Chemistry: A Molecular Approach 2nd Ed. - Chapter 1 PDF

Chemistry: A Molecular Approach, 2nd Ed. Nivaldo Tro Chapter 1 Matter, Measurement, and Problem Solving Roy Kennedy Massachusetts Bay Community College Wellesley Hills, MA Copyright  2011 Pearson Education, Inc. ...

Chemistry: A Molecular Approach, 2nd Ed. Nivaldo Tro Chapter 1 Matter, Measurement, and Problem Solving Roy Kennedy Massachusetts Bay Community College Wellesley Hills, MA Copyright  2011 Pearson Education, Inc.  Composition of Matter Atoms and Molecules Scientific Method Tro: Chemistry: A Molecular Approach, 2/e Copyright  2011 Pearson Education, Inc.  Structure Determines Properties The properties of matter are determined by the atoms and molecules that compose it carbon monoxide carbon dioxide 1. composed of one carbon 1. composed of one carbon atom and one oxygen atom atom and two oxygen atoms 2. colorless, odorless gas 2. colorless, odorless gas 3. burns with a blue flame 3. incombustible 4. binds to hemoglobin 4. does not bind to hemoglobin Tro: Chemistry: A Molecular Approach, 2/e 3 Copyright  2011 Pearson Education, Inc.  Atoms and Molecules Atoms  are submicroscopic particles  are the fundamental building blocks of ordinary matter Molecules  are two or more atoms attached together in a specific geometrical 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 Tro: Chemistry: A Molecular Approach, Approach 2/e 4 Copyright  2011 Pearson Education, Inc.  The Scientific Approach to Knowledge Philosophers try to understand the universe by reasoning and thinking about “ideal” behavior Scientists try to understand the universe through empirical knowledge gained through observation and experiment Tro: Chemistry: A Molecular Approach, Approach 2/e 5 Copyright  2011 Pearson Education, Inc.  Gathering Empirical Knowledge ─ Observation Some observations are descriptions of 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.” Tro: Chemistry: A Molecular Approach, Approach 2/e 6 Copyright  2011 Pearson Education, Inc.  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 Tro: Chemistry: A Molecular Approach, Approach 2/e 7 Copyright  2011 Pearson Education, Inc.  Testing Ideas Ideas in science are tested with experiments An experiment is a set of highly controlled procedures designed to test whether an idea about nature is valid The experiment generates observations that will either validate or invalidate the idea Tro: Chemistry: A Molecular Approach, Approach 2/e 8 Copyright  2011 Pearson Education, Inc.  From Specific to General Observations A scientific law is a statement that summarizes all past observations and predicts future observations  Law of Conservation of Mass – “In a chemical reaction matter is neither created nor destroyed.” A scientific law allows you to predict future observations  so you can test the law with experiments Unlike state laws, you cannot choose to violate a scientific law! Tro: Chemistry: A Molecular Approach, Approach 2/e 9 Copyright  2011 Pearson Education, Inc.  From Specific to General Understanding A hypothesis is a potential explanation for a single or small number of observations A scientific theory is a general explanation for why things in nature are the way they are and behave the way they do  models  pinnacle of scientific knowledge  validated or invalidated by experiment and observation Tro: Chemistry: A Molecular Approach, Approach 2/e 10 Copyright  2011 Pearson Education, Inc.  Procedure Scientific Method designed to Tentative explanation of a test an idea single or small number of observations General explanation of natural phenomena Careful noting and recording of natural Generally observed phenomena occurence in nature Tro: Chemistry: A Molecular Approach, Approach 2/e 11 Copyright  2011 Pearson Education, Inc.  Relationships Between Pieces of the Scientific Method Tro: Chemistry: A Molecular Approach, Approach 2/e 12 Copyright  2011 Pearson Education, Inc.  Classification of Matter States of Matter Physical and Chemical Properties Physical and Chemical Changes Tro: Chemistry: A Molecular Approach, 2/e Copyright  2011 Pearson Education, Inc.  