Copyright©2004 by Houghton Mifflin Company. All rights reserved 1 Introductory Chemistry: A Foundation FIFTH EDITION by Steven S. Zumdahl University of Illinois

Copyright©2004 by Houghton Mifflin Company. All rights reserved 2 Measurements and Calculations Chapter 2

Copyright©2004 by Houghton Mifflin Company. All rights reserved 3 Measurement Quantitative Observation Comparison Based on an Accepted Scale –e.g. Meter Stick Has 2 Parts – the Number and the Unit –Number Tells Comparison –Unit Tells Scale

Copyright©2004 by Houghton Mifflin Company. All rights reserved 4 Scientific Notation Technique Used to Express Very Large or Very Small Numbers Based on Powers of 10 To Compare Numbers Written in Scientific Notation –First Compare Exponents of 10 –Then Compare Numbers

Copyright©2004 by Houghton Mifflin Company. All rights reserved 5 Writing Numbers in Scientific Notation 1Locate the Decimal Point 2Move the decimal point to the right of the non- zero digit in the largest place –The new number is now between 1 and 10 3Multiply the new number by 10 n –where n is the number of places you moved the decimal point 4Determine the sign on the exponent n –If the decimal point was moved left, n is + –If the decimal point was moved right, n is – –If the decimal point was not moved, n is 0

Copyright©2004 by Houghton Mifflin Company. All rights reserved 6 Writing Numbers in Standard Form 1Determine the sign of n of 10 n –If n is + the decimal point will move to the right –If n is – the decimal point will move to the left 2Determine the value of the exponent of 10 –Tells the number of places to move the decimal point 3Move the decimal point and rewrite the number

Copyright©2004 by Houghton Mifflin Company. All rights reserved 7 Related Units in the Metric System All units in the metric system are related to the fundamental unit by a power of 10 The power of 10 is indicated by a prefix The prefixes are always the same, regardless of the fundamental unit

Copyright©2004 by Houghton Mifflin Company. All rights reserved 8 Length SI unit = meter (m) –About 3½ inches longer than a yard 1 meter = one ten-millionth the distance from the North Pole to the Equator = distance between marks on standard metal rod in a Paris vault = distance covered by a certain number of wavelengths of a special color of light Commonly use centimeters (cm) –1 m = 100 cm –1 cm = 0.01 m = 10 mm –1 inch = 2.54 cm (exactly)

Copyright©2004 by Houghton Mifflin Company. All rights reserved 9 Volume Measure of the amount of three-dimensional space occupied by a substance SI unit = cubic meter (m 3 ) Commonly measure solid volume in cubic centimeters (cm 3 ) –1 m 3 = 10 6 cm 3 –1 cm 3 = m 3 = m 3 Commonly measure liquid or gas volume in milliliters (mL) –1 L is slightly larger than 1 quart –1 L = 1 dL 3 = 1000 mL = 10 3 mL –1 mL = L = L –1 mL = 1 cm 3

Copyright©2004 by Houghton Mifflin Company. All rights reserved 10 Mass Measure of the amount of matter present in an object SI unit = kilogram (kg) Commonly measure mass in grams (g) or milligrams (mg) –1 kg = pounds, 1 lbs.. = g –1 kg = 1000 g = 10 3 g, 1 g = 1000 mg = 10 3 mg –1 g = kg = kg, 1 mg = g = g

Copyright©2004 by Houghton Mifflin Company. All rights reserved 11 Uncertainty in Measured Numbers A measurement always has some amount of uncertainty Uncertainty comes from limitations of the techniques used for comparison To understand how reliable a measurement is, we need to understand the limitations of the measurement

Copyright©2004 by Houghton Mifflin Company. All rights reserved 12 Reporting Measurements To indicate the uncertainty of a single measurement scientists use a system called significant figures The last digit written in a measurement is the number that is considered to be uncertain Unless stated otherwise, the uncertainty in the last digit is ±1

Copyright©2004 by Houghton Mifflin Company. All rights reserved 13 Rules for Counting Significant Figures Nonzero integers are always significant Zeros –Leading zeros never count as significant figures –Captive zeros are always significant –Trailing zeros are significant if the number has a decimal point Exact numbers have an unlimited number of significant figures

Copyright©2004 by Houghton Mifflin Company. All rights reserved 14 Rules for Rounding Off If the digit to be removed is less than 5, the preceding digit stays the same is equal to or greater than 5, the preceding digit is increased by 1 In a series of calculations, carry the extra digits to the final result and then round off Don’t forget to add place-holding zeros if necessary to keep value the same!!

