1 Chemistry and Its Methods Jeffrey Mack California State University, Sacramento Hypothesis: A tentative explanation or prediction based on experimental observations. Law: A concise verbal or mathematical statement of a behavior or a relation that seems always to be the same under the same conditions. Theory: 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 Qualitative Observations 4 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. 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 Classifying Matter: States of Matter 6 A quantity or attribute that is measureable is specified. Numbers with units are expressed from measurements. Dimensions are given such as mass, time, distance, volume, density, temperature, color specified as a wavelength etc...
Classifying Matter: States of Matter 7 States of Matter 8 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. SOLIDS have rigid shape, fixed volume. External shape may reflect the atomic and molecular arrangement. Reasonably well understood. LIQUIDS have no fixed shape and may not fill a container completely. Structure not well understood. GASES expand to fill their container completely. Well defined theoretical understanding. Classifying Matter 9 Classifying Matter 10 Mixtures: Homogeneous and Heterogeneous A 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. A heterogeneous mixture does not have uniform composition. Its components are easily visually distinguishable. When separated, the components of both types of mixtures yields pure substances. Classifying Matter 11 Classifying Matter 1 Pure Substances A pure substance has well defined physical and chemical properties. Pure 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.
3 Matter and its Representation What we observe To what we can t see! 13 The Representation of Matter 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 10-1 cm 14 Chemical symbols allow us to connect Elements 15 Chemical Compounds 16 The elements are recorded on the PERIODIC TABLE There are 117 recorded elements at this time. The Periodic table will be discussed further in chapter. Chemical compounds are composed of two or more atoms. Chemical Compounds 17 Chemical Compounds 18 Molecule: Ammonia (NH 3 ) Ionic Compound Iron pyrite (FeS ) 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.
4 Molecular Formula 19 Physical Properties 0 A molecule is the smallest unit of a compound that retains the chemical characteristics of the compound. Composition of molecules is given by a molecular formula. H O C 8 H 10 N 4 O - caffeine Some physical properties: Color State (s, g or liq) Melting and Boiling point Density (massunit volume) Extensive properties (mass) depend upon the amount of substance. Intensive properties (density) do not. Physical Properties 1 Physical Properties Physical properties are a function of intermolecular forces. Methane (16 gmol) gas at 5 o C H H C H H Water (18 gmol) liquid at 5 o C H O H Physical properties are affected by temperature (molecular motion). The density of water is seen to change with temperature. Water molecules are attracted to one another by hydrogen bonds. Methane molecules only exhibit week London Forces. Physical Properties 3 Chemical Properties 4 Mixtures may be separated by physical properties: Physical Property Density Boiling point State of Matter Intermolecular Forces Vapor pressure Magnetism Solubility Means of Separation Decantation, centrifugation Distillation Filtration Chromatography Evaporation Magnets Filtration Chemical properties are really chemical changes. The chemical properties of elements and compounds are related to periodic trends and molecular structure.
