Spencer L. Seager Michael R. Slabaugh www.cengage.com/chemistry/seager Chapter 1: Matter, Measurements, and Calculations Part 1 Jennifer P. Harris MATTER & MASS • Matter is anything that has mass and occupies space. • Mass is a measurement of the amount of matter in an object. • Mass is independent of the location of an object. • An object on the earth has the same mass as the same object on the moon. WEIGHT • Weight is a measurement of the gravitational force acting on an object. • Weight depends on the location of an object. • An object weighing 1.0 lb on earth weighs about 0.17 lb on the moon. MEASUREMENTS & UNITS • Measurements consist of two parts, a number and a unit or label such as feet, pounds, or gallons. • Measurement units are agreed upon by those making and using the measurements. • Measurements are made using measuring devices (e.g. rulers, balances, graduated cylinders, etc.). METRIC SYSTEM • The metric system is a decimal system in which larger and smaller units are related by factors of 10. • TYPES OF METRIC SYSTEM UNITS • Basic or defined units [e.g. 1 meter (1 m)] are used to calculate derived units [e.g. 1 square meter (1 m2)]. THE USE OF PREFIXES • Prefixes are used to relate basic and derived units. • The common prefixes are given in the following table: TEMPERATURE SCALES • The three most commonly-used temperature scales are the Fahrenheit, Celsius and Kelvin scales. • The Celsius and Kelvin scales are used in scientific work. TEMPERATURE CONVERSIONS • Readings on one temperature scale can be converted to the other scales by using mathematical equations. • Converting Fahrenheit to Celsius. 5 C F 32 9 • Converting Celsius to Fahrenheit. 9 F C 32 5 • Converting Kelvin to Celsius. C K 273 • Converting Celsius to Kelvin. K C 273 TEMPERATURE CONVERSION PRACTICE • Covert 22°C and 54°C to Fahrenheit and Kelvin. 9 F 22 C 32 71.6 F 72 F 5 K 22 C 273 295 K 9 F 54 C 32 129.2 F 129 F 5 K 54 C 273 327 K COMMONLY USED METRIC UNITS SCIENTIFIC NOTATION • Scientific notation provides a convenient way to express very large or very small numbers. • Numbers written in scientific notation consist of a product of two parts in the form M x 10n, where M is a number between 1 and 10 (but not equal to 10) and n is a positive or negative whole number. • The number M is written with the decimal in the standard position. SCIENTIFIC NOTATION (continued) • STANDARD DECIMAL POSITION • The standard position for a decimal is to the right of the first nonzero digit in the number M. • SIGNIFICANCE OF THE EXPONENT n • A positive n value indicates the number of places to the right of the standard position that the original decimal position is located. • A negative n value indicates the number of places to the left of the standard position that the original decimal position is located. SCIENTIFIC NOTATION MULTIPLICATION • Multiply the M values (a and b) of each number to give a product represented by M'. • Add together the n values (y and z) of each number to give a sum represented by n'. • Write the final product as M' x 10n'. • Move decimal in M' to the standard position and adjust n' as necessary. a 10 b 10 a b10 3.0 10 4.0 10 3.0 4.0 10 y 8 yz z -2 12 10 6 1.2 10 7 ( 8 )( 2 ) SCIENTIFIC NOTATION DIVISION • Divide the M values (a and b) of each number to give a quotient represented by M'. • Subtract the denominator (bottom) n value (z) from the numerator (top) n value (y) to give a difference represented by n'. • Write the final quotient as M' x 10n'. • Move decimal in M' to the standard position and adjust n' as necessary. a 10 a 10 b 10 b y y-z z 3.0 10 3.0 10 4.0 10 4.0 8 (8) - (-2) -2 0.75 1010 7.5 10 9 SIGNIFICANT FIGURES • Significant figures are the numbers in a measurement that represent the certainty of the measurement, plus one number representing an estimate. • COUNTING ZEROS AS SIGNIFICANT FIGURES • Leading zeros are never significant figures. • Buried zeros are always significant figures. • Trailing zeros are generally significant figures. SIGNIFICANT FIGURES (continued) • The answer obtained by multiplication or division must contain the same number of significant figures (SF) as the quantity with the fewest number of significant figures used in the calculation. 4.325 4.5 19.4625 19 4 SF 2 SF 2 SF 4.325 4.5 0.961 0.96 4 SF 2 SF 2 SF SIGNIFICANT FIGURES (continued) • The answer obtained by addition or subtraction must contain the same number of places to the right of the decimal (prd) as the quantity in the calculation with the fewest number of places to the right of the decimal. 