Slide 1: Introductory Chemistry: A Foundation, 6th Ed. Introductory Chemistry, 6th Ed. Basic Chemistry, 6th Ed. by Steven S. Zumdahl, Donald J. DeCoste University of Illinois
Slide 2: Chapter 2 Measurements and Calculations
Slide 3: Measurement • Quantitative observation • Comparison based on an accepted scale – e.g. Meter stick • Has 2 parts – number and unit – Number tells comparison – Unit tells scale Copyright © Houghton Mifflin Company. All rights reserved. 2|3
Slide 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 © Houghton Mifflin Company. All rights reserved. 2|4
Slide 5: Writing Numbers in Scientific Notation 1 Locate the decimal point 2 Move the decimal point to the right of the nonzero digit in the largest place – The new number is now between 1 and 10 3 Multiply the new number by 10n – Where n is the number of places you moved the decimal point 4 Determine 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 © Houghton Mifflin Company. All rights reserved. 2|5
Slide 6: Writing Numbers in Standard Form 1 Determine the sign of n of 10n – If n is + the decimal point will move to the right – If n is – the decimal point will move to the left 2 Determine the value of the exponent of 10 – Tells the number of places to move the decimal point 3 Move the decimal point and rewrite the number Copyright © Houghton Mifflin Company. All rights reserved. 2|6
Slide 7: Related Units in the Metric System • All units in the metric system are related to the fundamental unit by a power of 10 • Power of 10 is indicated by a prefix • Prefixes are always the same, regardless of the fundamental unit Copyright © Houghton Mifflin Company. All rights reserved. 2|7
Slide 8: Some Fundamental SI Units Copyright © Houghton Mifflin Company. All rights reserved. 2|8
Slide 9: Prefixes • All units in the metric system utilize the same prefixes Copyright © Houghton Mifflin Company. All rights reserved. 2|9
Slide 10: Length Copyright © Houghton Mifflin Company. All rights reserved. 2 | 10
Slide 11: Volume • Measure of the amount of 3-D space occupied by a substance • SI unit = cubic meter (m3) • Commonly measure solid volume in cubic centimeters (cm3) • 1 mL = 1 cm3 Copyright © Houghton Mifflin Company. All rights reserved. 2 | 11
Slide 12: 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 = 2.2046 pounds, 1 lb = 453.59 g Copyright © Houghton Mifflin Company. All rights reserved. 2 | 12
Slide 13: 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 © Houghton Mifflin Company. All rights reserved. 2 | 13
Slide 14: Reporting Measurements • Significant figures: system used by scientists to indicate the uncertainty of a single measurement • Last digit written in a measurement is the number that is considered uncertain • Unless stated otherwise, uncertainty in the last digit is ±1 Copyright © Houghton Mifflin Company. All rights reserved. 2 | 14
Slide 15: 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 © Houghton Mifflin Company. All rights reserved. 2 | 15
Slide 16: 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, then round off • Don’t forget to add place-holding zeros if necessary to keep value the same!! Copyright © Houghton Mifflin Company. All rights reserved. 2 | 16
Slide 17: Exact Numbers • Exact numbers: numbers known with certainty – Counting numbers • number of sides on a square – Defined numbers • 100 cm = 1 m, 12 in = 1 ft, 1 in = 2.54 cm • 1 minute = 60 seconds • Have unlimited number of significant figures Copyright © Houghton Mifflin Company. All rights reserved. 2 | 17
Slide 18: 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 a calculation Copyright © Houghton Mifflin Company. All rights reserved. 2 | 18
Slide 19: 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 Copyright © Houghton Mifflin Company. All rights reserved. 2 | 19
Slide 20: Multiplication/Division with Significant Figures (cont.) • Then 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 0.200 cm = 2 sig figs 3 sig figs 2 sig figs 0.90 cm2 Copyright © Houghton Mifflin Company. All rights reserved. 2 | 20
Slide 21: 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” Copyright © Houghton Mifflin Company. All rights reserved. 2 | 21
Slide 22: Adding/Subtracting Numbers with Significant Figures (cont.) • Then round answer to the same decimal place 450 mL + 27.5 mL = 480 mL precise to 10’s place precise to 0.1’s place precise to 10’s place Copyright © Houghton Mifflin Company. All rights reserved. 2 | 22
Slide 23: Problem Solving and Dimensional Analysis • Many problems in chemistry involve using equivalence statements to convert one unit of measurement to another • Conversion factor = relationship between two units – May be exact or measured – Both parts of the conversion factor should have the same number of significant figures Copyright © Houghton Mifflin Company. All rights reserved. 2 | 23
Slide 24: Problem Solving and Dimensional Analysis (cont.) • Conversion factors generated from equivalence statements 2.54cm – e.g. 1 inch = 2.54 cm can give 1in 1in or 2.54cm Copyright © Houghton Mifflin Company. All rights reserved. 2 | 24
Slide 25: Problem Solving and Dimensional Analysis (cont.) • 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 Copyright © Houghton Mifflin Company. All rights reserved. 2 | 25
Slide 26: Converting One Unit to Another • Find the relationship(s) between starting and goal units. Write equivalence statement for each relationship. • Write a conversion factor for each equivalence statement. • Arrange the conversion factor(s) to cancel with starting unit and result in goal unit. Copyright © Houghton Mifflin Company. All rights reserved. 2 | 26
Slide 27: Converting One Unit to Another (cont.) • Check that units cancel properly • Multiply and divide the numbers to give the answer with the proper unit. • Check significant figures • Check that your answer makes sense! Copyright © Houghton Mifflin Company. All rights reserved. 2 | 27
Slide 28: Temperature Scales Copyright © Houghton Mifflin Company. All rights reserved. 2 | 28
Slide 29: Density • Density = property of matter representing the mass per unit volume Mass Density  Volume • Volume of a solid can be determined by water displacement Copyright © Houghton Mifflin Company. All rights reserved. 2 | 29
Slide 30: Density (cont.) Copyright © Houghton Mifflin Company. All rights reserved. 2 | 30
Slide 31: Using Density in Calculations Mass Density  Volume Mass Volume  Density Mass  Density  Volume Copyright © Houghton Mifflin Company. All rights reserved. 2 | 31