Lecture Slides Chapter 1 - Science and Measurement - Interactive General Chemistry 2.0

Science and Measurement Chapter 1 Lecture Slides Interactive General Chemistry 2.0 Reactions First © 2023 Macmillan Learning 1 Interactive General Chemistry 2.0, © 2023 Macmillan Learning...

Science and Measurement Chapter 1 Lecture Slides Interactive General Chemistry 2.0 Reactions First © 2023 Macmillan Learning 1 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Chapter Outline Section 1.1 Classification Section 1.5 The of Matter International System of Units Section 1.2 Properties of Matter Section 1.6 Significant Digits Section 1.3 Matter and Energy Section 1.7 Dimensional Analysis Section 1.4 The Scientific Method, Section 1.8 Density Hypotheses, Theories, Section 1.9 Temperature 2 Scales Interactive General Chemistry 2.0, © 2023 Macmillan Learning Section 1.1 Classification of Matter Classify matter into types based on its composition. 3 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Matter Chemistry is the study of matter and energy. Matter is anything that has mass and occupies space. All the matter on Earth is composed of about a hundred elements. Elements are the simplest form of matter that has distinct physical and chemical properties and cannot be broken down chemically into simpler, stable substances. Elements are the building blocks for everything in the universe. 4 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Pure Substances An atom is the smallest amount of an element that still has the characteristics of that element. Atoms of different elements can form attractions called chemical bonds that hold the atoms together. These bonds can then be broken and new bonds formed with different atoms. A compound is a chemical combination of elements that has its own set of properties and a definite composition. Elements and compounds are the two types of pure 5 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Figure 1.1 Elements, Compound s, and Mixtures 6 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Example 1.1 Identify the components of each of the three different mixtures in Figure 1.1 as elements or compounds. a. b. c. 7 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Example 1.1 Solution Identify the components of each of the three different mixtures in Figure 1.1 as elements or compounds. a. a. All three components of this mixture are elements. b. b. This mixture contains one element and one compound. c. c. This mixture contains two different compounds. 8 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Mixtures Two or more pure substances can be physically combined to produce a mixture. The components of a mixture are not chemically bonded to each other and can be separated from one another by physical means. Mixtures do not have definite compositions and can be either heterogeneous or homogeneous. In heterogeneous mixtures, the substances that make up the mixture are not uniformly mixed, so two samples taken from the same mixture might have different 9 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Solutions Homogeneous mixtures are also called solutions. Solutions can be found in any phase. The atmosphere is a gas-phase solution. Metal alloys are solid-phase solutions. The most common solutions are aqueous solutions, which have water as the major component. 10 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Table 1.1 Classification of Matter Classification Subclassificatio Examples n Hydrogen, Pure Substances Element sodium Pure Substances Compound Water, table salt Oil and water Heterogeneous Mixtures mixture, chicken mixture noodle soup Homogeneous Mixtures Brass, vodka mixture 11 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Figure 1.2 Classificatio n of Matter 12 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Example 1.2 The percentage of carbon in a small box of the pure substance sucrose (table sugar) is 42.1%. a. Is sucrose an element or a compound? b. What is the percentage of carbon in a large box of sucrose? 13 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Example 1.2 Solution The percentage of carbon in a small box of the pure substance sucrose (table sugar) is 42.1%. a. Is sucrose an element or a compound? Sucrose is a compound. b. What is the percentage of carbon in a large box of sucrose? 42.1%; the same as in a small box 14 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Example 1.3 If you stir a teaspoon of sugar into a glass of water and a teaspoon of mud into another glass of water, the sugar will eventually dissolve into the water, but the mud will not. Which mixture is a solution? 15 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Example 1.3 Solution If you stir a teaspoon of sugar into a glass of water and a teaspoon of mud into another glass of water, the sugar will eventually dissolve into the water, but the mud will not. Which mixture is a solution? The mud and water form a heterogeneous mixture (photo a). The sugar forms a solution, a homogeneous mixture, with the water (photo b). 16 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Example 1.4 Indicate whether each of the following statements is true or false. a. Every compound is a pure substance. b. Every compound contains two or more elements. c. Every mixture contains two or more compounds. d. Every pure substance is a compound. e. All mixtures are homogeneous. 17 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Example 1.4 Solution Indicate whether each of the following statements is true or false. a. Every compound is a pure substance. a. True b. Every compound contains two or more b. True elements. c. False c. Every mixture contains two or more compounds. d. False d. Every pure substance is a compound. e. False e. All mixtures are homogeneous. 18 Interactive General Chemistry 2.0, © 2023 Macmillan Learning 1.1 Section Review (1 of 2) Matter has mass and occupies space. An element is the simplest form of matter that has distinct physical and chemical properties. There are about 100 different chemical elements. Elements can be combined chemically to form compounds. Elements and compounds are pure substances. 