5.325 5.5 10.825 10.8 3 prd 1prd 1 prd 5.325 5.5 0.175 0.2 3 prd 1prd 1 prd ROUNDING RULES FOR NUMBERS • If the first of the nonsignificant figures to be dropped from an answer is 5 or greater, all the nonsignificant figures are dropped and the last remaining significant figure is increased by one. • If the first of the nonsignificant figures to be dropped from an answer is less than 5, all nonsignificant figures are dropped and the last remaining significant figure is left unchanged. Round 10.825 to 1 place to the right of the decimal. ⇒10.8 Round −0.175 to 1 place to the right of the decimal. ⇒ −0.2 EXACT NUMBERS • Exact numbers are numbers that have no uncertainty (they do not affect significant figures). • A number used as part of a defined relationship between quantities is an exact number (e.g. 100 cm = 1 m). • A counting number obtained by counting individual objects is an exact number (e.g. 1 dozen eggs = 12 eggs). • A reduced simple fraction is an exact number (e.g. 5/9 in equation to convert ºF to ºC). USING UNITS IN CALCULATIONS • The factor-unit method for solving numerical problems is a four-step systematic approach to problem solving. • Step 1: Write down the known or given quantity. Include both the numerical value and units of the quantity. • Step 2: Leave some working space and set the known quantity equal to the units of the unknown quantity. • Step 3: Multiply the known quantity by one or more factors, such that the units of the factor cancel the units of the known quantity and generate the units of the unknown quantity. • Step 4: After you generate the desired units of the unknown quantity, do the necessary arithmetic to produce the final numerical answer. SOURCES OF FACTORS • The factors used in the factor-unit method are fractions derived from fixed relationships between quantities. These relationships can be definitions or experimentally measured quantities. • An example of a definition that provides factors is the relationship between meters and centimeters: 1m = 100cm. This relationship yields two factors: 1m 100 cm and 100 cm 1m FACTOR UNIT METHOD EXAMPLES • A length of rope is measured to be 1834 cm. How many meters is this? • Solution: Write down the known quantity (1834 cm). Set the known quantity equal to the units of the unknown quantity (meters). Use the relationship between cm and m to write a factor (100 cm = 1 m), such that the units of the factor cancel the units of the known quantity (cm) and generate the units of the unknown quantity (m). Do the arithmetic to produce the final numerical answer. 1834 cm m 1m 1834 cm 18.34 m 100 cm PERCENTAGE • The word percentage means per one hundred. It is the number of items in a group of 100 such items. • PERCENTAGE CALCULATIONS • Percentages are calculated using the equation: part % 100 whole • In this equation, part represents the number of specific items included in the total number of items. EXAMPLE PERCENTAGE CALCULATION • A student counts the money she has left until pay day and finds she has $36.48. Before payday, she has to pay an outstanding bill of $15.67. What percentage of her money must be used to pay the bill? • Solution: Her total amount of money is $36.48, and the part is what she has to pay or $15.67. The percentage of her total is calculated as follows: part 15.67 % 100 100 42.96% whole 36.48 DENSITY • Density is the ratio of the mass of a sample of matter divided by the volume of the same sample. mass density volume or m d v DENSITY CALCULATION EXAMPLE • A 20.00 mL sample of liquid is put into an empty beaker that had a mass of 31.447 g. The beaker and contained liquid were weighed and had a mass of 55.891 g. Calculate the density of the liquid in g/mL. • Solution: The mass of the liquid is the difference between the mass of the beaker with contained liquid, and the mass of the empty beaker or 55.891g -31.447 g = 24.444 g. The density of the liquid is calculated as follows: m 24.444 g g d 1.222 v 20.00 mL mL PARTICULATE MODEL OF MATTER • All matter is made up of tiny particles called molecules and atoms. • MOLECULES • A molecule is the smallest particle of a pure substance that is capable of a stable independent existence. • ATOMS • Atoms are the particles that make up molecules. MOLECULE CLASSIFICATION • Diatomic molecules contain two atoms. • Triatomic molecules contain three atoms. • Polyatomic molecules contain more than three atoms. MOLECULE CLASSIFICATION (continued) • HOMOATOMIC MOLECULES • The atoms contained in homoatomic molecules are of the same kind. • HETEROATOMIC MOLECULES • The atoms contained in heteroatomic molecules are of two or