Classification of Matter Matter is anything that occupies space and has mass We can classify matter based on its state and its composition  whether it’s solid, liquid, or gas  its basic components Tro: Chemistry: A Molecular Approach, Approach 2/e 14 Copyright  2011 Pearson Education, Inc.  Classifying Matter by Physical State Matter can be classified as solid, liquid, or gas based on the characteristics it exhibits Tro: Chemistry: A Molecular Approach, Approach 2/e 15 Copyright  2011 Pearson Education, Inc.  Solids The particles in a solid are packed close together and are fixed in position  though they may vibrate The close packing of the particles results in solids being incompressible The inability of the particles to move around results in solids retaining their shape and volume when placed in a new container, and prevents the solid from flowing Tro: Chemistry: A Molecular Approach, Approach 2/e 16 Copyright  2011 Pearson Education, Inc.  Crystalline Solids Some solids have their particles arranged in patterns with long-range repeating order – we call these crystalline solids  salt  diamonds  sugar Tro: Chemistry: A Molecular Approach, Approach 2/e 17 Copyright  2011 Pearson Education, Inc.  Amorphous Solids Some solids have their particles randomly distributed without any long-range pattern – we call these amorphous solids  plastic  glass  charcoal Tro: Chemistry: A Molecular Approach, Approach 2/e 18 Copyright  2011 Pearson Education, Inc.  Liquids The particles in a liquid are closely packed, but they have some ability to move around The close packing results in liquids being incompressible The ability of the particles to move allows liquids to take the shape of their container and to flow – however, they don’t have enough freedom to escape or expand to fill the container Tro: Chemistry: A Molecular Approach, Approach 2/e 19 Copyright  2011 Pearson Education, Inc.  Gases In the gas state, the particles have freedom of motion and are not held together The particles are constantly flying around, bumping into each other and the container In the gas state, there is a lot of empty space between the particles  on average Tro: Chemistry: A Molecular Approach, Approach 2/e 20 Copyright  2011 Pearson Education, Inc.  Gases Because there is a lot of empty space, the particles can be squeezed closer together – therefore gases are compressible Because the particles are not held in close contact and are moving freely, gases expand to fill and take the shape of their container, and will flow Tro: Chemistry: A Molecular Approach, Approach 2/e 21 Copyright  2011 Pearson Education, Inc.  Classifying Matter by Composition Another way to classify matter is to examine its composition Composition includes  types of particles  arrangement of the particles  attractions and attachments between the particles Tro: Chemistry: A Molecular Approach, Approach 2/e 22 Copyright  2011 Pearson Education, Inc. Tro: Chemistry: A Molecular Approach, Approach 2/e 23 Copyright  2011 Pearson Education, Inc.  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 Tro: Chemistry: A Molecular Approach, Approach 2/e 24 Copyright  2011 Pearson Education, Inc.  Classification of Matter by Composition 1. made of one type of 1. made of multiple particle types of particles 2. all samples show 2. samples may show the same intensive different intensive properties properties Tro: Chemistry: A Molecular Approach, Approach 2/e 25 Copyright  2011 Pearson Education, Inc.  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 Tro: Chemistry: A Molecular Approach, Approach 2/e 26 Copyright  2011 Pearson Education, Inc.  Classification of Pure Substances  Compounds Pure 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 Tro: Chemistry: A Molecular Approach, Approach 2/e 27 Copyright  2011 Pearson Education, Inc.  