Foundations of College Chemistry PDF

Foundations of College Chemistry Fifteenth Edition Morris Hein, Susan Arena, and Cary Willard Chapter 2 Standards for Measurement This slide deck contains animations. Please disable animations if they cause issues with your device. Standards...

Foundations of College Chemistry Fifteenth Edition Morris Hein, Susan Arena, and Cary Willard Chapter 2 Standards for Measurement This slide deck contains animations. Please disable animations if they cause issues with your device. Standards for Measurement Careful and accurate measurements of ingredients are important both when cooking and in the chemistry laboratory! Copyright ©2016 John Wiley & Sons, Inc. 2  Chapter Outline 2.1 Scientific Notation 2.2 Measurement and Uncertainty 2.3 Significant Figures Rounding Off Numbers 2.4 Significant Figures in Calculations Addition or Subtraction, Multiplication or Division 2.5 The Metric System Measurement of Length, mass, volume 2.6 Dimensional Analysis: A Problem-Solving Method 2.7 Percent 2.8 Measurement of Temperature 2.9 Density Copyright ©2016 John Wiley & Sons, Inc. 3  Learning Objectives 2.1 Scientific Notation-Write decimal numbers in scientific notation. 2.2 Measurement and Uncertainty-Explain the significance of uncertainty in measurements in chemistry and how significant figures are used to indicate a measurement’s certainty. 2.3 Significant Figures-Determine the number of significant figures in a given measurement and round measurements to a specific number of significant figures. 2.4 Significant Figures in Calculations-Apply the rules for significant figures in calculations involving addition, subtraction, multiplication, and division. 2.5 The Metric System-Name the units for mass, length, and volume in the metric system and convert from one unit to another. 2.6 Dimensional Analysis: A Problem -Solving Method-Use dimensional analysis to solve problems involving unit conversions. 2.7 Percent-Solve problems involving percent. 2.8 Measurement of Temperature-Convert measurements among the Fahrenheit, Celsius and Kelvin temperature scales. 2.9 Density-Solve problems involving density. Copyright ©2016 John Wiley & Sons, Inc. 4 2.1 Scientific Notation Scientific Notation: A way to write very large or small numbers (measurements) in a compact form. Method for Writing a Number in Scientific Notation 1. Move the decimal point in the original number so that it is located after the first nonzero digit. 2. Multiply this number by 10 raised to the number of places the decimal point was moved. 3. Exponent sign indicates which direction the decimal was moved. Copyright ©2016 John Wiley & Sons, Inc. 5 Scientific Notation Practice 1) Write 0.000423 in scientific notation. −4 4.23 ×10 2) What is the correct scientific notation for the number 353,000 (to 3 significant figures)? a. 35.3 x 104 b. 3.53 x 105 c. 0.353 x 106 d. 3.53 x 10 -5 Copyright ©2016 John Wiley & Sons, Inc. 6 2.2 Measurement and Uncertainty Measurement: A quantitative observation. Examples: 1 cup, 3 eggs, 5 molecules, etc. Measurements are expressed by 1. a numerical value and 2. a unit of the measurement. A measurement always requires a unit. Copyright ©2016 John Wiley & Sons, Inc. 7 Measurement and Uncertainty (1 of 2) Numerical values obtained from measurements are never exact values. Uncertainty exists in the last digit of the measurement. The other digits are certain. Because of this level of uncertainty, any measurement is expressed by a limited number of digits, significant 21.0 degrees 22.11 degrees figures. Celsius (℃) Celsius (℃) Copyright ©2016 John Wiley & Sons, Inc. 8 Measurement and Uncertainty By convention, a measurement typically includes all certain digits plus one digit that is estimated. Ex. 20.6 mL 3 Sig. Fig. Copyright ©2016 John Wiley & Sons, Inc. 9 2.3 Rules for Counting Significant Figures 1. All nonzero digits are significant. 