Copyright©2004 by Houghton Mifflin Company. All rights reserved 15 Exact Numbers Exact Numbers are numbers known with certainty Unlimited number of significant figures They are either –counting numbers number of sides on a square –or defined 100 cm = 1 m, 12 in = 1 ft, 1 in = 2.54 cm 1 kg = 1000 g, 1 LB = 16 oz 1000 mL = 1 L; 1 gal = 4 qts. 1 minute = 60 seconds

Copyright©2004 by Houghton Mifflin Company. All rights reserved 16 Calculations with Significant Figures Calculators/computers do not know about significant figures!!! Exact numbers do not affect the number of significant figures in an answer Answers to calculations must be rounded to the proper number of significant figures –round at the end of the calculation

Copyright©2004 by Houghton Mifflin Company. All rights reserved 17 Multiplication/Division with Significant Figures Result has the same number of significant figures as the measurement with the smallest number of significant figures Count the number of significant figures in each measurement Round the result so it has the same number of significant figures as the measurement with the smallest number of significant figures 4.5 cm x cm = 0.90 cm 2 2 sig figs3 sig figs 2 sig figs

Copyright©2004 by Houghton Mifflin Company. All rights reserved 18 Adding/Subtracting Numbers with Significant Figures Result is limited by the number with the smallest number of significant decimal places Find last significant figure in each measurement Find which one is “left-most” Round answer to the same decimal place 450 mL mL = 480 mL precise to 10’s placeprecise to 0.1’s placeprecise to 10’s place

Copyright©2004 by Houghton Mifflin Company. All rights reserved 19 Problem Solving and Dimensional Analysis Many problems in chemistry involve using equivalence statements to convert one unit of measurement to another Conversion factors are relationships between two units –May be exact or measured –Both parts of the conversion factor should have the same number of significant figures Conversion factors generated from equivalence statements –e.g. 1 inch = 2.54 cm can giveor

Copyright©2004 by Houghton Mifflin Company. All rights reserved 20 Arrange conversion factors so starting unit cancels –Arrange conversion factor so starting unit is on the bottom of the conversion factor May string conversion factors Problem Solving and Dimensional Analysis

Copyright©2004 by Houghton Mifflin Company. All rights reserved 21 Converting One Unit to Another Find the relationship(s) between the starting and goal units. Write an equivalence statement for each relationship. Write a conversion factor for each equivalence statement. Arrange the conversion factor(s) to cancel starting unit and result in goal unit.

Copyright©2004 by Houghton Mifflin Company. All rights reserved 22 Converting One Unit to Another Check that the units cancel properly Multiply and Divide the numbers to give the answer with the proper unit. Check your significant figures Check that your answer makes sense!

Copyright©2004 by Houghton Mifflin Company. All rights reserved 23 Temperature Scales Fahrenheit Scale, °F –Water’s freezing point = 32°F, boiling point = 212°F Celsius Scale, °C –Temperature unit larger than the Fahrenheit –Water’s freezing point = 0°C, boiling point = 100°C Kelvin Scale, K –Temperature unit same size as Celsius –Water’s freezing point = 273 K, boiling point = 373 K

Copyright©2004 by Houghton Mifflin Company. All rights reserved 24 Density Density is a property of matter representing the mass per unit volume For equal volumes, denser object has larger mass For equal masses, denser object has small volume Solids = g/cm 3 –1 cm 3 = 1 mL Liquids = g/mL Gases = g/L Volume of a solid can be determined by water displacement Density : solids > liquids >>> gases In a heterogeneous mixture, denser object sinks

Copyright©2004 by Houghton Mifflin Company. All rights reserved 25 Using Density in Calculations