Classification of Pure Substances 1. made of one 1. made of one type of atom type of (some molecule, or elements an array of found as multi- ions atom 2. units contain molecules in two or more nature) different kinds 2. combine of atoms together to make compounds Tro: Chemistry: A Molecular Approach, Approach 2/e 28 Copyright  2011 Pearson Education, Inc.  Classification of Mixtures Homogeneous mixtures are mixtures that have 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 mixtures are mixtures that do not have uniform composition throughout  regions within the sample can have different characteristics  atoms or molecules not mixed uniformly Tro: Chemistry: A Molecular Approach, Approach 2/e 29 Copyright  2011 Pearson Education, Inc.  Classification of Mixtures 1. made of 1. made of multiple multiple substances, substances, whose but appears to presence can be one be seen substance 2. portions of a 2. all portions of sample have an individual different sample have composition the same and composition properties and properties Tro: Chemistry: A Molecular Approach, Approach 2/e 30 Copyright  2011 Pearson Education, Inc.  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 Tro: Chemistry: A Molecular Approach, Approach 2/e 31 Copyright  2011 Pearson Education, Inc.  Physical Changes in Matter The boiling of water is a physical change. The water molecules are separated from each other, but their structure and composition do not change. Tro: Chemistry: A Molecular Approach, Approach 2/e 32 Copyright  2011 Pearson Education, Inc.  Chemical Changes in Matter The rusting of iron is a chemical change. The iron atoms in the nail combine with oxygen atoms from O2 in the air to make a new substance, rust, with a different composition. Tro: Chemistry: A Molecular Approach, Approach 2/e 33 Copyright  2011 Pearson Education, Inc.  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 Tro: Chemistry: A Molecular Approach, Approach 2/e 34 Copyright  2011 Pearson Education, Inc.  Common Physical Changes Processes that cause Dissolving Subliming of of sugar dry ice changes in the matter C12H22O11(s) that do not change its CO2(g) composition State changes Dry Ice  boiling / condensing  melting / freezing  subliming CO2(s) Dissolving C12H22O11(aq) Tro: Chemistry: A Molecular Approach Approach, 2/e 35 Copyright  2011 Pearson Education, Inc.  Common Chemical Changes Processes that cause changes in the matter that change its composition Rusting Burning Dyes fading or changing color C3H8(g) + 5 O2(g) → 3 CO2(g) + 4 H2O(l) Tro: Chemistry: A Molecular Approach, Approach 2/e 36 Copyright  2011 Pearson Education, Inc.  Energy Tro: Chemistry: A Molecular Approach, 2/e Copyright  2011 Pearson Education, Inc.  Energy Changes in Matter Changes in matter, both physical and chemical, result in the matter either gaining or releasing energy Energy is the capacity to do work Work is the action of a force applied across a distance  a force is a push or a pull on an object  electrostatic force is the push or pull on objects that have an electrical charge Tro: Chemistry: A Molecular Approach, Approach 2/e 38 Copyright  2011 Pearson Education, Inc.  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 Tro: Chemistry: A Molecular Approach, Approach 2/e 39 Copyright  2011 Pearson Education, Inc.  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 Tro: Chemistry: A Molecular Approach, Approach 2/e 40 Copyright  2011 Pearson Education, Inc.  Energy of Matter − Potential Potential energy is energy that is stored in the matter  due to the composition of the matter and its position relative to other things  chemical potential energy arises from electrostatic attractive forces between atoms, molecules, and subatomic particles Tro: Chemistry: A Molecular Approach, Approach 2/e 41 Copyright  2011 Pearson Education, Inc.  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 Tro: Chemistry: A Molecular Approach, Approach 2/e 42 Copyright  2011 Pearson Education, Inc.  