19 Interactive General Chemistry 2.0, © 2023 Macmillan Learning 1.1 Section Review (2 of 2) All pure substances have definite compositions. Mixtures do not have definite compositions. Homogeneous mixtures have a uniform composition. Heterogeneous mixtures do not have a uniform composition. 20 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Section 1.2 Properties of Matter Recognize different types of properties and use these properties to help identify substances. Differentiate between physical and chemical changes. 21 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Properties of Matter Every substance has a definite set of properties, which are the characteristics by which something can be identified. Properties that describe or identify a substance without changing its chemical composition, such as color, melting point, and conductivity, are physical properties. The characteristic chemical reactions a substance undergoes are its chemical properties. 22 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Figure 1.3 Properti es of Iron 23 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Extensive and Intensive Properties Properties that depend on the amount of substance present are extensive properties. Examples of extensive properties are mass and volume. Properties that are the same regardless of sample size are intensive properties. Examples of intensive properties are density, color, and melting point. 24 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Example 1.5 a. If sample A weighs twice as much as sample B, is it possible to tell which sample is iron and which is powdered sugar? b. If sample A is attracted by a magnet and sample B is a white powder, is it possible to tell which sample is iron and which is powdered sugar? 25 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Example 1.5a Solution a. If sample A weighs twice as much as sample B, is it possible to tell which sample is iron and which is powdered sugar? No. Weight is an extensive property and does not identify a substance. 26 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Example 1.5b Solution b. If sample A is attracted by a magnet and sample B is a white powder, is it possible to tell which sample is iron and which is powdered sugar? Yes. Magnetism and physical appearance are both intensive properties and can be used distinguish between the two substances. 27 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Properties of Compounds and Mixtures The properties of compounds are constant and typically are different from the properties of the elements that compose them. Hydrogen and oxygen are both colorless gases at room temperature that can combine to form water, a colorless liquid at room temperature. The properties of mixtures are similar to the properties of the components that make up the mixture, but change depending on the amount of each component in the mixture. Dissolving one spoonful of sugar in a glass of water yields a sweet solution (a homogeneous mixture), while dissolving three spoonsful Interactive of sugar in the same amount General Chemistry 2.0, © 2023 Macmillan Learning of water yields a 28 Online Resource: Figure 1.4 - Iron, Sulfur, and a Mixture of the Two - Video Figure 1.4 Iron, Sulfur, and a Mixture of the Two 29 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Changing Matter: Physical Changes When a physical change occurs, the chemical composition of a substance is not altered. Iron and sulfur can be mixed but remain iron and sulfur. They can be separated based on their different solubilities (another physical property). Melting ice changes solid water to liquid water. Solid CO2 sublimes directly to the gas phase. 30 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Online Resource: Figure 1.5 - Physical Change - Video Figure 1.5 Physical Change 31 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Changing Matter: Chemical Changes The starting material in a chemical change is known as the reactant, and the resulting material is the product. During the reaction, the reactants rearrange their chemical compositions to form the products. Iron and sulfur, when heated, react to form a new substance with properties that are very different from either iron or sulfur. 32 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Online Resource: Figure 1.6 - Reaction of Iron and Sulfur - Video Figure 1.6 Reaction of Iron and Sulfur 33 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Table 1.2 Some Properties of Iron, Sulfur, and an Iron–Sulfur Compound Iron–Sulfur Iron Sulfur Compound Phase Solid Solid Solid Luster Shiny Dull Dull Magnetic Propertie Magnetic Not magnetic Not magnetic s Color Black Yellow Dull black Mechanic al Malleable Brittle Brittle Propertie s 34 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Chemical Changes Chemical changes change the chemical structure of a substance by breaking and/or forming chemical bonds. When bonds are broken, energy is absorbed from the surroundings. When bonds are formed, energy is released to the surroundings. 35 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Online Resource: Figure 1.7 - Chemical Change - Video Figure 1.7 Chemical Change 36 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Example 1.6a A pure substance is heated in air until no further reaction takes place. A different pure substance is produced that has a mass that is 58.5% of that of the original substance. Can you tell whether each substance in this reaction is an element or a compound? 37 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Example 1.6a Solution A pure substance is heated in air until no further reaction takes place. A different pure substance is produced that has a mass that is 58.5% of that of the original substance. Can you tell whether each substance in this reaction is an element or a compound? One product has much less mass than the reactant, indicating that another product was a gas that escaped. Thus, the reactant is a compound that decomposes upon heating to produce two new substances. There is not enough information to tell if the products38 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Example 1.6b After a different pure substance is heated in air, a new pure substance is formed that has a mass of 138% of that of the original substance. Can you tell whether each substance in these reactions is an element or a compound? 