Chapter 2 a Measurements and Calculations Chapter 2

Chapter 2 a Measurements and Calculations

Chapter 2 Table of Contents 2. 1 2. 2 2. 3 2. 4 2. 5 Scientific Notation Units Measurements of Length, Volume, and Mass Uncertainty in Measurement Significant Figures Return to TOC

Section 2. 1 Scientific Notation Measurement • Quantitative observation. • Has 2 parts – number and unit. § Number tells comparison. § Unit tells scale. Return to TOC

Section 2. 1 Scientific Notation • Technique used to express very large or very small numbers. • Expresses a number as a product of a number between 1 and 10 and the appropriate power of 10. Return to TOC

Section 2. 1 Scientific Notation Using Scientific Notation • Any number can be represented as the product of a number between 1 and 10 and a power of 10 (either positive or negative). • The power of 10 depends on the number of places the decimal point is moved and in which direction. Return to TOC

Section 2. 1 Scientific Notation Using Scientific Notation • The number of places the decimal point is moved determines the power of 10. The direction of the move determines whether the power of 10 is positive or negative. Return to TOC

Section 2. 1 Scientific Notation Using Scientific Notation • If the decimal point is moved to the left, the power of 10 is positive. 345 = 3. 45 × 102 very large number • If the decimal point is moved to the right, the power of 10 is negative. 0. 0671 = 6. 71 × 10– 2 very small number In Webassign homework use format: 345 = 3. 45 e 02 0. 0671 = 6. 71 e-02 Return to TOC

Section 2. 1 Scientific Notation Concept Check Which of the following correctly expresses 7, 882 in scientific notation? a) b) c) d) 7. 882 × 104 788. 2 × 103 7. 882 × 10– 3 Return to TOC

Section 2. 1 Scientific Notation Concept Check Which of the following correctly expresses 0. 0000496 in scientific notation? a) b) c) d) 4. 96 × 10– 5 4. 96 × 10– 6 4. 96 × 10– 7 496 × 107 Return to TOC

Section 2. 1 Scientific Notation Precision vs. Accuracy good precision poor accuracy poor precision good accuracy good precision good accuracy Return to TOC

Section 2. 1 Scientific Notation Measurement Accuracy How long is this line? There is no such thing as a totally accurate measurement! Return to TOC

Section 2. 2 Units Nature of Measurement • • Quantitative observation consisting of two parts. § number § scale (unit) Examples § 20 grams § 6. 63 × 10– 34 joule·seconds If a CHP asks you what do you have and you answer I have 3 kilos, you may go to jail. You should have said I have 3 kg of doughnuts for my chemistry instructor. Return to TOC

Section 2. 1 lll Scientific Notation British SI System Measurement in Chemistry Length Mass meter gram Liter second Km=1000 m Kg=1000 g KL=1000 L 1 min=60 sec 100 cm=1 m 1000 mg=1 g 1000 m. L=1 L 60 min=1 hr 1000 mm=1 m Volume Time http: //www. kickstarter. com/projects/52746223/thestate-of-the-unit-the-kilogram-documentary-fil Foot pound gallon second 12 in=1 ft 16 oz=1 lb 4 qt=1 gal (same) 3 ft=1 yd 2000 lb=1 ton 2 pts=1 qt 5280 ft=1 mile Return to TOC

Section 2. 1 Scientific Notation Conversion between British and SI Units 2. 54 cm = 1 in 454 g = 1 lb 1 (cm)3 = 1 cc = 1 ml = 1 gwater 1. 06 qt = 1 L Return to TOC

Section 2. 2 Units Prefixes Used in the SI System • Prefixes are used to change the size of the unit. Return to TOC

Section 2. 3 Measurements of Length, Volume, and Mass Length • Fundamental SI unit of length is the meter. Return to TOC

Section 2. 3 Measurements of Length, Volume, and Mass Volume • • • Measure of the amount of 3 -D space occupied by a substance. SI unit = cubic meter (m 3) Commonly measure solid volume in cm 3. 1 m. L = 1 cm 3 1 L = 1 dm 3 Return to TOC

Section 2. 3 Measurements of Length, Volume, and Mass • • Measure of the amount of matter present in an object. SI unit = kilogram (kg) 1 kg = 2. 2046 lbs 1 lb = 453. 59 g Return to TOC