Spontaneous Processes Materials that possess high potential energy are less stable Processes in nature tend to occur on their own when the result is material with lower total potential energy  processes that result in materials with higher total potential energy can occur, but generally will not happen without input of energy from an outside source Tro: Chemistry: A Molecular Approach, Approach 2/e 43 Copyright  2011 Pearson Education, Inc.  Changes in Energy If a process results in the system having less potential energy at the end than it had at the beginning, the “lost” potential energy was converted into kinetic energy, which is released to the environment During the conversion of form, energy that is released can be harnessed to do work Tro: Chemistry: A Molecular Approach, Approach 2/e 44 Copyright  2011 Pearson Education, Inc.  Potential to Kinetic Energy Tro: Chemistry: A Molecular Approach, Approach 2/e 45 Copyright  2011 Pearson Education, Inc.  Standard Units of Measure Tro: Chemistry: A Molecular Approach, 2/e Copyright  2011 Pearson Education, Inc.  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 Tro: Chemistry: A Molecular Approach, Approach 2/e 47 Copyright  2011 Pearson Education, Inc.  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) Tro: Chemistry: A Molecular Approach, Approach 2/e 48 Copyright  2011 Pearson Education, Inc.  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 lbs. 3 oz. Commonly measure mass in grams (g) or milligrams (mg)  1 kg = 2.2046 pounds, 1 lb. = 453.59 g  1 kg = 1000 g = 103 g  1 g = 1000 mg = 103 mg  1 g = 0.001 kg = 10−3 kg  1 mg = 0.001 g = 10−3 g Tro: Chemistry: A Molecular Approach, Approach 2/e 49 Copyright  2011 Pearson Education, Inc.  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–133 Tro: Chemistry: A Molecular Approach, Approach 2/e 50 Copyright  2011 Pearson Education, Inc.  Temperature Measure of the average amount of kinetic energy caused by motion of the particles  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 flows from hot object to cold  heat is exchanged through molecular collisions between the two materials ( F  32) C  1.8 K  C  273.15 Tro: Chemistry: A Molecular Approach, Approach 2/e 51 Copyright  2011 Pearson Education, Inc.  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 Tro: Chemistry: A Molecular Approach, Approach 2/e 52 Copyright  2011 Pearson Education, Inc.  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 Tro: Chemistry: A Molecular Approach, Approach 2/e 53 Copyright  2011 Pearson Education, Inc.  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 Tro: Chemistry: A Molecular Approach, Approach 2/e 54 Copyright  2011 Pearson Education, Inc.  Example 1.2: Convert 40.00 °C into K and °F Find the equation that Given: 40.00 °C relates the given quantity to Find: K the quantity you want to find Equation: K = °C + 273.15 Because the equation is K = °C + 273.15 solved for the quantity you K = 40.00 + 273.15 want to find, substitute and K = 313.15 K compute Find the equation that Given: 40.00 °C relates the given quantity to Find: °F the quantity you want to find Equation: Solve the equation for the quantity you want to find Substitute and compute Tro: Chemistry: A Molecular Approach, Approach 2/e 55 Copyright  2011 Pearson Education, Inc.  Practice – Convert 0.0°F into Kelvin Tro: Chemistry: A Molecular Approach, Approach 2/e 56 Copyright  2011 Pearson Education, Inc.  Practice – Convert 0.0°F into Kelvin Sort Given: 0.0 °F information Find: Kelvin Strategize Concept °F °C K Plan: Equations: Follow the Solution: concept plan to solve the problem Sig. figs. and Round: 255.37 K = 255 K round Check Check: Because kelvin temperatures are always positive and generally between 250 and 300, the answer makes sense Tro: Chemistry: A Molecular Approach, Approach 2/e 57 Copyright  2011 Pearson Education, Inc.  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 Tro: Chemistry: A Molecular Approach, Approach 2/e 58 Copyright  2011 Pearson Education, Inc.  Common Prefix Multipliers in the SI System Tro: Chemistry: A Molecular Approach, Approach 2/e 59 Copyright  2011 Pearson Education, Inc.  