1. Jeffrey Mack California State University, Sacramento

2. 2 HypothesisHypothesis: A tentative explanation or prediction based on experimental observations. LawLaw: A concise verbal or mathematical statement of a behavior or a relation that seems always to be the same under the same conditions. TheoryTheory: a well-tested, unifying principle that explains a body of facts and the laws based on them. It is capable of suggesting new hypotheses that can be tested experimentally. Chemistry and Its Methods

3. 3 Experimental results should be reproducible. Furthermore, these results should be reported in the scientific literature in sufficient detail that they can be used or reproduced by others. Conclusions should be reasonable and unbiased. Credit should be given where it is due. Chemistry and Its Methods

4. 4 No numbers involved Color, appearance, statements like “large” or “small: Stating that something is hot or cold without specifying a temperature. Identifying something by smell No measurements Qualitative Observations

5. 5 A quantity or attribute that is measureable is specified.A quantity or attribute that is measureable is specified. Numbers with units are expressed from measurements.Numbers with units are expressed from measurements. Dimensions are given such as mass, time, distance, volume, density, temperature, color specified as a wavelength etc...Dimensions are given such as mass, time, distance, volume, density, temperature, color specified as a wavelength etc... Qualitative Observations

6. 6 Classifying Matter: States of Matter

7. 7 In solids these particles are packed closely together, usually in a regular array. The particles vibrate back and forth about their average positions, but seldom does a particle in a solid squeeze past its immediate neighbors to come into contact with a new set of particles. The atoms or molecules of liquids are arranged randomly rather than in the regular patterns found in solids. Liquids and gases are fluid because the particles are not confined to specific locations and can move past one another. Under normal conditions, the particles in a gas are far apart. Gas molecules move extremely rapidly and are not constrained by their neighbors. The molecules of a gas fly about, colliding with one another and with the container walls. This random motion allows gas molecules to fill their container, so the volume of the gas sample is the volume of the container.

8. 8 SOLIDSSOLIDS — have rigid shape, fixed volume. External shape may reflect the atomic and molecular arrangement. –Reasonably well understood. LIQUIDSLIQUIDS — have no fixed shape and may not fill a container completely. –Structure not well understood. GASESGASES — expand to fill their container completely. –Well defined theoretical understanding. States of Matter

9. 9 Classifying Matter

10. 10 Mixtures: Homogeneous and Heterogeneous homogeneousA homogeneous mixture consists of two or more substances in the same phase. No amount of optical magnification will reveal a homogeneous mixture to have different properties in different regions. heterogeneousA heterogeneous mixture does not have uniform composition. Its components are easily visually distinguishable. pure substancesWhen separated, the components of both types of mixtures yields pure substances. Classifying Matter

11. 11 Classifying Matter

12. 12 Pure Substances A pure substance has well defined physical and chemical properties. elementscompoundsPure substances can be classified as elements or compounds. Compounds can be further reduced into two or more elements. Elements consist of only one type of atom. They cannot be decomposed or further simplified by ordinary means. Classifying Matter

13. 13 Chemical symbols allow us to connect… What we observe… To what we can’t see! Matter and its Representation

14. 14 In chemistry we use chemical formulas and symbols to represent matter.Why? We are “macroscopic”: large in size on the order of 100’s of cm. Atoms and molecules are “microscopic”: on the order of 10 -12 cm The Representation of Matter

15. 15 PERIODIC TABLEThe elements are recorded on the PERIODIC TABLE There are 117 recorded elements at this time. The Periodic table will be discussed further in chapter 2.Elements

16. 16 Chemical compounds are composed of two or more atoms. Chemical Compounds

17. 17 Chemical Compounds Molecule: Ammonia (NH 3 ) Ionic Compound Iron pyrite (FeS 2 )

18. 18 Chemical Compounds All Compounds are made up of molecules or ions. A molecule is the is the smallest unit of a compound that retains its chemical characteristics. Ionic compounds are described by a “formula unit”. Molecules are described by a “molecular formula”.

19. 19 Molecular Formula moleculeA molecule is the smallest unit of a compound that retains the chemical characteristics of the compound. molecular formulaComposition of molecules is given by a molecular formula. H2OH2O C 8 H 10 N 4 O 2 - caffeine

20. 20 Physical Properties Some physical properties: −Color −State (s, g or liq) −Melting and Boiling point −Density (mass/unit volume) Extensive properties Extensive properties (mass) depend upon the amount of substance. Intensive properties Intensive properties (density) do not.