Section 2. 3 Measurements of Length, Volume, and Mass Concept Check Choose the statement(s) that contain improper use(s) of commonly used units (doesn’t make sense)? § § A gallon of milk is equal to about 4 L of milk. A 200 -lb man has a mass of about 90 kg. A basketball player has a height of 7 m tall. A nickel is 6. 5 cm thick. Return to TOC Copyright © Cengage Learning. All rights reserved

Section 2. 4 Uncertainty in Measurement • • • A digit that must be estimated is called uncertain. A measurement always has some degree of uncertainty. Record the certain digits and the first uncertain digit (the estimated number). Return to TOC

Section 2. 4 Uncertainty in Measurement of Length Using a Ruler • The length of the pin occurs at about 2. 85 cm. § Certain digits: 2. 85 Estimate between smallest division! § Uncertain digit: 2. 85 Return to TOC Copyright © Cengage Learning. All rights reserved

Section 2. 4 Uncertainty in Measurement Significant Figures • Numbers that measure or contribute to our accuracy. • The more significant figures we have the more accurate our measurement. • Significant figures are determined by our measurement device or technique. Return to TOC Copyright © Cengage Learning. All rights reserved

Section 2. 4 Uncertainty in Measurement Rules of Determining the Number of Significant Figures 1. All non-zero digits are significant. 234 = 3 sig figs 1. 333 = 4 sig figs 1, 234. 2 = 5 sig figs 2. All zeros between non-zero digits are significant. 203 = 3 sig figs 1. 003 = 4 sig figs 1, 030. 2 = 5 sig figs Return to TOC

Section 2. 4 Uncertainty in Measurement Rules of Determining the Number of Significant Figures 3. All zeros to the right of the decimal and to the right of the last non-zero digit are significant. 2. 30 = 3 sig figs 1. 000 = 4 sig figs 3. 4500 = 5 sig figs 4. All zeros to the left of the first non-zero digit are NOT significant. 0. 0200 = 3 sig figs 0. 1220 = 4 sig figs 0. 000000012210 = 5 sig figs Return to TOC

Section 2. 4 Uncertainty in Measurement Rules of Determining the Number of Significant Figures 5. Zeros to the right of the first non-zero digit and to the left of the decimal may or may not be significant. They must be written in scientific notation. 2300 = 2. 3 x 103 or 2. 300 x 103 2 sig figs 3 sig figs 4 sig figs Return to TOC

Section 2. 4 Uncertainty in Measurement Rules of Determining the Number of Significant Figures 6. Some numbers have infinite significant figures or are exact numbers. 233 people 14 cats (unless in biology lab) 7 cars on the highway 36 schools in town Return to TOC

Section 2. 4 Uncertainty in Measurement How many significant figures are in each of the following? 1) 23. 34 4 significant figures 2) 21. 003 5 significant figures 3). 0003030 4 significant figures 4) 210 2 or 3 significant figures 5) 200 students infinite significant figures 6) 3000 1, 2, 3, or 4 significant figures Return to TOC

Section 2. 4 Uncertainty in Measurement Chapter 2 b Measurements and Calculations Return to TOC

Section 2. 4 Uncertainty in Measurement 2. 5 Significant Figures 2. 6 Problem Solving and Dimensional Analysis 2. 7 Temperature Conversions: An Approach to Problem Solving 2. 8 Density Return to TOC

Section 2. 4 Uncertainty in Measurement Using Significant Figures in Calculations Addition and Subtraction 1. 2. 3. Line up the decimals. Add or subtract. Round off to first full column. 23. 345 +14. 5 + 0. 523 = ? 23. 345 14. 5 + 0. 523 38. 368 = 38. 4 or three significant figures Return to TOC

Section 2. 4 Uncertainty in Measurement Using Significant Figures in Calculations Multiplication and Division 1. 2. Do the multiplication or division. Round answer off to the same number of significant figures as the least number in the data. (23. 345)(14. 5)(0. 523) = ? 177. 0368075 = 177 or three significant figures Return to TOC

Section 2. 5 Significant Figures Rules for Rounding Off 1. If the digit to be removed is less than 5, the preceding digit stays the same. § 5. 64 rounds to 5. 6 (if final result to 2 sig figs) Return to TOC

Section 2. 5 Significant Figures Rules for Rounding Off 1. If the digit to be removed is equal to or greater than 5, the preceding digit is increased by 1. § § 5. 64 rounds to 5. 6 (if final result to 2 sig figs) 3. 861 rounds to 3. 9 (if final result to 2 sig figs) Return to TOC