Volume Derived unit  any length unit cubed Measure of the amount of space occupied SI unit = cubic meter (m3) Commonly measure solid volume in cubic centimeters (cm3)  1 m3 = 106 cm3  1 cm3 = 10−6 m3 = 0.000 001 m3 Commonly measure liquid or gas volume in milliliters (mL)  1 L is slightly larger than 1 quart  1 L = 1 dm3 = 1000 mL = 103 mL  1 mL = 0.001 L = 10−3 L  1 mL = 1 cm3 Tro: Chemistry: A Molecular Approach, Approach 2/e 60 Copyright  2011 Pearson Education, Inc.  Common Units and Their Equivalents Length 1 kilometer (km) = 0.6214 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 Tro: Chemistry: A Molecular Approach, Approach 2/e 61 Copyright  2011 Pearson Education, Inc.  Common Units and Their Equivalents Mass 1 kilogram (km) = 2.205 pounds (lb) 1 pound (lb) = 453.59 grams (g) 1 ounce (oz) = 28.35 grams (g) Volume 1 liter (L) = 1000 milliliters (mL) 1 liter (L) = 1000 cubic centimeters (cm3) 1 liter (L) = 1.057 quarts (qt) 1 U.S. gallon (gal) = 3.785 liters (L) Tro: Chemistry: A Molecular Approach, Approach 2/e 62 Copyright  2011 Pearson Education, Inc.  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 Tro: Chemistry: A Molecular Approach, Approach 2/e 63 Copyright  2011 Pearson Education, Inc.  Density Tro: Chemistry: A Molecular Approach, 2/e Copyright  2011 Pearson Education, Inc.  Intensive and Extensive Properties Extensive properties are properties whose 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? Intensive properties are properties whose value is independent of the quantity of matter  intensive properties are often used to identify the type of matter samples with identical intensive properties are usually the same material Tro: Chemistry: A Molecular Approach, Approach 2/e 65 Copyright  2011 Pearson Education, Inc.  Mass & Volume Two main physical properties of matter Mass and volume are extensive properties Even though mass and volume are individual properties, for a given type of matter they are related to each other! Volume vs. Mass of Brass 160 140 120 Mass, g 100 y = 8.38x 80 60 40 20 0 0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0 18.0 Volume, cm 3 Tro: Chemistry: A Molecular Approach, Approach 2/e 66 Copyright  2011 Pearson Education, Inc.  Density Density is the ratio of mass to volume  is an intensive property Solids = g/cm3  1 cm3 = 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! Tro: Chemistry: A Molecular Approach, Approach 2/e 67 Copyright  2011 Pearson Education, Inc.  Density For equal volumes, denser object has larger mass For equal masses, denser object has smaller volume Heating an object generally causes it to expand, therefore the density changes with temperature Tro: Chemistry: A Molecular Approach, Approach 2/e 68 Copyright  2011 Pearson Education, Inc.  Example 1.3: Decide if a ring with a mass of 3.15 g that displaces 0.233 cm3 of water is platinum Write down the given Given: mass = 3.15 g quantities and the quantity volume = 0.233 cm3 you want to find Find: density, g/cm3 Find the equation that Equation: relates the given quantity to the quantity you want to find Solve the equation for the quantity you want to find, check the units are correct, then substitute and compute Compare to accepted value Density of platinum = of the intensive property 21.4 g/cm3 therefore not platinum Tro: Chemistry: A Molecular Approach, Approach 2/e 69 Copyright  2011 Pearson Education, Inc.  Calculating Density What is the density of a brass sample if 100.0 g added to a cylinder of water causes the water level to rise from 25.0 mL to 36.9 mL? Tro: Chemistry: A Molecular Approach, Approach 2/e 70 Copyright  2011 Pearson Education, Inc.  Practice — What is the density of the brass sample? Sort Given: mass = 100 g information vol displ: 25.0 36.9 mL Find: d, g/cm3 Strategize Concept m, V d Plan: Equation: Solve the Solution: equation for V = 36.9−25.0 the unknown = 11.9 mL variable = 11.9 cm3 Sig. figs. and Round: 8.4033 g/cm3 = 8.40 g/cm3 round Check Check: units and number make sense Tro: Chemistry: A Molecular Approach, Approach 2/e 71 Copyright  2011 Pearson Education, Inc.  