39 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Example 1.6b Solution After a different pure substance is heated in air, a new pure substance is formed that has a mass of 138% of that of the original substance. Can you tell whether each substance in these reactions is an element or a compound? The product gained in mass, indicating that the original substance combined with a gas in the air. Thus, the product must be a compound. However, there is not sufficient information to determine if the two reactants are elements or compounds. Interactive General Chemistry 2.0, © 2023 Macmillan Learning 40 1.2 Section Review (1 of 2) Every substance has its own characteristic set of properties. Physical properties describe a substance. Color, mass, volume, freezing point, boiling point, solubility, taste, texture, and hardness are all examples of physical properties. Chemical properties describe whether or not a substance undergoes a chemical change. For example, flammability and reactivity with acids are chemical properties. Extensive properties, such as mass and volume, depend on how much sample is present; intensive properties, such as color and malleability, do not. 41 Interactive General Chemistry 2.0, © 2023 Macmillan Learning 1.2 Section Review (2 of 2) Intensive properties are useful for identifying substances. Physical changes do not alter the chemical composition of a substance, although they may change its size or its physical state. The product(s) of a physical change always have the same chemical composition as the reactant(s). Chemical changes result in products that are chemically different from the reactants. Chemical changes occur when chemical bonds between atoms break and/or new chemical bonds form. 42 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Section 1.3 Matter and Energy Explain the difference among matter, mass, and weight. Differentiate between matter and energy. 43 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Mass The mass of an object measures how much matter is in the object. Mass is directly proportional to weight. An object has one weight on Earth and another on the Moon, but its mass does not change. 44 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Energy The definition of energy is the capacity to do work. Law of conservation of energy: Energy cannot be created or destroyed but can be converted from one form to another. Examples of forms of energy include heat, chemical, nuclear, mechanical (kinetic and potential), electrical, sound, and electromagnetic radiation. 45 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Example 1.7 Which energy conversions are exhibited by: a. using the flashlight app on your cell phone? b. recharging your cell phone battery by plugging it into a wall outlet? 46 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Example 1.7a Solution Which energy conversions are exhibited by: a. using the flashlight app on your cell phone? Chemical energy in the cell phone battery is converted to electrical energy, which is converted to light. 47 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Example 1.7b Solution Which energy conversions are exhibited by: b. recharging your cell phone battery by plugging it into a wall outlet? Electrical energy from the wall outlet is converted to chemical energy in the phone’s battery. 48 Interactive General Chemistry 2.0, © 2023 Macmillan Learning 1.3 Section Review Mass is a measure of the quantity of matter in a sample. Energy exists in many different forms and can be converted between forms, but it can never be created or destroyed. 49 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Section 1.4 The Scientific Method, Hypotheses, Theories, and Laws Explain the scientific method. Distinguish among hypotheses, theories, and laws. 50 Interactive General Chemistry 2.0, © 2023 Macmillan Learning The Scientific Method The scientific method is a process that combines observation, hypothesis, and experimentation. 1. What background information, data, or observations do you have? 2. What is your initial explanation for the background information and data? (This is your hypothesis, which should be supported by your initial observations and any other available data.) 3. How can you check? (This is the experiment, where you interact with the subject being studied.) 51 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Hypotheses, Theories, and Laws Hypotheses are the initial explanation for some observed fact or facts, are based on observation and evidence, and are to be tested and revised through experimentation. Theories are broader in scope, and explain and predict many different observations that are linked by the same underlying phenomena. Theories are generally widely accepted by scientists in the field as valid explanations of phenomena. Scientific observations that are always true are referred to as scientific laws. Laws are statements of 52 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Figure 1.8 The Scientific Method 53 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Figure 1.9 Laws Versus Theories 54 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Law of Conservation of Mass The law of conservation of mass states that in any chemical reaction or physical change, the total mass present after the change is equal to the total mass present before the change. This law was discovered by Lavoisier in 1785, but it wasn’t explained until Dalton’s atomic theory was proposed in 1803. In the 20th century, the law of conservation of mass was found not to apply to nuclear reactions, illustrating that even scientific laws must be revised at times. 