5 Chemical Properties 5 The Nature of Matter 6 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. Gold Mercury Chemists are interested in the nature of matter and how this is related to its atoms and molecules. A Chemist s View of Water Particulate Macroscopic H O (gas, liquid, solid) Symbolic H (g) + O (g) H O(g) Energy: Some Basic Principles Energy can be classified as Kinetic or Potential. Kinetic 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. 8 Energy: Some Basic Principles 9 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). Jeffrey Mack California State University, Sacramento
6 The Tools of Quantitative Chemistry 31 Note About Math & Chemistry 3 "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." 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. Lord Kelvin, "Electrical Units of Measurement", 1883-05-03 Units of Measure Science predominantly uses the SI (System International) system of units, more commonly known as the Metric System. 33 Units of Measure The base units are modified by a series of prefixes which you will need to memorize. 34 Temperature Units 35 Temperature Conversion 36 Temperature is measured in the Celsius an the Kelvin temperature scale. 1K T(K) T C 73.15 C 1C 1K 5.0 C 73.15 C 98.K 1C
7 Length, Volume, and Mass 37 Length, Volume, and Mass 38 The base unit of length in the metric system is the meter. Depending on the object measured, the meter is scaled accordingly. Unit conversions: How many picometers are there in 5.4 nm? How many yards? nm m pm 1 1m 1 10 pm 4 5.4nm.54 10 pm 9 1 10 nm 1m m cm in ft yd 10 cm 1in 1ft 1yd 5.4m 7.8 yards 1m.54cm 1in 3ft Length, Volume, and Mass 39 Length, Volume, and Mass 40 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 The base unit of volume in the metric system is the gram. 1kg = 10 3 g L ml cm 3 3 10 ml 1cm 5.4 L.54 10 cm 1 L 1 ml 3 4 3 ng g kg 1g 1kg 1 10 ng 1 10 g 11 5.4ng.54 10 g 9 3 Energy Units 41 Making Measurements: Precision 4 Energy is confined as the capacity to do work. The SI unite for energy is the joule (J). The precision of a measurement indicates how well several determinations of the same quantity agree. kg m 1 J = s Energy is also measured in calories (cal) 1 cal = 4.184J A kcal (kilocalorie) is often written as Cal. 1 Cal =10 3 cal
8 Making Measurements: Accuracy Accuracy is the agreement of a measurement with the accepted value of the quantity. Accuracy is often reflected by Experimental error. Experimental value - Accepted value Percent Error = 100 Accepted value 43 Making Measurements: 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). _ æ ö åç xn - x Standard Deviaton = è ø n -1 Measurements are often reported to the standard deviation to report the precision of a measurement. 44 Mathematics of Chemistry 45 Exponential or Scientific Notation 46 Exponential or Scientific Notation: Most often in science, numbers are expressed in a format the conveys the order of magnitude. 1.3 10 4 385 ft = 3.85 10 3 ft 0.0015kg =.15 10 3 kg Coefficient or Mantissa (this number is 1 and <10 in scientific notation Base Exponential part Exponent Mathematics of Chemistry 47 Counting Significant Figures 48 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 ( 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! 1. All non zero numbers are significant. 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).
9 Determining Significant Figures 49 Rounding Numbers 50 Determine the number of Sig. Figs. in the following numbers 156 1056007 0.000345 0.00046909 4 sf 7 sf 3 sf 5 sf not trapped by a decimal place. 1. Find the last digit that is to be kept.. 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. zeros written explicitly behind the decimal are significant 1780 770.0 3 sf 4 sf 0.08040 4 sf Rounding Numbers 51 5 Round the following to significant figures: 1056007 1100000 0.000345 0.00035 1780 1800 MultiplicationDivision The number of significant figures in the answer is limited by the factor with the smallest number of significant figures. AdditionSubtraction 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. 53 54 Determine the correct number of sig. figs. in the following calculation, express the answer in scientific notation. Determine the correct number of sig. figs. in the following calculation, express the answer in scientific notation. from the calculator: 4 sf 4 sf sf 3.50 0.001 17 = 1996.501749 10 sf Your calculator knows nothing of sig. figs.!!! in sci. notation: 1.996501749 10 3 Rounding to sf:.0 10 3
