles of Chemistry: A Molecular Approach Measurements Density Significant Figure Precision Accuracy 43 LECTURE 3:

44 Tro, Principles of Chemistry: A Molecular Approach Common Prefix Multipliers in the SI System PrefixSymbol Decimal Equivalent Power of 10 mega-M1,000,000Base x 10 6 kilo-k 1,000Base x 10 3 deci-d 0.1Base x 10 −1 centi-c 0.01Base x 10 −2 milli-m 0.001Base x 10 −3 micro-  or mc Base x 10 −6 nano-n Base x 10 −9 picop Base x 10 −12 44

45 Tro, Principles of Chemistry: A Molecular Approach Common Units and Their Equivalents Length 1 kilometer (km)= mile (mi) 1 meter (m)=39.37 inches (in) 1 meter (m)=1.094 yards (yd) 1 foot (ft)=30.48 centimeters (cm) 1 inch (in)=2.54 centimeters (cm) exactly 45

46 Tro, Principles of Chemistry: A Molecular Approach Common Units and Their Equivalents Volume 1 liter (L)=1000 milliliters (mL) 1 liter (L)=1000 cubic centimeters (cm 3 ) 1 liter (L)=1.057 quarts (qt) 1 U.S. gallon (gal)=3.785 liters (L) Mass 1 kilogram (km)=2.205 pounds (lb) 1 pound (lb)= grams (g) 1 ounce (oz)=28.35 grams (g) 46

47 Tro, Principles of Chemistry: A Molecular Approach Practice — Which of the Following Units Would Be Best Used for Measuring the Diameter of a Quarter? a)kilometer b)meter c)centimeter d)micrometer e)megameters a)kilometer b)meter c)centimeter d)micrometer e)megameters 47

48 Tro, Principles of Chemistry: A Molecular Approach Mass and Volume two main physical properties of matter Mass and volume are extensive properties. The value depends on the quantity of matter. Extensive properties cannot be used to identify what type of matter something is.  If you are given a large glass containing 100 g of a clear, colorless liquid and a small glass containing 25 g of a clear, colorless liquid, are both liquids the same stuff? Even though mass and volume are individual properties, for a given type of matter they are related to each other! 48

49 Tro, Principles of Chemistry: A Molecular Approach Mass vs. Volume of Brass 49

50 Tro, Principles of Chemistry: A Molecular Approach Volume vs. Mass of Brass y = 8.38x Volume, cm 3 Mass, g 50 Note a linear relationship

51 Tro, Principles of Chemistry: A Molecular Approach Density Ratio of mass:volume is an intensive property. value independent of the quantity of matter solids = g/cm 3 1 cm 3 = 1 mL liquids = g/mL gases = g/L volume of a solid can be determined by water displacement – Archimedes principle density: solids > liquids >>> gases except ice is less dense than liquid water! 51

52 Tro, Principles of Chemistry: A Molecular Approach Density For equal volumes, the denser object has larger mass. For equal masses, the denser object has smaller volume. Heating an object generally causes it to expand; therefore, the density changes with temperature. 52

53 Tro, Principles of Chemistry: A Molecular Approach Example 1.3 Decide whether a ring with a mass of 3.15 g that displaces cm 3 of water is platinum Density of platinum = 21.4 g/cm 3 ; therefore, not platinum Compare to accepted value of the intensive property. Since the equation is solved for the quantity you want to find, and the units are correct, substitute and compute. mass = 3.15 g volume = cm 3 density, g/cm 3 Given: Find: Equation: Find the equation that relates the given quantity to the quantity you want to find. 53

54 Tro, Principles of Chemistry: A Molecular Approach Calculating Density What is the density of brass if g added to a cylinder of water causes the water level to rise from 25.0 mL to 36.9 mL? 54

55 Tro, Principles of Chemistry: A Molecular Approach What is the density of brass? Units and magnitude make sense.Check:Check g/cm 3 = 8.40 g/cm 3 Round:Sig. figs. and round Solution: V = 36.9−25.0 = 11.9 mL = 11.9 cm 3 Solve the equation for the unknown variable Conceptual Plan: Equation: Strategize mass = 100 g Vol displ: 25.0  36.9 mL d, g/cm 3 Given: Find: Sort information m, Vd 55