21. 21 Physical properties are a function of intermolecular forces. O H H Water (18 g/mol) liquid at 25 o C Methane (16 g/mol) gas at 25 o C C H H H H Physical Properties Water molecules are attracted to one another by “hydrogen bonds”. Methane molecules only exhibit week “London Forces”.

22. 22 Physical properties are affected by temperature (molecular motion). The density of water is seen to change with temperature. Physical Properties

23. 23 Mixtures may be separated by physical properties: Physical Properties

24. 24 Chemical properties are really chemical changes. The chemical properties of elements and compounds are related to periodic trends and molecular structure. Chemical Properties

25. 25 Chemical Properties A chemical property indicates whether and sometimes how readily a material undergoes a chemical change with another material. For example, a chemical property of hydrogen gas is that it reacts vigorously with oxygen gas.

26. 26 Chemists are interested in the nature of matter and how this is related to its atoms and molecules. GoldMercury The Nature of Matter

27. A Chemist’s View of Water H 2 O (gas, liquid, solid) Macroscopic Symbolic Particulate 2 H 2 (g) + O 2 (g)  2 H 2 O(g)

28. 28 KineticPotential Energy can be classified as Kinetic or Potential. Kinetic energyKinetic energy is energy associated with motion such as: The motion at the particulate level (thermal energy). The motion of macroscopic objects like a thrown baseball, falling water. The movement of electrons in a conductor (electrical energy). Wave motion, transverse (water) and compression (acoustic). Matter consists of atoms and molecules in motion. Energy: Some Basic Principles

29. 29 Potential energy Potential energy results from an object’s position: Gravitational: An object held at a height, waterfalls. Energy stored in an extended spring. Energy stored in molecules (chemical energy, food) The energy associated with charged or partially charged particles (electrostatic energy) Nuclear energy (fission, fusion). Energy: Some Basic Principles

30. Jeffrey Mack California State University, Sacramento

31. 31 "In physical science the first essential step in the direction of learning any subject is to find principles of numerical reckoning and practicable methods for measuring some quality connected with it. I often say that when you can measure what you are speaking about, and express it in numbers, you know something about it; but when you cannot measure it, when you cannot express it in numbers, your knowledge is of a meager and unsatisfactory kind; it may be the beginning of knowledge, but you have scarcely in your thoughts advanced to the state of Science, whatever the matter may be." Lord Kelvin, "Electrical Units of Measurement", 1883-05-03 The Tools of Quantitative Chemistry

32. 32 Note About Math & Chemistry Numbers and mathematics are an inherent and unavoidable part of general chemistry. Students must possess secondary algebra skills and the ability to recognize orders of magnitude quickly with respect to numerical information to assure success in this course. The material presented in this chapter is considered to be prerequisite to this course.

33. 33 Science predominantly uses the “SI” (System International) system of units, more commonly known as the “Metric System”. Units of Measure

34. 34 The base units are modified by a series of prefixes which you will need to memorize. Units of Measure

35. 35 Celsius Kelvin Temperature is measured in the Celsius an the Kelvin temperature scale. Temperature Units

36. 36 Temperature Conversion

37. 37 meter. The base unit of length in the metric system is the meter. Depending on the object measured, the meter is scaled accordingly. Length, Volume, and Mass

38. 38 Unit conversions: How many picometers are there in 25.4 nm? How many yards? Length, Volume, and Mass

39. 39 liter. The base unit of volume in the metric system is the liter. 1 L = 10 3 mL 1 mL=1 cm 3 1 cm 3 = 1 mL Length, Volume, and Mass

40. 40 gram The base unit of volume in the metric system is the gram. 1kg = 10 3 g Length, Volume, and Mass

41. 41 Energy Energy is confined as the capacity to do work. joule The SI unite for energy is the joule (J). Energy is also measured in calories (cal) 1 cal = 4.184J A kcal (kilocalorie) is often written as Cal. 1 Cal =10 3 cal Energy Units

42. 42 precision The precision of a measurement indicates how well several determinations of the same quantity agree. Making Measurements: Precision

43. 43 Accuracy Accuracy is the agreement of a measurement with the accepted value of the quantity. Experimental error Accuracy is often reflected by Experimental error. Making Measurements: Accuracy