2. Zeroes are significant when: They are in between nonzero digits Ex. 75.04 has 4 significant figures (7,5,0 and 4) They are at the end of a number after a decimal point. Ex. 32.410 has five significant figures (3,2,4,1 and 0) 3. Zeroes are not significant when: They appear before the first nonzero digit. Ex. 0.00321 has three significant figures (3,2 and 1) They appear at the end of a number without a decimal point. Ex. 6920 has three significant figures (6,9 and 2) 4. Exact numbers have an infinite number of sig figs. 12 inches (in.) = 1 foot (ft.), exact #s have no uncertainty Copyright ©2016 John Wiley & Sons, Inc. 10 Let’s Practice! (1 of 26) How many significant figures are in the following measurements? 3.2 inches 2 significant figures 25.0 grams 3 significant figures 103 people Exact number  number of sig figs  0.003 kilometers 1 significant figure Copyright ©2016 John Wiley & Sons, Inc. 11 Rounding Off Numbers With a calculator, answers are often expressed with more digits than the proper number of significant figures. These extra digits are omitted from the reported number, and the value of the last digit is determined by rounding off. Rules for Rounding Off If the first digit after the number that will be retained is: 1. < 5, the digit retained does not change. Ex. 53.2305 = 53.2 (other digits dropped) digit retained 2. 5, the digit retained is increased by one. Ex. 11.789 = 11.8 (other digits dropped) digit rounded up to 8 Copyright ©2016 John Wiley & Sons, Inc. 12 Let’s Practice! (2 of 26) Round off the following numbers to the given number of significant figures. 79.137 (four) 79.14 0.04345 (three) 0.0435 136.2 (three) 136 0.1790 (two) 0.18 Copyright ©2016 John Wiley & Sons, Inc. 13 2.4 Significant Figures in Calculations The results of a calculation are only as precise as the least precise measurement. Calculations Involving Multiplication or Division The significant figures of the answer are based on the measurement with the least number of significant figures. Example 79.2 ×1.1 = Copyright ©2016 John Wiley & Sons, Inc. 14 Let’s Practice! (3 of 26) Round the following calculation to the correct number of significant figures. ( 12.18 )( 5.2) =4.872 a. 4.9 13 b. 4.87 c. 4.8 d. 4.872 e. 5.0 Copyright ©2016 John Wiley & Sons, Inc. 15 Significant Figures in Calculations Calculations Involving Addition or Subtraction The significant figures of the answer are based on the precision of the least precise measurement (number with the least number of decimal places). Example Add 136.23 + 79 + 31.7 The least precise number is 79, so the answer should be rounded to 247. Copyright ©2016 John Wiley & Sons, Inc. 16 Let’s Practice! (5 of 26) Round the following calculation to the correct number of significant figures. 142.57 − 13.0 a. 129.57 b. 129.6 c. 130 d. 129.5 e. 129 The answer is rounded to the tenths place. Copyright ©2016 John Wiley & Sons, Inc. 17 Let’s Practice! (7 of 26) Round the following calculation to the correct number of significant figures. = a. 0.69109 b. 0.70 The numerator must be rounded to the tenths place. c. 0.693 7.0 d. 0.69 = 0.693069 10.1 Final answer is now rounded to 2 significant figures. Copyright ©2016 John Wiley & Sons, Inc. 18 Let’s Practice! (9 of 26) How many significant figures should the answer to the following calculation contain? 