55 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Example 1.8 A scientist conducts a few experiments in the lab and comes up with an initial explanation for their observations. a. What is the proper term for this initial explanation? b. Suppose that the scientist and several colleagues conduct numerous additional experiments and that none of the new results contradict the original explanation. What is the proper term for the explanation at this point? 56 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Example 1.8a Solution A scientist conducts a few experiments in the lab and comes up with an initial explanation for their observations. a. What is the proper term for this initial explanation? hypothesis 57 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Example 1.8b Solution A scientist conducts a few experiments in the lab and comes up with an initial explanation for their observations. b. Suppose that the scientist and several colleagues conduct numerous additional experiments and that none of the new results contradict the original explanation. What is the proper term for the explanation at this point? theory 58 Interactive General Chemistry 2.0, © 2023 Macmillan Learning 1.4 Section Review Experimental science generally follows the scientific method. A scientific law is an observation that is always seen to be true. A hypothesis is a tentative explanation for the observation, based on available evidence. If many additional experiments support the hypothesis and no evidence is found to contradict it, the hypothesis becomes generally accepted and is upgraded to a theory. A hypothesis can become a theory, but a theory can never become a law because laws are simply observations, whereas hypotheses and theories are explanations. 59 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Section 1.5 The International System of Units Recognize SI units and prefixes to convert measurements between units. 60 Interactive General Chemistry 2.0, © 2023 Macmillan Learning SI Base Units (1 of 2) Length, mass, time, electric current, temperature, amount of substance, and luminous intensity are fundamental quantities that can be combined to describe every other quantity. These units are defined by a particular physical measurement, such as the length of a path of light, and are collectively called base units, or fundamental units. The ones studied most in chemistry are length, mass, time, temperature, and amount of substance. 61 Interactive General Chemistry 2.0, © 2023 Macmillan Learning SI Base Units (2 of 2) The meter, m, is the base SI unit of length. Shorter distances are often expressed in centimeters, cm, where 1 cm is 1/100 m. 1 in = 2.54 cm (exactly) Longer distances are often given in kilometers, km, where 1 km is 1000 m, approximately 0.62 mi. The kilogram, kg, is the SI base unit of mass. The gram (1/1000 kg) is often used to measure the mass of solid substances in a chemistry lab. One kilogram is equal to approximately 2.2 lb. 62 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Figure 1.10 One-Kilogram Samples 63 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Table 1.3 SI Base Units Quantity Unit Symbol Length Meter m Mass Kilogram kg Time Second s Temperature Kelvin K Amount of Mole mol substance Electric current Ampere A Luminous intensity Candela cd 64 Interactive General Chemistry 2.0, © 2023 Macmillan Learning SI Prefixes The SI prefixes can be added to the base units to describe very large or very small measurements. Examples: The prefix kilo-, k, multiplies the unit by 103 or 1000. The prefix centi-, c, multiplies the unit by 10−2 or 1/100. 65 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Table 1.4 SI Prefixes Abbreviati Meani Abbreviati Meani Prefix Prefix on ng on ng Tera- T 1012 Milli- m 10−3 Giga- G 109 Micro μ 10−6 - Mega M 106 Nano- n 10−9 - Kilo- k 103 Pico- p 10−12 Deci- d 10−1 Femto f 10–15 - Centi- c 10−2 66 Atto- Interactive General Chemistry 2.0, © 2023 Macmillan Learning a 10–18 Example 1.9 Which is larger: 1 mg or 1 Mg? 67 Interactive General Chemistry 2.0, © 2023 Macmillan Learning  Example 1.9 Solution Which is larger: 1 mg or 1 Mg? 1 mg = 0.001 g 1 Mg = 1,000,000 g Thus, 1 Mg (megagram) is much larger than 1 mg (milligram). 68 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Derived SI Units: Area and Volume Length is one dimensional. Area is two dimensional. The. Volume is three dimensional. The volume of a rectangular prism. 69 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Figure 1.11 The Area of a Square The area of this square is: 3 cm × 3 cm = 9 cm2 70 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Figure 1.12 The Volume of a Cube 2 m × 2 m × 2 m = (2 m)3 = 8 m3 71 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Table 1.5 SI Derived Units Quantity Unit Abbreviation Derivation Volume Cubic meter m3 Meter per Speed second m/s Meter per Acceleration second m/s2 squared Kilogram per Density cubic meter kg/m3 Frequency Hertz Hz s–1 Force Newton N Interactive General Chemistry 2.0, © 2023 Macmillan Learning kg · m/s2 72  Table 1.6 SI–English Conversions Length Mass Volume 1 m = 39.37 in 1 kg = 2.2046 lb 1 L = 1.057 qt 2.54 cm = 1 in 453.6 g = 1 lb 29.57 mL = 1 fl oz (exact) 1.609 km = 1 mi 28.35 g = 1 oz 3.785 L = 1 U.S. gal 1.609 km = 1760 1 metric ton = 2204.5 lb 0.473 L = 1 U.S. pint yd 1.609 km = 5280 ft 73 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Example 1.10 Determine which of the following values are given in SI base units, SI derived units, or English units. a. 1.5 gal b. 2.04 kg · m/s2 c. 298 K d. 8.25 s–1 74 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Example 1.10 Solution Determine which of the following values are given in SI base units, SI derived units, or English units. a. 1.5 gal a. English units b. 2.04 kg · m/s2 b. SI derived units c. 298 K c. SI units d. 8.25 s–1 d. SI derived units 75 Interactive General Chemistry 2.0, © 2023 Macmillan Learning 1.5 Section Review (1 of 2) The standard units of measurement in chemistry are the International System of Units, SI units. There are seven SI base units, and the ones used most often in chemistry are the meter (length), kilogram (mass), second (time), kelvin (temperature), and mole (amount of substance). 