56 Tro, Principles of Chemistry: A Molecular Approach

57 Significant Figures The non-place-holding digits in a reported measurement are called significant figures. Some zeroes in a written number are there only to help you locate the decimal point. Significant figures tell us the range of values to expect for repeated measurements. The more significant figures there are in a measurement, the smaller the range of values is cm has 3 sig. figs. and its range is 12.2 to 12.4 cm cm has 4 sig. figs. and its range is to cm 57

58 Tro, Principles of Chemistry: A Molecular Approach Rules for Counting Significant Figures 1) All nonzero digits are significant. 1.5 has 2 sig. figs. 2) Interior zeroes are significant has 3 sig. figs. 3) Leading zeroes are NOT significant has 4 sig. figs.  x 10 −3 58

59 Tro, Principles of Chemistry: A Molecular Approach Counting Significant Figures 4) Trailing zeroes may or may not be significant. a)Trailing zeroes after a decimal point are significant.  has 4 sig. figs. b)Trailing zeroes before a decimal point are significant if the decimal point is written.  has 4 sig. figs. c)Zeroes at the end of a number without a written decimal point are ambiguous and should be avoided by using scientific notation.  if 150 has 2 sig. figs. then 1.5 x 10 2  but if 150 has 3 sig. figs. then 1.50 x

60 Tro, Principles of Chemistry: A Molecular Approach Example 1.5 Determining the number of significant figures in a number How many significant figures are in each of the following? m km 10 dm = 1 m × 10 5 s mm 10,000 m 4 sig. figs.: the digits 4 and 5 and the trailing 0 5 sig. figs.: the digits 5 and 3 and the interior 0’s infinite number of sig. figs.: exact number 4 sig. figs.: the digit 1 and the trailing 0’s 1 sig. fig.: the digit 2, not the leading 0’s Ambiguous; generally assume 1 sig. fig. 60

61 Tro, Principles of Chemistry: A Molecular Approach Multiplication and Division with Significant Figures When multiplying or dividing measurements with significant figures, the result has the same number of significant figures as the measurement with the fewest number of significant figures × × 0.10= = 45 3 sig. figs.5 sig. figs. 2 sig. figs. 2 sig. figs ÷ 6.10 = = sig. figs. 3 sig. figs. 3 sig. figs. 61

62 Tro, Principles of Chemistry: A Molecular Approach Addition and Subtraction with Significant Figures When adding or subtracting measurements with significant figures, the result has the same number of decimal places as the measurement with the fewest number of decimal places = = dec. pl. 3 dec. pl. 3 dec. pl. 2 dec. pl. 4.8 − 3.965= = dec. pl. 3 dec. pl. 1 dec. pl. 62

63 Tro, Principles of Chemistry: A Molecular Approach Example 1.6 Perform the following calculations to the correct number of significant figures b) 63

64 Tro, Principles of Chemistry: A Molecular Approach Example 1.6 Perform the following calculations to the correct number of significant figures b) 64

65 Tro, Principles of Chemistry: A Molecular Approach Precision and Accuracy 65

66 Tro, Principles of Chemistry: A Molecular Approach Uncertainty in Measured Numbers Uncertainty comes from limitations of the instruments used for comparison, the experimental design, the experimenter, and nature’s random behavior. To understand how reliable a measurement is, we need to understand the limitations of the measurement. Accuracy is an indication of how close a measurement comes to the actual value of the quantity. Precision is an indication of how close repeated measurements are to each other. how reproducible a measurement is 66

67 Tro, Principles of Chemistry: A Molecular Approach Accuracy vs. Precision suppose 3 students are asked to determine the mass of an object whose known mass is g the results they report are as follows: Looking at the graph of the results shows that Student A is neither accurate nor precise, Student B is inaccurate, but is precise, and Student C is both accurate and precise. 67

68 Tro, Principles of Chemistry: A Molecular Approach Solving Chemical Problems Equations and Dimensional Analysis 68

69 Tro, Principles of Chemistry: A Molecular Approach Units Always write every number with its associated unit. Always include units in your calculations. You can do the same kind of operations on units as you can with numbers.  cm × cm = cm 2  cm + cm = cm  cm ÷ cm = 1 Using units as a guide to problem solving is called dimensional analysis. 69

70 Tro, Principles of Chemistry: A Molecular Approach Problem Solving and Dimensional Analysis Many problems in chemistry involve using relationships to convert one unit of measurement to another. Conversion factors are relationships between two units. may be exact or measured Conversion factors can be generated from equivalence statements. e.g., 1 inch = 2.54 cm can give or 70