44. 44 Standard Deviation The Standard Deviation of a series of measurements is equal to the square root of the sum of the squares of the deviations for each measurement from the average divided by one less than the number of measurements (n). Measurements are often reported to  the standard deviation to report the precision of a measurement. Making Measurements: Standard Deviation

45. 45 Exponential or Scientific Notation: Most often in science, numbers are expressed in a format the conveys the order of magnitude. 3285 ft = 3.285  10 3 ft 0.00215kg = 2.15  10  3 kg Mathematics of Chemistry

46. 46 1.23  10 4 Coefficient or Mantissa (this number is  1 and <10 in scientific notation BaseExponent Exponential part Exponential or Scientific Notation

47. 47 Significant figures: Significant figures: The number of digits represented in a number conveys the precision of the number or measurement. A mass measured to  0.1g is far less precise than a mass measured to  0.0001g. 1.1g vs. 1.0001g (2 sig. figs. vs. 5 sig. figs) In order to be successful in this course, you will need to master the identification and use of significant figures in measurements and calculations! Mathematics of Chemistry

48. 48 1.All non zero numbers are significant 2.All zeros between non zero numbers are significant 3.Leading zeros are NEVER significant. (Leading zeros are the zeros to the left of your first non zero number) 4.Trailing zeros are significant ONLY if a decimal point is part of the number. (Trailing zeros are the zeros to the right of your last non zero number). Counting Significant Figures

49. 49 Determining Significant Figures Determine the number of Sig. Figs. in the following numbers 4 sf 7 sf 3 sf 5 sf 3 sf 4 sf 1256 1056007 0.000345 0.00046909 0.08040 zeros written explicitly behind the decimal are significant… not trapped by a decimal place. 1780 770.0

50. 50 1. Find the last digit that is to be kept. 2. Check the number immediately to the right: If that number is less than 5 leave the last digit alone. If that number is 5 or greater increase the previous digit by one. Rounding Numbers

51. 51 1100000 1056007 0.000345 1780 0.00035 1800 Rounding Numbers Round the following to 2 significant figures:

52. 52 Multiplication/Division smallest number The number of significant figures in the answer is limited by the factor with the smallest number of significant figures. Addition/Subtraction least precise number The number of significant figures in the answer is limited by the least precise number (the number with its last digit at the highest place value). NOTE: counted numbers like 10 dimes never limit calculations. Sig. Figures in Calculations

53. 53 Determine the correct number of sig. figs. in the following calculation, express the answer in scientific notation. 23.50  0.2001  17 4 sf 2 sf = 1996.50174910 sf Your calculator knows nothing of sig. figs. !!! from the calculator: Sig. Figures in Calculations

54. 54 Determine the correct number of sig. figs. in the following calculation, express the answer in scientific notation. in sci. notation: 1.996501749  10 3 Rounding to 2 sf: 2.0  10 3 Sig. Figures in Calculations

55. 55 Determine the correct number of sig. figs. in the following calculation: 391  12.6 + 156.1456 Sig. Figures in Calculations

56. 56 To determine the correct decimal to round to, align the numbers at the decimal place: One must round the calculation to the least significant decimal. 391  12.6 +156.1456 391  12.6 +156.1456 no digits here Sig. Figures in Calculations

57. 57 one must round to here 391 -12.6 +156.1456 534.5456 (answer from calculator) round to here (units place) Answer: 535 Sig. Figures in Calculations

58. 58 Combined Operations: Combined Operations: When there are both addition & subtraction and or multiplication & division operations, the correct number of sf must be determined by examination of each step. Example: Complete the following math mathematical operation and report the value with the correct # of sig. figs. (26.05 + 32.1)  (0.0032 + 7.7) = ??? Sig. Figures in Calculations

59. 59 Example: Complete the following math mathematical operation and report the value with the correct # of sig. figs. (26.05 + 32.1)  (0.0032 + 7.7) = ??? 1 st determine the correct # of sf in the numerator (top) 2 nd determine the correct # of sf in the denominator (bottom) The result will be limited by the least # of sf (division rule) Sig. Figures in Calculations

60. 60 26.05 + 32.1 0.0032 + 7.7 3 sf 2 sf The result may only have 2 sf = 58.150 7.7032 Sig. Figures in Calculations