76 Interactive General Chemistry 2.0, © 2023 Macmillan Learning 1.5 Section Review (2 of 2) SI prefixes can be added to a unit to describe a very large or very small measurement. The prefixes differ by powers of 10. SI derived units are the products or powers of one or more base units. SI derived units include units of area, volume, speed, and acceleration. English–metric conversions are presented in this book only to give you an idea of the size of the metric unit. English units are rarely used in a chemistry lab. 77 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Section 1.6 Significant Digits Determine the correct number of digits to indicate the precision of a measurement or a calculated result. 78 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Qualitative and Quantitative Measurements make identifications of substances more precise and enable more scientific generalities to be made. In chemistry, qualitative descriptions refer to the identity or form of a substance present. Experiments that determine the amount of a substance present are quantitative measurements. 79 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Accuracy and Precision Scientific measurements are usually repeated three or more times because the average value of the measurements is probably closer to the true value than any individual measurement. The accuracy is the closeness of the average of a set of measurements to the true value. The precision is the closeness of all of a set of measured values to one another. 80 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Figure 1.13 Precision and Accuracy 81 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Example 1.11 Suppose a bathroom scale registers 2 lb with no load. An object is weighed repeatedly on this bathroom scale, and each results in a reading of 117 lb. a. Are the measurements precise? b. Are the measurements accurate? c. What is the probable true weight of the object? 82 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Example 1.11a Solution Suppose a bathroom scale registers 2 lb with no load. An object is weighed repeatedly on this bathroom scale, and each results in a reading of 117 lb. a. Are the measurements precise? The repeated measurements are identical, so yes, the measurements are precise. 83 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Example 1.11b Solution Suppose a bathroom scale registers 2 lb with no load. An object is weighed repeatedly on this bathroom scale, and each results in a reading of 117 lb. b. Are the measurements accurate? No, the measuring device was not zeroed properly. 84 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Example 1.11c Solution Suppose a bathroom scale registers 2 lb with no load. An object is weighed repeatedly on this bathroom scale, and each results in a reading of 117 lb. c. What is the probable true weight of the object? 117 lb − 2 lb = 115 lb 85 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Precision in Single Measurements Precision in single measurements is determined by the measuring device used. Different tools yield different levels of precision. When making a measurement, always estimate to one digit beyond the smallest scale division on the tool, if possible. 86 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Figure 1.14 Measurements of Different Precision 4.09 cm 4.1 cm 87 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Example 1.12 Determine the length of this screw, not including the head. 88 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Example 1.12 Solution Determine the length of this screw, not including the head. 1.75 cm 89 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Significant Digits Scientists report the precision of their measurements every time they write down a result. The number of digits they use consists of the absolutely certain digits plus one estimated digit. Every digit that reflects the precision of the measurement, including the estimated digit at the end, is called a significant digit or significant figure. 90 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Rules for Significant Digits (1 of 2) All nonzero numbers in a properly reported measurement are significant. Any zeros to the left of all nonzero digits are not significant; 0.03 contains only one significant digit. Any zeros between significant digits are significant; 903 contains three significant digits. 91 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Rules for Significant Digits (2 of 2) Any zeros to the right of all nonzero digits in a number with decimal-place digits are significant; 70.00 contains four significant digits. Any zeros to the right of all nonzero digits in an integer, such as in 4000, are uncertain unless further information is given; 4000 has only one significant digit. All the digits in the coefficient of a number in scientific notation are significant. 92 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Example 1.13 Underline the significant digits in each of the following measurements. a. 0.0020 m b. 1.200 m c. 10.002 m d. 6000 m 93 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Example 1.13 Solution Underline the significant digits in each of the following measurements. a. 0.0020 m b. 1.200 m c. 10.002 m d. 6000 m 94 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Significant Digits in Calculated Results: Addition and Subtraction Calculator answers must be rounded to the correct number of significant digits. In addition and subtraction, the last digit retained is the estimated digit farthest to the left in the measurements. The answer is rounded to the fewest number of Interactive General Chemistry 2.0, © 2023 Macmillan Learning 95 Example 1.14 Calculate the sum of 10.10 cm + 1.332 cm + 6.4 cm. Report the answer with the correct number of significant digits. 96 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Example 1.14 Solution Calculate the sum of 10.10 cm + 1.332 cm + 6.4 cm. Report the answer with the correct number of significant digits. 