Measurement and Significant Figures Tro: Chemistry: A Molecular Approach, 2/e Copyright  2011 Pearson Education, Inc.  What Is a Measurement? Quantitative observation Comparison to an agreed standard Every measurement has a number and a unit Tro: Chemistry: A Molecular Approach, Approach 2/e 73 Copyright  2011 Pearson Education, Inc.  A Measurement The unit tells you what standard you are comparing your object to The number tells you 1. what multiple of the standard the object measures 2. the uncertainty in the measurement Scientific measurements are reported so that every digit written is certain, except the last one, which is estimated Tro: Chemistry: A Molecular Approach, Approach 2/e 74 Copyright  2011 Pearson Education, Inc.  Estimating the Last Digit For instruments marked with a scale, you get the last digit by estimating between the marks  if possible Mentally divide the space into ten equal spaces, then estimate how many spaces over the indicator the mark is Tro: Chemistry: A Molecular Approach, Approach 2/e 75 Copyright  2011 Pearson Education, Inc. Tro: Chemistry: A Molecular Approach, Approach 2/e 76 Copyright  2011 Pearson Education, Inc.  Significant Figures The non-place-holding digits in a reported measurement are 12.3 cm has 3 sig. figs. called significant figures and its range is  some zeros in a written number 12.2 to 12.4 cm are only there to help you locate the decimal point Significant figures tell us the 12.30 cm range of values to expect for has 4 sig. figs. and its range is repeated measurements 12.29 to 12.31 cm  the more significant figures there are in a measurement, the smaller the range of values is Tro: Chemistry: A Molecular Approach, Approach 2/e 77 Copyright  2011 Pearson Education, Inc.  Counting Significant Figures 1. All non-zero digits are significant  1.5 has 2 sig. figs. 2. Interior zeros are significant  1.05 has 3 sig. figs. 3. Leading zeros are NOT significant  0.001050 has 4 sig. figs.  1.050 x 10−3 Tro: Chemistry: A Molecular Approach, Approach 2/e 78 Copyright  2011 Pearson Education, Inc.  Counting Significant Figures 4. Trailing zeros may or may not be significant a) Trailing zeros after a decimal point are significant  1.050 has 4 sig. figs. b) Trailing zeros before a decimal point are significant if the decimal point is written  150.0 has 4 sig. figs. c) Zeros 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 102  but if 150 has 3 sig. figs. then 1.50 x 102 Tro: Chemistry: A Molecular Approach, Approach 2/e 79 Copyright  2011 Pearson Education, Inc.  Significant Figures and Exact Numbers A number whose value is known with complete certainty is exact  from counting individual objects  from definitions 1 cm is exactly equal to 0.01 m  from integer values in equations  in the equation for the radius of a circle, the 2 is exact Exact numbers have an unlimited number of significant figures Tro: Chemistry: A Molecular Approach, Approach 2/e 80 Copyright  2011 Pearson Education, Inc.  Example 1.5: Determining the Number of Significant Figures in a Number How many significant figures are in each of the following? 0.04450 m 4 sig. figs.; the digits 4 and 5, and the trailing 0 5.0003 km 5 sig. figs.; the digits 5 and 3, and the interior 0’s 10 dm = 1 m infinite number of sig. figs., exact numbers 1.000 × 105 s 4 sig. figs.; the digit 1, and the trailing 0’s 0.00002 mm 1 sig. figs.; the digit 2, not the leading 0’s 10,000 m Ambiguous, generally assume 1 sig. fig. Tro: Chemistry: A Molecular Approach, Approach 2/e 81 Copyright  2011 Pearson Education, Inc.  Practice − Determine the number of significant figures, the expected range of precision, and indicate the last significant figure 0.00120 120. 12.00 1.20 x 103 Tro: Chemistry: A Molecular Approach, Approach 2/e 82 Copyright  2011 Pearson Education, Inc.  Practice − determine the number of significant figures, the expected range of precision, and indicate the last significant figure 0.00120 3 sig. figs. 0.00119 to 0.00121 120. 