61. 61 2 sig figs! 3 sig figs 7.7032 58.150 = 7.5488= 7.5 2 sf Round to here Carry all of the digits through the calculation and round at the end. Sig. Figures in Calculations

62. 62 Dimensional Analysis: conversion factors (CF’s). Dimensional analysis converts one unit to another by using conversion factors (CF’s). The resulting quantity is equivalent to the original quantity, it differs only by the units. = unit (2)unit (1) conversion factor  conversion factor Problem Solving and Chemical Arithmetic

63. 63 Dimensional Analysis: conversion factors (CF’s). Dimensional analysis converts one unit to another by using conversion factors (CF’s). Conversion factors come from equalities: 1 m = 100 cm 1 m 100 cm or 1 m 100 cm Problem Solving and Chemical Arithmetic

64. 64 Exact Conversion Factors: Exact Conversion Factors: Those in the same system of units 1 m = 100 cm Use of exact CF’s will not affect the significant figures in a calculation. Examples of Conversion Factors

65. 65 1.000 kg = 2.205 lb SI units British Std. Use of inexact CF’s will affect significant figures. (4 sig. figs.) Inexact Conversion Factors: Inexact Conversion Factors: CF’s that relate quantities in different systems of units Examples of Conversion Factors

66. 66 Problem solving in chemistry requires “critical thinking skills”. Most questions go beyond basic knowledge and comprehension. (Who is buried in Grant’s tomb?) You must first have a plan to solve a problem before you plug in numbers. You must evaluate the result to see if it makes sense. (units, order of magnitude) You must also practice to become proficient because... Chem – is – try Problem Solving and Chemical Arithmetic

67. 67 Strategy MapBefore starting a problem, devise a “Strategy Map”. Use this to collect the information given to work your way through the problem. Solve the problem using Dimensional Analysis. Check to see that you have the correct units along the way. Problem Solving and Chemical Arithmetic

68. 68 Most importantly, before you start... PUT YOUR CALCULATOR DOWN! Your calculator wont help you until you are ready to solve the problem based on your strategy map. Problem Solving and Chemical Arithmetic

69. 69 Example Example: How many meters are there in 125 miles? First: Outline of the conversion: Problem Solving and Chemical Arithmetic

70. 70 Example Example: How many meters are there in 125 miles? First: Outline of the conversion: m miles  ft  in  cm  Each arrow indicates the use of a conversion factor. Problem Solving and Chemical Arithmetic

71. 71 Example Example: How many meters are there in 125 miles? = Second: Setup the problem using Dimensional Analysis: m miles  ft  in  cm  Problem Solving and Chemical Arithmetic

72. 72 Example Example: How many meters are there in 125 miles? Third: Check your sig. figs. & cancel out units. m = miles  ft  in  cm  3 sfexact 3 sf Problem Solving and Chemical Arithmetic / / / / // //

73. 73 Example Example: How many meters are there in 125 miles? Fourth: Now use your calculator. : m / / / / / / / / = miles  ft  in  cm  3 sfexact 3 sf Carry though all digits, round at end Problem Solving and Chemical Arithmetic

74. 74 Example Example: How many meters are there in 125 miles? / / / 2.01168  10 5 = or 2.01  10 5 m (3 sf) 3 sfexact 3 sf Lastly: Check your answer for sig. figs & magnitude. m / / miles  ft  in  cm  / / / Problem Solving and Chemical Arithmetic

75. 75 Example Example: How many square feet are there in 25.4 cm 2 ? Map out your conversion: ft 2 / / / / 2.73403  10 -2 ft 2 = cm 2  in 2  or 2.73  10 -2 ft 2 (3 sf) 3 sfexact Problem Solving and Chemical Arithmetic

76. 76 Example Example: How many cubic feet are there in 25.4 cm 3 ? Map out your conversion: ft 3 / / / / 8.96993  10 -4 ft 3 = cm 3  in 3  or 8.97  10 -4 ft 3 (3 sf) 3 sfexact Problem Solving and Chemical Arithmetic

77. 77 Example Example: What volume in cubic feet would 0.851 grams of air occupy if the density is 1.29 g/L? Map out your conversion: ft 3 L  in 3  cm 3  g  / 3 sf exact3 sf / / / / / / / Problem Solving and Chemical Arithmetic