1.6 + 23 – 0.005 a. 1 b. 2 c. 3 d. 4 Round to least precise number (23). Round to the ones place (25). Copyright ©2016 John Wiley & Sons, Inc. 19 2.5 The Metric System Metric or International System (SI): Standard system of measurements for mass, length, time and other physical quantities. Quantity Unit Name Abbreviation Length Meter m Mass Kilogram kg Temperature Kelvin K Time Second s Amount of Substance Mole mol Electric current Ampere A The metric system is also called decimal-based system, standard units change based on factors of 10. Prefixes are used to indicate multiples of 10. Copyright ©2016 John Wiley & Sons, Inc. 20 The Metric System (1 of 2) Table 2.1 Common Prefixes and Numerical Values for SI Units Prefix Symbol Numerical value Power of 10 equivalent 10 to the power of 9. giga G 1,000,000,000 9 10 10 to the power of 6. mega M 1,000,000 6 10 10 to the power of 3 kilo k 1,000 3 10 10 to the power of 2 hecto h 100 102 10 to the power of 1 deka da 10 1 10 10 to the power 0 of zero. — — 1 10 deci d 0.1 10 1 10 to the power of negative 1. centi c 0.01 10 to the power of negative 2. 10 2 Learn the prefixes in bold!! Copyright ©2016 John Wiley & Sons, Inc. 21 The Metric System (2 of 2) Prefix Symbol Numerical value Power of 10 equivalent milli m 0.001 10 to the power of negative 3 10 3 micro µ 0.000001 10 to the power of negative 6. 10 6 nano n 0.000000001 10 to the power of negative 9. 10 9 pico p 0.000000000001 10 to the power of negative 12. 10 12 femto f 0.000000000000001 10 to the power of negative 15. 10 15 Copyright ©2016 John Wiley & Sons, Inc. 22 Measurements of Length Meter (m): standard unit of length of the metric system. Definition: the distance light travels in a vacuum during 1/299,792,458 of a second. Common Length Relationships: 1 meter m  = 100 centimeters cm  = 1000 millimeters (mm) 1 kilometer km  = 1000 meters Relationship Between the Metric and English System: 1 inch (in.) = 2.54 cm Copyright ©2016 John Wiley & Sons, Inc. 23 2.6 Dimensional Analysis: A Problem-Solving Method Dimensional analysis: converts one unit of measure to another by using conversion factors, a ratio of equivalent quantities. Example: 1 km = 1000 m Conversion factor: 1 km 1000 m or 1000 m 1 km Any unit can be converted to another unit by multiplying the quantity by a conversion factor. Unit × conversion factor = Unit 1 2 1 km Example: Convert 2 m to km. 2m× =0.002 km 1000 m Copyright ©2016 John Wiley & Sons, Inc. 24 Dimensional Analysis: A Problem-Solving Method Many chemical principles or problems are illustrated mathematically. A systematic method to solve these types of numerical problems is key. Our approach: the dimensional analysis method Create solution maps to solve problems. Overall outline for a calculation/conversion progressing from known to desired quantities. Copyright ©2016 John Wiley & Sons, Inc. 25 Dimensional Analysis: A Problem Solving Practice (1 of 2) Convert 215 centimeters (cm) to meters (m). Solution Map: Known quantity cm m desired quantity 1m 215cm × =2.15m 100 cm Convert 125 meters (m) to kilometers (km). Solution Map: Known quantity m km desired quantity 1km 125m× =0.125 km 1000m Copyright ©2016 John Wiley & Sons, Inc. 26 Let’s Practice! (11 of 26) How many micrometers are in 0.03 meters? a. 30,000 b. 300,000 Solution Map: c. 300 known quantity m→μm desired quantity d. 3000 1,000,000 μm 0.03m× =30,000 μm 1m Copyright ©2016 John Wiley & Sons, Inc. 27 Dimensional Analysis: A Problem Solving Method Some problems require a series of conversions to get to the desired unit. Each arrow in the solution map corresponds to the use of a conversion factor. Example Convert from days to seconds. Solution Map: days hours minutes seconds 24 hour 60 minute 60 seconds 1 day    8.64 104 sec 1 day 1 hour 1 minute Copyright ©2016 John Wiley & Sons, Inc. 28 Dimensional Analysis: A Problem Solving Practice Metric to English Conversions How many feet are in 250 centimeters? Solution Map: cm inches ft 1 inch 1 foot 250 cm   8.20 ft 2.54 cm 12 inches Copyright ©2016 John Wiley & Sons, Inc. 29 Let’s Practice! (13 