3 sig. figs. 119 to 121 12.00 4 sig. figs. 11.99 to 12.01 1.20 x 103 3 sig. figs. 1190 to 1210 Tro: Chemistry: A Molecular Approach, Approach 2/e 83 Copyright  2011 Pearson Education, Inc.  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 lowest number of significant figures 5.02 × 89.665 × 0.10 = 45.0118 = 45 3 sig. figs. 5 sig. figs. 2 sig. figs. 2 sig. figs. 5.892 ÷ 6.10 = 0.96590 = 0.966 4 sig. figs. 3 sig. figs. 3 sig. figs. Tro: Chemistry: A Molecular Approach, Approach 2/e 84 Copyright  2011 Pearson Education, Inc.  Addition and Subtraction with Significant Figures When adding or 2. 3 4 5 subtracting measurements 0. 0 7 5.41 with significant figures, the 2. 9 9 7 5 5. 4 12 5 result has the same number of decimal places 5.9 as the measurement with  2. 2 2 1  5.7 the lowest number of 5.6 7 9 decimal places Tro: Chemistry: A Molecular Approach, Approach 2/e 85 Copyright  2011 Pearson Education, Inc.  Rounding When rounding to the correct number of significant figures, if the number after the place of the last significant figure is a) 0 to 4, round down  drop all digits after the last sig. fig. and leave the last sig. fig. alone  add insignificant zeros to keep the value if necessary b) 5 to 9, round up  drop all digits after the last sig. fig. and increase the last sig. fig. by one  add insignificant zeros to keep the value if necessary To avoid accumulating extra error from rounding, round only at the end, keeping track of the last sig. fig. for intermediate calculations Tro: Chemistry: A Molecular Approach, Approach 2/e 86 Copyright  2011 Pearson Education, Inc.  Rounding Rounding to 2 significant figures 2.34 rounds to 2.3  because the 3 is where the last sig. fig. will be and the number after it is 4 or less 2.37 rounds to 2.4  because the 3 is where the last sig. fig. will be and the number after it is 5 or greater 2.349865 rounds to 2.3  because the 3 is where the last sig. fig. will be and the number after it is 4 or less Tro: Chemistry: A Molecular Approach, Approach 2/e 87 Copyright  2011 Pearson Education, Inc.  Rounding Rounding to 2 significant figures 0.0234 rounds to 0.023 or 2.3 × 10−2  because the 3 is where the last sig. fig. will be and the number after it is 4 or less 0.0237 rounds to 0.024 or 2.4 × 10−2  because the 3 is where the last sig. fig. will be and the number after it is 5 or greater 0.02349865 rounds to 0.023 or 2.3 × 10−2  because the 3 is where the last sig. fig. will be and the number after it is 4 or less Tro: Chemistry: A Molecular Approach, Approach 2/e 88 Copyright  2011 Pearson Education, Inc.  Rounding Rounding to 2 significant figures 234 rounds to 230 or 2.3 × 102  because the 3 is where the last sig. fig. will be and the number after it is 4 or less 237 rounds to 240 or 2.4 × 102  because the 3 is where the last sig. fig. will be and the number after it is 5 or greater 234.9865 rounds to 230 or 2.3 × 102  because the 3 is where the last sig. fig. will be and the number after it is 4 or less Tro: Chemistry: A Molecular Approach, Approach 2/e 89 Copyright  2011 Pearson Education, Inc.  Both Multiplication/Division and Addition/Subtraction with Significant Figures When doing different kinds of operations with measurements with significant figures, do whatever is in parentheses first, evaluate the significant figures in the intermediate answer, then do the remaining steps 3.489 × (5.67 – 2.3) = 2 dp 1 dp 3.489 × 3.37 = 12 4 sf 1 dp & 2 sf 2 sf Tro: Chemistry: A Molecular Approach, Approach 2/e 90 Copyright  2011 Pearson Education, Inc. Example 1.6: Perform the Following Calculations to the Correct Number of Significant Figures Tro: Chemistry: A Molecular Approach, Approach 2/e 91 Copyright  2011 Pearson Education, Inc.  Example 1.6 Perform the Following Calculations to the Correct Number of Significant Figures Tro: Chemistry: A Molecular Approach, Approach 2/e 92 Copyright  2011 Pearson Education, Inc.  Precision and Accuracy Tro: Chemistry: A Molecular Approach, 2/e Copyright  2011 Pearson Education, Inc.  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 Tro: Chemistry: A Molecular Approach, Approach 2/e 94 Copyright  2011 Pearson Education, Inc.  