10 55 56 To determine the correct decimal to round to, align the numbers at the decimal place: Determine the correct number of sig. figs. in the following calculation: 391 1.6 + 156.1456 391 1.6 +156.1456 391 1.6 +156.1456 no digits here One must round the calculation to the least significant decimal. 57 58 391-1.6 +156.1456 one must round to here 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. 534.5456 (answer from calculator) round to here (units place) Answer: 535 Example: Complete the following math mathematical operation and report the value with the correct # of sig. figs. (6.05 + 3.1) (0.003 + 7.7) =??? 59 60 Example: Complete the following math mathematical operation and report the value with the correct # of sig. figs. (6.05 + 3.1) (0.003 + 7.7) =??? 3 sf 6.05 1 st determine the correct # of sf in the numerator (top) (6.05 + 3.1) (0.003 + 7.7) = nd determine the correct # of sf in the denominator (bottom) The result will be limited by the least # of sf (division rule) (6.05 + 3.1) (0.003 + 7.7) = + 3.1 0.003 + 7.7 sf 58.150 = 7.703 The result may only have sf
11 61 6 Carry all of the digits through the calculation and round at the end. (6.05 + 3.1) 58.150 3 sig figs = (0.003 + 7.7) 7.703 sig figs! Round to here = 7.5488 = 7.5 sf Dimensional Analysis: Dimensional analysis converts one unit to another by using conversion factors (CF s). unit (1) conversion factor = unit () The resulting quantity is equivalent to the original quantity, it differs only by the units. 63 Examples of Conversion Factors 64 Dimensional Analysis: 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 100 cm 1 m Exact Conversion Factors: Those in the same system of units 1 m = 100 cm 1 m 10 cm or 10 cm 1 m Use of exact CF s will not affect the significant figures in a calculation. Examples of Conversion Factors Inexact Conversion Factors: CF s that relate quantities in different systems of units (4 sig. figs.) SI units 1.000 kg =.05 lb 1.000 kg.05 lb or.05 lb 1.000 kg British Std. Use of inexact CF s will affect significant figures. 65 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 66
1 Before 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. 67 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. 68 Example: How many meters are there in 15 miles? 69 Example: How many meters are there in 15 miles? 70 First: Outline of the conversion: First: Outline of the conversion: miles ft in cm m Each arrow indicates the use of a conversion factor. Example: How many meters are there in 15 miles? 71 Example: How many meters are there in 15 miles? 7 Third: Check your sig. figs. & cancel out units. Second: Setup the problem using Dimensional Analysis: miles ft in cm m 580 ft 15 miles 1 mile 1 in 1 ft.54 cm 1 m = 1 in 10 cm miles ft in cm m 580 ft 1 in 15 miles 1 mile 1 ft.54 cm 1 m = 1 in 10 cm 3 sf exact exact 3 sf exact
13 Example: How many meters are there in 15 miles? Fourth: Now use your calculator. : miles ft in cm m 73 Example: How many meters are there in 15 miles? Lastly: Check your answer for sig. figs & magnitude. miles ft in cm m 74 580 ft 1 in 15 miles 1 mile 1 ft.54 cm 1 m 1 in 10 cm 3 sf exact exact 3 sf exact Carry though all digits, round at end =.54 cm 580 ft 1 in 1 m 15 miles 1 in = 1 mile 1 ft 10 cm 3 sf exact exact 3 sf exact.01168 10 5 or.01 10 5 m (3 sf) 75 76 Example: How many square feet are there in 5.4 cm? Example: How many cubic feet are there in 5.4 cm 3? Map out your conversion: Map out your conversion: cm in ft cm 3 in 3 ft 3 5.4 cm æ 1.00 in ö æ 1 ft ö ç ç =.73403 10 - ft è.54cm ø è1 in ø 3 sf exact exact 5.4 cm 3 3 3 æ 1.00 in ö æ 1 ft ö ç ç = 8.96993 10-4 ft 3 è.54cm ø è1 in ø 3 sf exact exact or.73 10 - ft (3 sf) or 8.97 10-4 ft 3 (3 sf) 77 Example: What volume in cubic feet would 0.851 grams of air occupy if the density is 1.9 gl? Map out your conversion: g L cm 3 in 3 ft 3 3 3 3 3 1 L 10 cm 1 in 1 ft æ ö æ ö 0.851 g ç ç = 1.9g 1 L è.54 cm ø è 1 in ø 3 sf 3 sf 3 sf 3 sf exact.33 10 ft - 3 3 sf