10.10 cm 1.332 cm  6.4 cm 17.832 cm 17.8 cm Of the values added, 6.4 has only one decimal place, so the final answer is rounded to one decimal place. 97 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Significant Digits in Calculated Results: Multiplication and Division For multiplication and division, the number of significant digits in the measurement with the fewest significant digits limits the number of significant digits 4.1 cm21.07 cm 86.387 cm2 86 cm2 in the answer: The answer is rounded to the fewest number of significant figures that are present in the multiplied or divided values. 98 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Example 1.15 Perform the following calculations, and report the answers to the correct number of significant digits. a. 2.171 cm4.20 cm 4.92 g b. 1.64 cm3 99 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Example 1.15 Solution Perform the following calculations, and report the answers to the correct number of significant digits. a. 2.171 cm4.20 cm 9.1182 cm 9.12 cm 2 2 4.92 g b. 3.00 g/cm3 1.64 cm 3  100 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Exact Numbers Exact numbers do not limit the number of significant figures in a calculated result. Exact numbers include the following: Numbers that are definitions and not measurements, such as the number of centimeters in a meter (100) Counted items, such as the number of students in a classroom Integers within formulas, such as the 2 in d = 2r. 101 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Example 1.16 The radius of a circle is 13.7 cm. Calculate the diameter of the circle to the correct number of significant digits. 102 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Example 1.16 Solution The radius of a circle is 13.7 cm. Calculate the diameter of the circle to the correct number of significant digits. The diameter of a circle is twice the radius. d 2r 213.7 cm 27.4 cm The measurement with the fewest significant digits is 13.7. 103 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Significant Digits in Calculated Results: Mixed Operations Follow order of operations rules 1. Perform any calculations in parentheses. 2. Perform any exponential calculations. 3. Perform any multiplication or division calculations (from left to right). 4. Perform any addition or subtraction calculations (from left to right). The part done first must have its significant digits noted before the next operation is performed because the rules for determining which digits are retained are different. 104 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Example 1.17 Find the result of each of the following calculations to the proper number of significant digits. a. 80.21 g  79.93 g 65.22 cm 3 b. (92.12 mL)(0.912 g/mL)  223.02 g 105 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Example 1.17 Solution Find the result of each of the following calculations to the proper number of significant digits. a. 80.21 g  79.93 g 0.28 g 0.0043 g/cm3 65.22 cm3 65.22 cm3   b. (92.12 mL)(0.912 g/mL)  223.02 g 84.01 g  233.02 g 307.0 g *The 1 in 84.01 is not significant, but is carried through to avoid rounding errors. 106 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Logarithms and Significant Digits The number of digits after the decimal point of log(x) should be equal to the number of significant figures log(3.510 ) 5.54 5 of x. For an inverse log of x (10x), the number of significant figures in the answer is equal to the number of digits after the decimal point in x. 10  3.421 3.7910 4 107 Interactive General Chemistry 2.0, © 2023 Macmillan Learning 1.6 Section Review (1 of 2) The precision that was used to make a measurement is reflected in the number of significant digits reported. The rules for significant digits in addition and subtraction are different from those in multiplication and division. Significant digits and decimal-place digits (such as the tenths place and hundredths place) are not the same. There is no necessary relationship between the two. 108 Interactive General Chemistry 2.0, © 2023 Macmillan Learning 1.6 Section Review (2 of 2) In general, calculators do not give the proper number of significant digits. All the digits in the coefficient of a number in scientific notation are significant. 109 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Section 1.7 Dimensional Analysis Use the units of a measurement as a guide in setting up calculations. 110 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Measurements Include Units Every measurement results in a number and a unit. Reporting the unit is just as important as reporting the number. Always use full spellings or standard abbreviations for all units. Units can provide a clue to which operation— multiplication or division—should be performed in calculations. 111 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Dimensional Analysis What are the total wages of a student who is paid $9  $9  per hour for 30 hours of work? total wages 30 h   $270  h time worked (in hours)hourly rate in dollars/hour total wages in dollars This method, dimensional analysis, treats units as algebraic quantities. 112 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Steps of Dimensional Analysis 1. Write down the quantity given or, occasionally, a ratio to be converted. 2. Multiply the quantity by one or more conversion factors (rates or ratios), which will change the units given to those required for the answer. The conversion factors may be given in the problem, or they may be constants of known value. 113 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Example 1.18 Convert 5445 min to hours. 114 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Example 1.18 Solution Convert 5445 min to hours.  1h  5445 min   90.75 h  60 min  115 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Example 1.19 Calculate the time required for a student aide to earn $378 at $9 per hour. 116 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Example 1.19 Solution Calculate the time required for a student aide to earn $378 at $9 per hour. 1h  378 dollars   42 h  9 dollars   117 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Example 1.20 How many meters are in: a. 5.200 km? b. 5.200 μm? 118 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Example 1.20a Solution How many meters are in: a. 5.200 km? The SI prefix k (kilo) = 103. 