Precision Imprecision in measurements is caused by random errors  errors that result from random fluctuations  no specific cause, therefore cannot be corrected We determine the precision of a set of measurements by evaluating how far they are from the actual value and each other Even though every measurement has some random error, with enough measurements these errors should average out Tro: Chemistry: A Molecular Approach, Approach 2/e 95 Copyright  2011 Pearson Education, Inc.  Accuracy Inaccuracy in measurement caused by systematic errors  errors caused by limitations in the instruments or techniques or experimental design  can be reduced by using more accurate instruments, or better technique or experimental design We determine the accuracy of a measurement by evaluating how far it is from the actual value Systematic errors do not average out with repeated measurements because they consistently cause the measurement to be either too high or too low Tro: Chemistry: A Molecular Approach, Approach 2/e 96 Copyright  2011 Pearson Education, Inc.  Accuracy vs. Precision Suppose three students are asked to determine the mass of an object whose known mass is 10.00 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. Tro: Chemistry: A Molecular Approach, Approach 2/e 97 Copyright  2011 Pearson Education, Inc.  Solving Chemical Problems Equations & Dimensional Analysis Tro: Chemistry: A Molecular Approach, 2/e Copyright  2011 Pearson Education, Inc.  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 on numbers cm × cm = cm2 cm + cm = cm cm ÷ cm = 1  using units as a guide to problem solving is called dimensional analysis Tro: Chemistry: A Molecular Approach, Approach 2/e 99 Copyright  2011 Pearson Education, Inc.  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 Tro: Chemistry: A Molecular Approach, Approach 2/e 100 Copyright  2011 Pearson Education, Inc.  Problem Solving and Dimensional Analysis Arrange conversion factors so the starting unit cancels  arrange conversion factors so the starting unit is on the bottom of the first conversion factor May string conversion factors  so you do not need to know every relationship, as long as you can find something else the starting and desired units are related to Tro: Chemistry: A Molecular Approach, Approach 2/e 101 Copyright  2011 Pearson Education, Inc.  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 Tro: Chemistry: A Molecular Approach, Approach 2/e 102 Copyright  2011 Pearson Education, Inc.  Conceptual Plans and Conversion Factors Convert inches into centimeters 1. Find relationship equivalence: 1 in. = 2.54 cm 2. Write a conceptual plan in. in. cm cm 3. Change equivalence into conversion factors with starting units on the bottom Tro: Chemistry: A Molecular Approach, Approach 2/e 103 Copyright  2011 Pearson Education, Inc.  Systematic Approach to Problem Solving Sort the information from the problem  identify the given quantity and unit, the quantity and unit you want to find, any relationships implied in the problem Design a strategy to solve the problem  devise a conceptual plan  sometimes may want to work backward  each step involves a conversion factor or equation Apply the steps in the conceptual plan to solve the problem  check that units cancel properly  multiply terms across the top and divide by each bottom term Check the answer  double-check the set-up 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  because centimeters are smaller than inches, converting inches to centimeters should result in a larger number Tro: Chemistry: A Molecular Approach, Approach 2/e 104 Copyright  2011 Pearson Education, Inc.  Example 1.7: Convert 1.76 yd to centimeters Sort the Given: 1.76 yd information Find: length, cm Strategize Conceptual yd m cm Plan: 1 m = 1.094 yd Relationships: 1 m = 100 cm Follow the Solution: conceptual plan to solve the problem Sig. figs. and Round: 160.8775 cm = 161 cm round Check Check: units are correct; number makes sense: cm