Document Sample

Measurement and Calculation Chapter 2 Zumdahl's Introductory Chemistry - 1 Chapter 2 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 Zumdahl's Introductory Chemistry - 2 Chapter 2 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 Zumdahl's Introductory Chemistry - 3 Chapter 2 Writing Numbers in Scientific Notation 1 Locate the Decimal Point 2 Move the decimal point to the right of the non- zero 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 Zumdahl's Introductory Chemistry - 4 Chapter 2 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 Zumdahl's Introductory Chemistry - 5 Chapter 2 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 Zumdahl's Introductory Chemistry - 6 Chapter 2 Length • SI unit = meter (m) About 3› 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) Zumdahl's Introductory Chemistry - 7 Chapter 2 Volume • Measure of the amount of three-dimensional space occupied by a substance • SI unit = cubic meter (m3) • Commonly measure solid volume in cubic centimeters (cm3) 1 m3 = 106 cm3 1 cm3 = 10-6 m3 = 0.000001 m3 • Commonly measure liquid or gas volume in milliliters (mL) 1 L is slightly larger than 1 quart 1 L = 1 dL3 = 1000 mL = 103 mL 1 mL = 0.001 L = 10-3 L 1 mL = 1 cm3 Zumdahl's Introductory Chemistry - 8 Chapter 2 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 lbs. = 453.59 g 1 kg = 1000 g = 103 g, 1 g = 1000 mg = 103 mg 1 g = 0.001 kg = 10-3 kg, 1 mg = 0.001 g = 10-3 g Zumdahl's Introductory Chemistry - 9 Chapter 2 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 Zumdahl's Introductory Chemistry - 10 Chapter 2 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 Zumdahl's Introductory Chemistry - 11 Chapter 2 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 Zumdahl's Introductory Chemistry - 12 Chapter 2 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!! Zumdahl's Introductory Chemistry - 13 Chapter 2 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 Zumdahl's Introductory Chemistry - 14 Chapter 2 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 Zumdahl's Introductory Chemistry - 15 Chapter 2 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 0.200 cm = 0.90 cm2 2 sig figs 3 sig figs 2 sig figs Zumdahl's Introductory Chemistry - 16 Chapter 2 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 + 27.5 mL = 480 mL precise to 10’s place precise to 0.1’s place precise to 10’s place Zumdahl's Introductory Chemistry - 17 Chapter 2 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 give 2.54cm or 1in 1in 2.54cm Zumdahl's Introductory Chemistry - 18 Chapter 2 Problem Solving and Dimensional Analysis • 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 Zumdahl's Introductory Chemistry - 19 Chapter 2 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. Zumdahl's Introductory Chemistry - 20 Chapter 2 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! Zumdahl's Introductory Chemistry - 21 Chapter 2 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 Zumdahl's Introductory Chemistry - 22 Chapter 2 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/cm3 1 cm3 = 1 mL Mass • Liquids = g/mL Density • Gases = g/L Volume • Volume of a solid can be determined by water displacement • Density : solids > liquids >>> gases • In a heterogeneous mixture, denser object sinks Zumdahl's Introductory Chemistry - 23 Chapter 2 Using Density in Calculations Mass Density Volume Mass Volume Density Mass Density Volume Zumdahl's Introductory Chemistry - 24 Chapter 2

DOCUMENT INFO

Shared By:

Categories:

Tags:

Stats:

views: | 16 |

posted: | 3/29/2012 |

language: | |

pages: | 24 |

OTHER DOCS BY ert554898

How are you planning on using Docstoc?
BUSINESS
PERSONAL

By registering with docstoc.com you agree to our
privacy policy and
terms of service, and to receive content and offer notifications.

Docstoc is the premier online destination to start and grow small businesses. It hosts the best quality and widest selection of professional documents (over 20 million) and resources including expert videos, articles and productivity tools to make every small business better.

Search or Browse for any specific document or resource you need for your business. Or explore our curated resources for Starting a Business, Growing a Business or for Professional Development.

Feel free to Contact Us with any questions you might have.