General, Organic, and Biological ChemistryCopyright © 2010 Pearson Education, Inc.1 Chapter 1 Measurements 1.1 Units of Measurement

General, Organic, and Biological ChemistryCopyright © 2010 Pearson Education, Inc.2 Measurement in Chemistry In chemistry, we  measure quantities  do experiments  calculate results  use numbers to report measurements  compare results to standards

General, Organic, and Biological ChemistryCopyright © 2010 Pearson Education, Inc.3 Stating a Measurement In every measurement, a number is followed by a unit. Observe the following examples of measurements: Number and Unit 35 m 0.25 L 225 lb 3.4 h

General, Organic, and Biological ChemistryCopyright © 2010 Pearson Education, Inc.4 The Metric System (SI) The metric system and SI (international system) are  related decimal systems based on 10  used in most of the world  used everywhere by scientists

General, Organic, and Biological ChemistryCopyright © 2010 Pearson Education, Inc.5 Units in the Metric System In the metric and SI systems, one unit is used for each type of measurement: MeasurementMetricSI Lengthmeter (m)meter (m) Volumeliter (L)cubic meter (m 3 ) Massgram (g)kilogram (kg) Timesecond (s)second (s) TemperatureCelsius (  C)Kelvin (K)

General, Organic, and Biological ChemistryCopyright © 2010 Pearson Education, Inc.6 Length Measurement Length  is measured using a meter stick  uses the unit meter (m) in both the metric and SI systems

General, Organic, and Biological ChemistryCopyright © 2010 Pearson Education, Inc.7 Inches and Centimeters The unit of an inch  is equal to exactly 2.54 centimeters in the metric (SI) system 1 in. = 2.54 cm

General, Organic, and Biological ChemistryCopyright © 2010 Pearson Education, Inc.8 Volume Measurement Volume  is the space occupied by a substance  uses the unit liter (L) in the metric system 1 L = 1.06 qt  uses the unit cubic meter (m 3 ) in the SI system  is measured using a graduated cylinder

General, Organic, and Biological ChemistryCopyright © 2010 Pearson Education, Inc.9 Mass Measurement The mass of an object  is a measure of the quantity of material it contains  is measured on a balance  uses the unit gram (g) in the metric system  uses the unit kilogram (kg) in the SI system

General, Organic, and Biological ChemistryCopyright © 2010 Pearson Education, Inc. 10 Temperature Measurement The temperature  indicates how hot or cold a substance is  is measured on the Celsius (  C) scale in the metric system  in the SI system uses the Kelvin (K) scale  on this thermometer is 18 °C or 64 °F.

General, Organic, and Biological ChemistryCopyright © 2010 Pearson Education, Inc.11 Time Measurement Time measurement  uses the unit second (s) in both the metric and SI systems.  is based on an atomic clock that uses a frequency emitted by cesium atoms

General, Organic, and Biological ChemistryCopyright © 2010 Pearson Education, Inc Scientific Notation Scientific notation  is used to write very large or very small numbers  for the width of a human hair ( m) is written 8 x m  for a large number such as s is written 4.5 x 10 6 s

General, Organic, and Biological ChemistryCopyright © 2010 Pearson Education, Inc.13 Writing Numbers in Scientific Notation  A number in scientific notation contains a coefficient and a power of 10. coefficient power of ten coefficient power of ten 1.5 x x  To write a number in scientific notation, the decimal point is placed after the first digit.  The spaces moved are shown as a power of ten = 5.2 x = 3.78 x spaces left 3 spaces right

General, Organic, and Biological ChemistryCopyright © 2010 Pearson Education, Inc.14 Some Powers of Ten

General, Organic, and Biological ChemistryCopyright © 2010 Pearson Education, Inc.15 Comparing Numbers in Standard and Scientific Notation Here are some numbers written in standard format and in scientific notation. Number in Standard Format Scientific Notation Diameter of the Earth m1.28 x 10 7 m Mass of a human 68 kg 6.8 x 10 1 kg Length of a virus cm3 x cm

General, Organic, and Biological ChemistryCopyright © 2010 Pearson Education, Inc Measured Numbers A measuring tool  is used to determine a quantity such as height or the mass of an object  provides numbers for a measurement called measured numbers

General, Organic, and Biological ChemistryCopyright © 2010 Pearson Education, Inc.17. l l.... l l.... l 4.. cm Reading a Meter Stick  The markings on the meter stick at the end of the blue line are read as The first digit 2 plus the second digit 2.7  The last digit is obtained by estimating.  The end of the line might be estimated between 2.7 and 2.8 as 0.05 or 0.06, which gives a reported length of 2.75 cm or 2.76 cm.

General, Organic, and Biological ChemistryCopyright © 2010 Pearson Education, Inc.18 Known + Estimated Digits In the length reported as 2.76 cm:  The digits 2 and 7 are certain (known).  The final digit 6 was estimated (uncertain).  All three digits (2.76) are significant, including the estimated digit.