of 26) Metric to English Conversions How many meters are in 5 yards? a. 9.14 b. 457 c. 45.7 Solution Map: d. 4.57 yards feet inches cm m 3 feet 12 inches 2.54 cm 1m 5 yards     4.57 m 1 yard 1 foot 1 inch 100 cm Copyright ©2016 John Wiley & Sons, Inc. 30 Let’s Practice! (15 of 26) Metric to English Conversions How many cm3 are in a box that measures 2.20 × 4.00 × 6.00 inches? Solution Map: 3 in cm  2.20 in 4.00 in 6.00 in 52.8 in 3 3 3 2.54 cm  3 52.8 in   865 cm  1 in  Copyright ©2016 John Wiley & Sons, Inc. 31 Measurement of Mass (1 of 2) Mass: amount of matter in an object, it is measured on a balance. Weight: effect of gravity on an object, it is measured on a scale. Mass is independent of location, but weight is not. Mass is the standard measurement of the metric system. The SI unit of mass is the kilogram (kg). (The gram is too small a unit of mass to be the standard unit.) Copyright ©2016 John Wiley & Sons, Inc. 32 Measurement of Mass (2 of 2) 1 kilogram (kg) is the mass of a Pt-Ir cylinder standard. Metric to English Conversions 1 kg = 2.2015 pounds (lbs) Metric Units of Mass Table 2.5 Metric Units of Mass Unit Abbreviation Gram equivalent Exponential equivalent 10 to the3power of 3, g. kilogram kg 1000 g 10 g 10 to the power of zero, g. gram g 1g 10 g0 10 to the power  1 of negative 1, g. decigram dg 0.1 g 10 g 10 to the power  2 of negative 2, g. centigram cg 0.01 g 10 g 10 to the power of negative 3, g. milligram mg 0.001 g 10 g 3 10 to the power  6 of negative 6, g. microgram µg 0.000001 g 10 g Copyright ©2016 John Wiley & Sons, Inc. 33 Let’s Practice! (16 of 26) Convert 343 grams to kilograms. Solution Map: g kg Use the new conversion factor: 1 kg 1000 g or 1000 g 1 kg 1kg 343 g  0.343kg 1000 g Copyright ©2016 John Wiley & Sons, Inc. 34 Let’s Practice! (17 of 26) How many centigrams are in 0.12 kilograms? a. 120 cg b. 1.2 x 104 cg Solution Map: c. 1200 cg kg g cg d. 1.2 cg 1000 g 100 cg 0.12 kg   1.2 104 cg 1 kg 1g Copyright ©2016 John Wiley & Sons, Inc. 35 Measurement of Volume (1 of 2) Volume: the amount of space occupied by matter. The SI unit of volume is the cubic meter m  3 The metric volume more typically used is the liter (L) or milliliter (mL). Copyright ©2016 John Wiley & Sons, Inc. 36 Measurement of Volume (2 of 2) Common Volume Relationships 1 L 1000 mL 1000 cm 3 1 mL 1 cm3 1 L 1.057 quarts qt  Volume Problem Convert 0.345 liters to milliliters. Solution Map: L mL 1000 mL 0.345 L  345 mL 1L Copyright ©2016 John Wiley & Sons, Inc. 37 Let’s Practice! (19 of 26) How many milliliters (mL) are in a cube with sides measuring 13.1 inches (in.) each? a. 3690 Solution Map: b. 3.69 in. cm cm3 mL c. 369 Convert from inches to cm: d. 3.69 104 2.54 cm 13.1 in.  33.3 cm Determine the volume of the cube: 1 in. Volume 33.3 cm 33.3 cm 33.3 cm  3.69 10 4 cm 3 Convert to the proper units: 4 3 1 mL 4 3.69 10 cm  3  3.69 10 mL 1 cm Copyright ©2016 John Wiley & Sons, Inc. 38  2.7 Percent The composition of many mixtures is often given in percent. percent ¿ parts ( total parts ×100% ) Ex. In a genetics experiment there are 25 red flowers, 33 yellow flowers and 22 white flowers. What is the percentage of red flowers? parts Use the formula percent  100% total parts What is the total number flowers? 25 + 33 + 22 = 75 total 25 red percent red flowers  100% 33% 75 total Copyright ©2016 John Wiley & Sons, Inc. 39 Mass percent  mass part  mass percent    100%  mass total  Since the same units cancel out any mass units can be used in the formula Ex. A sample of nickel oxide (NiO) is composed of 14.00g nickel and 7.64g oxygen. Calculate the percentage of nickel and oxygen.  