more kinds. homoatomic heteroatomic MOLECULE CLASSIFICATION EXAMPLE • Classify the molecules in these diagrams using the terms diatomic, triatomic, or polyatomic molecules. • Solution: H2O2 is a polyatomic molecule, H2O is a triatomic molecule, and O2 is a diatomic molecule. • Classify the molecules using the terms homoatomic or heteroatomic molecules. • Solution: H2O2 and H2O are heteroatomic molecules and O2 is a homoatomic molecule. CLASSIFICATION OF MATTER • Matter can be classified into several categories based on chemical and physical properties. • PURE SUBSTANCES • Pure substances have a constant composition and a fixed set of other physical and chemical properties. • Example: pure water (always contains the same proportions of hydrogen and oxygen and freezes at a specific temperature) CLASSIFICATION OF MATTER (continued) • MIXTURES • Mixtures can vary in composition and properties. • Example: mixture of table sugar and water (can have different proportions of sugar and water) • A glass of water could contain one, two, three, etc. spoons of sugar. • Properties such as sweetness would be different for the mixtures with different proportions. HETEROGENEOUS MIXTURES • The properties of a sample of a heterogeneous mixture depends on the location from which the sample was taken. • A pizza pie is a heterogeneous mixture. A piece of crust has different properties than a piece of pepperoni taken from the same pie. HOMOGENEOUS MIXTURES • Homogeneous mixtures are also called solutions. The properties of a sample of a homogeneous mixture are the same regardless of where the sample was obtained from the mixture. • Samples taken from any part of a mixture made up of one spoon of sugar mixed with a glass of water will have the same properties, such as the same taste. PHYSICAL & CHEMICAL PROPERTIES AND CHANGES • PHYSICAL PROPERTIES OF MATTER • Can be observed or measured without attempting to change the composition of the matter being observed. • Examples: color, shape and mass • PHYSICAL CHANGES OF MATTER • Take place without a change in composition. • Examples: freezing, melting, or evaporation of a substance (e.g. water) • CHEMICAL PROPERTIES OF MATTER • Can be observed or measured only by attempting to change the matter into new substances. • Examples: flammability and the ability to react (e.g. when vinegar and baking soda are mixed) • CHEMICAL CHANGES OF MATTER • Always accompanied by a change in composition. • Examples: burning of paper and the fizzing of a mixture of vinegar and baking soda PARTICULATE MODEL OF MATTER • All matter is made up of tiny particles called molecules and atoms. • MOLECULES • A molecule is the smallest particle of a pure substance that is capable of a stable independent existence. • ATOMS • Atoms are the particles that make up molecules. MOLECULE CLASSIFICATION • Diatomic molecules contain two atoms. • Triatomic molecules contain three atoms. • Polyatomic molecules contain more than three atoms. MOLECULE CLASSIFICATION (continued) • HOMOATOMIC MOLECULES • The atoms contained in homoatomic molecules are of the same kind. • HETEROATOMIC MOLECULES • The atoms contained in heteroatomic molecules are of two or more kinds. homoatomic heteroatomic MOLECULE CLASSIFICATION EXAMPLE • Classify the molecules in these diagrams using the terms diatomic, triatomic, or polyatomic molecules. • Solution: H2O2 is a polyatomic molecule, H2O is a triatomic molecule, and O2 is a diatomic molecule. • Classify the molecules using the terms homoatomic or heteroatomic molecules. • Solution: H2O2 and H2O are heteroatomic molecules and O2 is a homoatomic molecule. ELEMENTS • Elements are pure substances that are made up of homoatomic molecules or individual atoms of the same kind. • Examples: oxygen gas made up of homoatomic molecules and copper metal made up of individual copper atoms COMPOUNDS • Compounds are pure substances that are made up of heteroatomic molecules or individual atoms (ions) of two or more different kinds. • Examples: pure water made up of heteroatomic molecules and table salt made up of sodium atoms (ions) and chlorine atoms (ions) MATTER CLASSIFICATION SUMMARY MATTER CLASSIFICATION EXAMPLE • Classify H2, F2, and HF using the classification scheme from the previous slide. • Solution: • H2, F2, and HF are all pure substances because they have a constant composition and a fixed set of physical and chemical properties. • H2 and F2 are elements because they are pure substances composed of homoatomic molecules. • HF is a compound because it is a pure substance composed of heteroatomic molecules.