General, Organic, and Biological ChemistryCopyright © 2010 Pearson Education, Inc.19  For this measurement, the first and second known digits are 4.5.  Because the line ends on a mark, the estimated digit in the hundredths place is 0.  This measurement is reported as 4.50 cm. Zero as a Measured Number. l l.... l l.... l 5.. cm

General, Organic, and Biological ChemistryCopyright © 2010 Pearson Education, Inc.20 Significant Figures in Measured Numbers Significant figures  Significant figures obtained from a measurement include all of the known digits plus the estimated digit.  The number of significant figures reported in a measurement depends on the measuring tool.

General, Organic, and Biological ChemistryCopyright © 2010 Pearson Education, Inc.21 Significant Figures

General, Organic, and Biological ChemistryCopyright © 2010 Pearson Education, Inc.22 Significant Figures in Scientific Notation In scientific notation:  All digits, including zeros in the coefficient, are significant. Scientific NotationNumber of Significant Figures___________ 8 x 10 4 m1 8.0 x 10 4 m x 10 4 m3

General, Organic, and Biological ChemistryCopyright © 2010 Pearson Education, Inc.23 Examples of Exact Numbers

General, Organic, and Biological ChemistryCopyright © 2010 Pearson Education, Inc.24 Rounding Off Calculated Answers  When the first digit dropped is 4 or less, the retained numbers remain the same. To round to 3 significant figures drop the digits 32 = 45.8  When the first digit dropped is 5 or greater, the last retained digit is increased by 1. To round to 2 significant figures drop the digits 884 = 2.5 (increase by 0.1)

General, Organic, and Biological ChemistryCopyright © 2010 Pearson Education, Inc.25 Adding Significant Zeros  Sometimes a calculated answer requires more significant digits. Then one or more zeros are added. Calculated answerZeros added to give 3 significant figures

General, Organic, and Biological ChemistryCopyright © 2010 Pearson Education, Inc.26 When multiplying or dividing use  the same number of significant figures (SF) as the measurement with the fewest significant figures  rounding rules to obtain the correct number of significant figures Example: x = = 5.3 (rounded) 4SFs 2SFs calculator 2SFs Multiplication and Division

General, Organic, and Biological ChemistryCopyright © 2010 Pearson Education, Inc.27 When adding or subtracting, use  the same number of decimal places as the measurement with the fewest decimal places  rounding rules to adjust the number of digits in the answer 25.2 one decimal place two decimal places 26.54calculated answer 26.5 final answer (with one decimal place) Addition and Subtraction

General, Organic, and Biological ChemistryCopyright © 2010 Pearson Education, Inc Prefixes A prefix  in front of a unit increases or decreases the size of that unit  makes units larger or smaller than the initial unit by one or more factors of 10  indicates a numerical value PrefixValue 1 kilometer=1000 meters 1 kilogram=1000 grams

General, Organic, and Biological ChemistryCopyright © 2010 Pearson Education, Inc.29 Metric and SI Prefixes (continued)

General, Organic, and Biological ChemistryCopyright © 2010 Pearson Education, Inc.30 An equality  states the same measurement in two different units  can be written using the relationships between two metric units Example: 1 meter is the same as 100 cm and 1000 mm. 1 m = 100 cm 1 m = 1000 mm Metric Equalities

General, Organic, and Biological ChemistryCopyright © 2010 Pearson Education, Inc Exact and Measured Numbers in Equalities Equalities between units of  the same system are definitions with numbers that are exact  different systems (metric and U.S.) are measurements with numbers that are significant figures

General, Organic, and Biological ChemistryCopyright © 2010 Pearson Education, Inc.32 A conversion factor  is a fraction obtained from an equality Equality: 1 in. = 2.54 cm  is written as a ratio with a numerator and denominator  can be inverted to give two conversion factors for every equality 1 in. and 2.54 cm 2.54 cm 1 in. Conversion Factors

General, Organic, and Biological ChemistryCopyright © 2010 Pearson Education, Inc.33 A conversion factor  may be obtained from information in a word problem  is written for that problem only Example 1: The price of one pound (1 lb) of red peppers is $ lb red peppers and$1.39 $1.391 lb red peppers Example 2: The cost of one gallon (1 gal) of gas is $ gallon of gasand $2.25 $2.251 gallon of gas Conversion Factors in a Problem

General, Organic, and Biological ChemistryCopyright © 2010 Pearson Education, Inc.34 A percent factor  gives the ratio of the parts to the whole % =Parts x 100% Whole  uses the same units for the parts and whole  uses the value 100  can be written as two factors Example: A food contains 18% (by mass) fat. 18 g fat and100 g food 100 g food18 g fat Percent as a Conversion Factor