1 km = 103 m  103 m  5.200 km  5.20010 m 3  1 km  119 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Example 1.20b Solution How many meters are in: b. 5.200 μm? The SI prefix μ (micro) = 10−6. 1 μm = 10−6 m  10 6 m  5.200 m  5.20010 m 6  1 m  120 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Example 1.21 Calculate the number of seconds in 5.175 h. 121 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Example 1.21 Solution (1 of 3) Calculate the number of seconds in 5.175 h. Start by converting hours to minutes.  60 min  5.175 h   310.5 min  1h  122 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Example 1.21 Solution (2 of 3) Calculate the number of seconds in 5.175 h. Then, convert minutes to seconds.  60 s  310.5 min   18,630 s  1 min  123 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Example 1.21 Solution (3 of 3) Calculate the number of seconds in 5.175 h. These two steps can be combined into one calculation. 124 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Example 1.22 Convert 755 mm to inches. There are exactly 2.54 cm in 1 in. 125 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Example 1.22 Solution Convert 755 mm to inches. There are exactly 2.54 cm in 1 in.  1 m   102 cm   1 in  755 mm  3  29.7 in  10 mm   1 m   2.54 cm    126 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Example 1.23 Calculate the number of years it would take to spend $1 billion ($1,000,000,000) if you spent $1000 per day. 127 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Example 1.23 Solution Calculate the number of years it would take to spend $1 billion ($1,000,000,000) if you spent $1000 per day. Start by converting dollars to days. Then convert days to years. 128 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Example 1.24 A student is offered two summer jobs. Job A pays $500 per week, whereas job B pays $11.25 per hour. Both jobs are 40 h per week. Which job pays more money? 129 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Example 1.24 Solution (Option 1) A student is offered two summer jobs. Job A pays $500 per week, whereas job B pays $11.25 per hour. Both jobs are 40 h per week. Which job pays more money? Convert the units for job A into dollars per hour. $500 1 week $12.50 week 40 h 1h   Job A pays a higher dollars per hour wage. 130 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Example 1.24 Solution (Option 2) A student is offered two summer jobs. Job A pays $500 per week, whereas job B pays $11.25 per hour. Both jobs are 40 h per week. Which job pays more money? Convert the units for job B into dollars per week. $11.25 40 h $450 1h 1 week 1 week   Job A pays a higher dollars per week wage. 131 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Example 1.25 A cheetah can reach a top speed of 75 mph. Convert 75 mph to units of feet per second. Hint: There are 5280 ft in 1 mi. 132 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Example 1.25 Solution A cheetah can reach a top speed of 75 mph. Convert 75 mph to units of feet per second. Hint: There are 5280 ft in 1 mi. 133 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Example 1.26 Calculate the number of square feet, ft2, that are in 12.0 square yards, yd2. 134 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Example 1.26 Solution Calculate the number of square feet, ft2, that are in 12.0 square yards, yd2. There are 3 ft in 1 yd. Square this relationship to convert yd2 to ft2.  3 ft  2 12.0 yd  2  1 yd   9 ft 2 12.0 yd  2 108 ft 2    1 yd  2  135 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Example 1.27 Earth’s volume is 1.08 × 1012 km3. What is this volume in units of cubic centimeters? 136 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Example 1.27 Solution Earth’s volume is 1.08 × 1012 km3. What is this volume in units of cubic centimeters?  10 m   1 cm  3 3 3 1.0810 km  12 3 1.08 1027 cm3  1 km   10 m    2    137 Interactive General Chemistry 2.0, © 2023 Macmillan Learning 1.7 Section Review In dimensional analysis, units may be canceled like variables in algebra. Placing the units so that they cancel to give the desired units will help you set up the calculation correctly. Some conversion factors are constant, such as the number of cents in a dollar. Others are variable, such as the number of miles traveled by a car per hour, and these must be given in the problem. 138 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Section 1.8 Density Calculate density, volume, or mass when two of three values are given. Identify substances using density. 139 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Density (1 of 2) Density is a measure of how much mass something has relative to how much space it takes up (its volume). Objects that are less dense float in fluids that are denser. Weather is the result of air masses with different densities interacting with one another. Earthquakes result from the movement of Earth’s tectonic plates (less dense) as the crust floats on the moving mantle (more dense) beneath. 140 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Density (2 of 2) Density is defined as mass per unit volume. mass m density  d= volume V Density units include both mass and volume units, such as g/mL or g/cm3. Density values can be used as conversion factors between the mass and volume of an object. 141 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Example 1.28 a. Objects A and B have the same volume, but A has a greater mass. Which is denser? b. Objects C and D have the same mass, but C is larger. Which is denser? 142 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Example 1.28 Solution a. Objects A and B have the same volume, but A has a greater mass. Which is denser? Object A has more mass per unit volume. b. Objects C and D have the same mass, but C is larger. Which is denser? Object D has more mass per unit volume. 