mass part  mass percent    100%  mass total  a. 14% O 7.64% Ni b. 65% O 35% Ni c. 35% O 65% Ni d. 53% O 47% Ni Copyright ©2016 John Wiley & Sons, Inc. 40 2.8 Measurement of Temperature Temperature: measure of the intensity of thermal energy of a system (i.e. how hot or cold). Heat: flow of energy due to a temperature difference. Heat flows from regions of higher to lower temperature. The SI unit of temperature is the Kelvin (K). Temperature is measured using a thermometer. Copyright ©2016 John Wiley & Sons, Inc. 41 Different Temperature Scales Celsius (℃), Fahrenheit (℉), and Kelvin (K) are co. Celsius and Fahrenheit are both measured in degrees, but the scales are different. H2O Degrees Celsius Degrees Fahrenheit K Freezing Point 0℃ 32 ℉ 273.15 K Boiling Point 100 ℃ 212 ℉ 373.15 K The Fahrenheit scale has a range of 180 degree between freezing and boiling. The lowest temperature possible on the Kelvin scale is absolute zero (−273.15 degrees Celsius). Copyright ©2016 John Wiley & Sons, Inc. 42 Converting Between Temperature Scales Mathematical Relationships Between Temperature Scales K  °C  273.15 9   F  5  C   32 Temperature Problem Convert 723 degrees Celsius to temperature in both K and degrees Fahrenheit. Solution Map:  C K K = 723 + 273.15 = 996 K  C  F 9  F  723  32 1333 F 5 Copyright ©2016 John Wiley & Sons, Inc. 43 Let’s Practice! (21 of 26) What is the temperature if 98.6 degrees Fahrenheit is converted to degrees Celsius? a. 37 Solution Map: b. 371  F  C c. 210 9 98.6  ( C)  32 5 d. 175 9 98.6  32  ( C) 5 9 66.6  ( C) 5 5  C    (66.6) 37 C  9 Copyright ©2016 John Wiley & Sons, Inc. 44 Let’s Practice! (22 of 26) What is the temperature if 98.6 degrees Fahrenheit is converted to degrees Celsius? a. Answer: 37 b. 371 c. 210 d. 175 Copyright ©2016 John Wiley & Sons, Inc. 45 2.9 Density Density is a physical property of a substance. Density (d): the ratio of the mass of a substance to the volume occupied by that mass. mass d  volume units of density: g/mL or g/cm3 for solids and liquids, g/L for gases. The volume of a liquid changes as a function of temp, so density must be specified for a given temperature. Ex. The density of H2O at 4 degrees Celsius is 1.0 g/mL while the density is 0.97 g/mL at 80 degrees Celsius. Copyright ©2016 John Wiley & Sons, Inc. 46 Density Copyright ©2016 John Wiley & Sons, Inc. 47 Let’s Practice! (23 of 26) Calculate the density of a substance if 323 g occupy a volume of 53.0 mL. Solution: mass d = volume 323 g  6.09 g ml 53.0 ml Copyright ©2016 John Wiley & Sons, Inc. 48 Let’s Practice! (24 of 26) The density of gold is 19.3 g/mL. What is the volume of 25.0 g of gold? Solution Map: Use density as a conversion factor! g Au mL Au 1 mL 25.0 g  1.30 mL 19.3 g Copyright ©2016 John Wiley & Sons, Inc. 49 Let’s Practice! (25 of 26) What is the mass of 1.50 mL of ethyl alcohol? (d = 0.789 g/mL at 4 degrees Celsius) a. 190 g Solution Map: b. 1.18 g c. 0.526 g mL g d. 2.32 g 0.789 g 1.50 mL  1.18 g e. 1.50 g 1 mL Copyright ©2016 John Wiley & Sons, Inc. 50 Let’s Practice! (26 of 26) What is the mass of 1.50 mL of ethyl alcohol? (d = 0.789 g/mL at 4 degrees Celsius) a. 190 g b. Answer: 1.18 g c. 0.526 g d. 2.32 g e. 1.50 g Copyright ©2016 John Wiley & Sons, Inc. 51 Copyright Copyright © 2016 John Wiley & Sons, Inc. All rights reserved. Reproduction or translation of this work beyond that permitted in Section 117 of the 1976 United States Act without the express written permission of the copyright owner is unlawful. Request for further information should be addressed to the Permissions Department, John Wiley & Sons, Inc. The purchaser may make back-up copies for his/her own use only and not for distribution or resale. The Publisher assumes no responsibility for errors, omissions, or damages, caused by the use of these programs or from the use of the information contained herein. Copyright ©2016 John Wiley & Sons, Inc. 52