General, Organic, and Biological ChemistryCopyright © 2010 Pearson Education, Inc.35 Percent Factor in a Problem The thickness of the skin fold at the waist indicates 11% body fat. What percent factors can be written for body fat using kg? Percent factors using kg 11 kg fat and 100 kg mass 100 kg mass11 kg fat

General, Organic, and Biological ChemistryCopyright © 2010 Pearson Education, Inc.36 Chapter 1 Measurements 1.7 Problem Solving

General, Organic, and Biological ChemistryCopyright © 2010 Pearson Education, Inc.37 To solve a problem  Identify the given unit.  Identify the needed unit. Problem: A person has a height of 2.0 meters. What is that height in inches? The given unit is meters (the unit of height). given unit = meters (m) The needed unit is inches (for the answer). needed unit = inches (in.) Initial and Final Units

General, Organic, and Biological ChemistryCopyright © 2010 Pearson Education, Inc.38  Write the given and needed units.  Write a unit plan to convert the given unit to the needed unit.  Write equalities and conversion factors.  Use conversion factors to cancel the given unit and provide the needed unit. Unit 1 x Unit 2 = Unit 2 Unit 1 Given x Conversion= Needed unit factor unit Problem Setup

General, Organic, and Biological ChemistryCopyright © 2010 Pearson Education, Inc.39 Guide to Problem Solving The steps in the Guide to Problem Solving are useful in setting up a problem with conversion factors.

General, Organic, and Biological ChemistryCopyright © 2010 Pearson Education, Inc.40 Setting up a Problem How many minutes are 2.5 h? Given unit = 2.5 h Needed unit =? min Plan =h min Set up problem to cancel hours (h). Given Conversion Needed unit factor unit 2.5 h x 60 min = 150 min (2 SF) 1 h

General, Organic, and Biological ChemistryCopyright © 2010 Pearson Education, Inc.41  Often, two or more conversion factors are required to obtain the unit needed for the answer. Unit 1 Unit 2 Unit 3  Additional conversion factors are placed in the setup to cancel each preceding unit. Given unit x factor 1 x factor 2 = Needed unit Unit 1 x Unit 2 x Unit 3 = Unit 3 Unit 1 Unit 2 Using Two or More Factors

General, Organic, and Biological ChemistryCopyright © 2010 Pearson Education, Inc.42 How many minutes are in 1.6 days? Given unit: days Needed unit: min Factor 1 Factor 2 Plan: days h min Set up problem: 1.6 days x 24 h x 60 min = 2300 = 2.3 x 10 3 min 1 day 1 h 2 SFs Exact Exact = 2 SFs Example: Problem Solving

General, Organic, and Biological ChemistryCopyright © 2010 Pearson Education, Inc.43  Be sure to check your unit cancellation in the setup.  The units in the conversion factors must cancel to give the correct unit for the answer. Example: What is wrong with the following setup? 1.4 day x 1 day x 1 h 24 h 60 min Units = day 2 /min, which is not the unit needed Units don’t cancel properly. Therefore, setup is wrong. Check the Unit Cancellation

General, Organic, and Biological ChemistryCopyright © 2010 Pearson Education, Inc.44 Guide to Problem Solving What is 165 lb in kg? STEP 1 Given: 165 lb Need: kg STEP 2 Plan: lb kg STEP 3 Equalities/conversion factors: 1 kg = 2.20 lb 2.20 lb and 1 kg 1 kg 2.20 lb STEP 4 Set up problem: 165 lb x 1 kg = 74.8 kg (3SF) 2.20 lb

General, Organic, and Biological ChemistryCopyright © 2010 Pearson Education, Inc.45 Percent Factor in a Problem If the thickness of the skin fold at the waist indicates an 11% body fat, how much fat is in a person with a mass of 86 kg? 11% body fat, 11 kg fat 100 kg percent factor 86 kg x 11 kg fat = 9.5 kg of fat 100 kg

General, Organic, and Biological ChemistryCopyright © 2010 Pearson Education, Inc.46 Density  compares the mass of an object to its volume  is the mass of a substance divided by its volume Density expression: D = mass = g or g = g/cm 3 volume mL cm 3 Note: 1 mL = 1 cm Density

General, Organic, and Biological ChemistryCopyright © 2010 Pearson Education, Inc.47 Volume by Displacement  A solid completely submerged in water displaces its own volume of water.  The volume of the solid is calculated from the volume difference mL – 35.5 mL = 9.5 mL = 9.5 cm 3

General, Organic, and Biological ChemistryCopyright © 2010 Pearson Education, Inc.48 Density Using Volume Displacement The density of the zinc object is calculated from its mass and volume. mass = g = 7.2 g/cm 3 volume 9.5 cm 3

General, Organic, and Biological ChemistryCopyright © 2010 Pearson Education, Inc.49 Sink or Float  Ice floats in water because the density of ice is less than the density of water.  Aluminum sinks in water because its density is greater than the density of water.