143 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Density Is an Intensive Property Because density is an intensive property, it is independent of the size of the sample. A large piece of aluminum and a small piece of aluminum have different masses and volumes but the same density. Density can be used to identify substances. 144 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Table 1.7 Densities of Some Common Substances at 25 Substance Density Substance Density (g/mL) (g/mL) Aluminum 2.70 Silver 10.5 Copper 8.96 Tin 7.26 Gold 19.3 Octane 0.7025 Iron 7.87 Salt (NaCl) 2.165 Lead 11.3 Sugar 1.56 Magnesium 1.74 (sucrose) Mercury 13.53 Water (at 0.997 25°C) Platinum 21.5 Water (at 4°C) 1.000 145 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Example 1.29 Calculate the mass of 41.0 mL of mercury (density = 13.53 g/mL). 146 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Example 1.29 Solution Calculate the mass of 41.0 mL of mercury (density = 13.53 g/mL).  13.53 g  41.0 mL   555 g  1 mL  147 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Example 1.30 Calculate the density of a piece of wood in a certain desk if its mass is 41.6 kg and its volume is 51.3 L. Give your answer in both kg/L and g/mL. Would this desk float in water? 148 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Example 1.30 Solution (1 of 2) Calculate the density of a piece of wood in a certain desk if its mass is 41.6 kg and its volume is 51.3 L. Give your answer in both kg/L and g/mL. Would this desk float in water? Calculate the density in kg/L first. m 41.6 kg d=  0.811 kg/L V 51.3 L 149 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Example 1.30 Solution (2 of 2) Calculate the density of a piece of wood in a certain desk if its mass is 41.6 kg and its volume is 51.3 L. Give your answer in both kg/L and g/mL. Would this desk float in water? Convert kg to g and L to mL to obtain the density in  0.811 kg   1 L   1000 g  g/mL.  0.811 g/mL  1 L   1000 mL   1 kg     The density of this wood is less than the density of water (1.0 g/mL), so it will float on water. 150 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Online Resource: Figure 1.18 - Density - Interactive Figure 1.20 Density Activity 151 Interactive General Chemistry 2.0, © 2023 Macmillan Learning 1.8 Section Review Density is equivalent to mass divided by volume. Mass and volume are measured, and density is calculated. Density may be used as a conversion factor, with either mass units or volume units in the numerator, to calculate the mass or volume of a sample. Density is an intensive property, so it can be used to identify substances. 152 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Section 1.9 Temperature Scales Distinguish among the Fahrenheit, Celsius, and Kelvin temperature scales. Convert temperature values between scales. 153 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Three Temperature Scales The three temperature scales in use in the United States are the Fahrenheit, Celsius, and Kelvin scales. On the Fahrenheit scale, water freezes at 32°F and boils at 212°F. On the Celsius scale, water freezes at 0°C and boils at 100°C. On the Kelvin scale, which is the SI scale, water freezes at 273.15 K and boils at 373.15 K. The coldest possible temperature is 0 K, absolute zero. 154 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Figure 1.21 Comparison of Temperature Scales 155 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Converting Between Temperature Scales To convert from degrees Fahrenheit (TF) to degrees Celsius (TC), or vice versa, use the following equations 5 TC  (TF  32) (the 32 is a definition and does not limit significant 9 digits in the calculation): 9 TF  TC  32 5 To convert from degrees Celsius to kelvins (TK or TK TC  273.15 just T), use the following equation: 156 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Example 1.31 What is 98.6°F (normal body temperature) on the Celsius scale? 157 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Example 1.31 Solution What is 98.6°F (normal body temperature) on the Celsius scale? Identify the appropriate conversion equation. 5 TC  (TF  32) 9 5 TC  (98.6 F 32) 37.0 C 9 158 Interactive General Chemistry 2.0, © 2023 Macmillan Learning 1.9 Section Review TF denotes a temperature given in degrees Fahrenheit, TC refers to degrees Celsius, and TK is a temperature given in kelvins. When units are not specified, assume that T means the Kelvin temperature. The following equations make it possible to convert among these 5 TC  (TF  32) three temperature scales: 9 9 TF  TC  32 5 TK TC  273.15 159 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Putting It Together Example 1.32 One hundred grams of pure solid substance X was heated for 1 h. Afterward, 56 g of a new solid Y was present, and 44 g of colorless gas Z was produced. None of substance X remained after heating. a. Is the original solid an element or a compound? b. Does the heating of the solid substance to produce less solid material and a gas describe a physical or chemical change in the original substance? c. The solid material present after the original substance was heated is light gray in color. Is the gray color a physical or chemical property of the material? 160 Interactive General Chemistry 2.0, © 2023 Macmillan Learning Putting It Together Example 1.32 Solution One hundred grams of pure solid substance X was heated for 1 h. Afterward, 56 g of a new solid Y was present, and 44 g of colorless gas Z was produced. None of substance X remained after heating. a. Is the original solid an element or a compound? compound b. Does the heating of the solid substance to produce less solid material and a gas describe a physical or chemical change in the original substance? chemical change c. The solid material present after the original substance was heated is light gray in color. Is the gray color a physical or chemical property of the material? 161 physical property Interactive General Chemistry 2.0, © 2023 Macmillan Learning