71 Tro, Principles of Chemistry: A Molecular Approach Arrange conversion factors so the starting unit cancels. Arrange conversion factor so the starting unit is on the bottom of the conversion factor. May string conversion factors We do not need to know every relationship, as long as we can find something else the starting and desired units are related to: Problem Solving and Dimensional Analysis 71

72 Tro, Principles of Chemistry: A Molecular Approach Conceptual Plan A conceptual plan is a visual outline that shows the strategic route required to solve a problem. For unit conversion, the conceptual plan focuses on units and how to convert one to another. For problems that require equations, the conceptual plan focuses on solving the equation to find an unknown value. 72

73 Tro, Principles of Chemistry: A Molecular Approach Conceptual Plans and Conversion Factors Convert inches into centimeters. 1)Find relationship equivalence: 1 in = 2.54 cm. 2)Write a conceptual plan. in cm 3)Change equivalence into conversion factors with Given unit on the bottom. 73

74 Tro, Principles of Chemistry: A Molecular Approach Systematic Approach Sort the information from the problem. Identify the given quantity and unit, the quantity and unit you want to find, and any relationships implied in the problem. Design a strategy to solve the problem Devise a conceptual plan.  sometimes may want to work backwards  Each step involves a conversion factor or equation. Apply the steps in the conceptual plan. Check that units cancel properly. Multiply terms across the top and divide by each bottom term. Check the answer. Double-check the setup to ensure the unit at the end is the one you wished to find. Check to see that the size of the number is reasonable.  Since centimeters are smaller than inches, converting inches to centimeters should result in a larger number. 74

75 Tro, Principles of Chemistry: A Molecular Approach Example 1.7 Convert 1.76 yd to centimeters Units and magnitude make sense. Check:Check cm = 161 cmRound:Sig. figs. and round Solution:Follow the conceptual plan to solve the problem 1 m = yd 0.01 m = 1 cm Conceptual Plan: Relationships: Strategize 1.76 yd length, cm Given: Find: Sort information ydmcm 75

76 Tro, Principles of Chemistry: A Molecular Approach Practice—Convert 30.0 mL to quarts (1 L = qt) 76

77 Tro, Principles of Chemistry: A Molecular Approach 30.0 mL volume, qts Practice—Convert 30.0 mL to quarts Units and magnitude make sense. Check:Check qt = qt Round:Sig. figs. and round Solution:Follow the Conceptual Plan to solve the problem 1 L = qt L = 1 mL Conceptual Plan: Relationships: Strategize Given: Find: Sort Information mLLqt 77

78 Tro, Principles of Chemistry: A Molecular Approach Conceptual Plans for Units Raised to Powers Convert cubic inches into cubic centimeters. 1) Find relationship equivalence: 1 in = 2.54 cm 2)Write conceptual plan. in 3 cm 3 3 )Change equivalence into conversion factors with given unit on the bottom. 78

79 Tro, Principles of Chemistry: A Molecular Approach Example 1.9 Convert 5.70 L to cubic inches Units and magnitude make sense. Check:Check in 3 = 348 in 3 Round:Sig. figs. and round Solution:Follow the conceptual plan to solve the problem. 1 mL = 1 cm 3, 1 mL = 10 −3 L 1 in = 2.54 cm Conceptual Plan: Relationships: Strategize 5.70 L volume, in 3 Given: Find: Sort Information LmLcm 3 in 3 79

80 Tro, Principles of Chemistry: A Molecular Approach Density as a Conversion Factor can use density as a conversion factor between mass and volume density of H 2 O = 1.0 g/mL  1.0 g H 2 O = 1 mL H 2 O density of Pb = 11.3 g/cm 3  11.3 g Pb = 1 cm 3 Pb How much does 4.0 cm 3 of lead weigh? 80

81 Tro, Principles of Chemistry: A Molecular Approach Example 1.10 What is the mass in kg of 173,231 L of jet fuel whose density is g/mL? Units and magnitude make sense. Check: Check x 10 5 = 1.33 x 10 5 kg Round: Sig. figs. and round Solution: Follow the conceptual plan to solve the problem. 1 mL = g, 1 mL = L 1 kg = 1000 g Conceptual Plan: Relationships: Strategize 173,231 L density = g/mL mass, kg Given: Find: Sort information LmLgkg 81

82 Tro, Principles of Chemistry: A Molecular Approach Practice—Calculate the following How much does 3.0 x 10 2 mL of ether weigh? (d = 0.71 g/mL) What volume does g of marble occupy? (d = 4.0 g/cm 3 ) 82


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