Section 2. 5 Significant Figures Rules for Rounding Off 2. In a series of calculations, do within the parenthesis first and determine the significant figures and use that answer to calculate and find the significant figures after the multiplication and/or division. Return to TOC

Section 2. 5 Significant Figures Concept Check You have water in each graduated cylinder shown. You then add both samples to a beaker (assume that all of the liquid is transferred). How would you write the number describing the total volume? 3. 08 m. L What limits the precision of the total volume? 2. 80 1 st graduated cylinder +. 280 2 ndgraduated cylinder 3. 080 or 3. 08 ml Return to TOC

Section 2. 6 Problem Solving and Dimensional Analysis Example #1 A golfer putted a golf ball 6. 8 ft across a green. How many inches does this represent? • To convert from one unit to another, use the equivalence statement that relates the two units. 1 ft = 12 in The two unit factors are: Return to TOC

Section 2. 6 Problem Solving and Dimensional Analysis Example #1 A golfer putted a golf ball 6. 8 ft across a green. How many inches does this represent? • Choose the appropriate conversion factor by looking at the direction of the required change (make sure the unwanted units cancel). Return to TOC Copyright © Cengage Learning. All rights reserved

Section 2. 6 Problem Solving and Dimensional Analysis Example #1 A golfer putted a golf ball 6. 8 ft across a green. How many inches does this represent? • Multiply the quantity to be converted by the conversion factor to give the quantity with the desired units. • Correct sig figs? Does my answer make sense? Return to TOC Copyright © Cengage Learning. All rights reserved

Section 2. 6 Problem Solving and Dimensional Analysis Example #2 An iron sample has a mass of 4. 50 lb. What is the mass of this sample in grams? (1 kg = 2. 2046 lbs; 1 kg = 1000 g) 454 g OR 4. 50 lbs x -------1 lb = 2043 g = 2. 04 x 103 g Return to TOC

Section 2. 6 Problem Solving and Dimensional Analysis Concept Check What data would you need to estimate the money you would spend on gasoline to drive your car from New York to Los Angeles? Provide estimates of values and a sample calculation. Sample Answer: Distance between New York and Los Angeles: 2500 miles Average gas mileage: 25 miles per gallon Average cost of gasoline: $3. 25 per gallon = $(3. 3 x 102) Return to TOC

Section 2. 7 Temperature Conversions: An Approach to Problem Solving Three Systems for Measuring Temperature • • • Fahrenheit Celsius Kelvin Gabriel Fahrenheit Lord Kelvin Return to TOC Copyright © Cengage Learning. All rights reserved

Section 2. 7 Temperature Conversions: An Approach to Problem Solving The Three Major Temperature Scales F = 1. 8 C + 32 C = (F-32)/1. 8 K = C + 273 What is 35 o. C in o. F? 95 o. F What is 90 o. F in o. C? 32 o. C What is 100 K in o. C? -173 o. C Return to TOC

Section 2. 7 Temperature Conversions: An Approach to Problem Solving Exercise The normal body temperature for a dog is approximately 102 o. F. What is this equivalent to on the Kelvin temperature scale? a) 373 K b) 312 K c) 289 K d) 202 K C = (F-32)/1. 8 = (102 -32)/1. 80 = 38. 9 o. C K = C + 273 = 38. 9 + 273 = 312 K Return to TOC

Section 2. 7 Temperature Conversions: An Approach to Problem Solving Exercise At what temperature does C = F? Return to TOC Copyright © Cengage Learning. All rights reserved

Section 2. 7 Temperature Conversions: An Approach to Problem Solving Solution • • • Since °C equals °F, they both should be the same value (designated as variable x). Use one of the conversion equations such as: Substitute in the value of x for both T°C and T°F. Solve for x. Return to TOC Copyright © Cengage Learning. All rights reserved

Section 2. 7 Temperature Conversions: An Approach to Problem Solving Solution 1. 80 x = x -32 0. 80 x = -32/0. 80 So – 40°C = – 40°F Return to TOC Copyright © Cengage Learning. All rights reserved

Section 2. 8 Density • • Mass of substance per unit volume of the substance. Common units are g/cm 3 or g/m. L. Return to TOC Copyright © Cengage Learning. All rights reserved

Section 2. 8 Density Measuring the Volume of a Solid Object by Water Displacement Return to TOC

Section 2. 8 Density Example #1 A certain mineral has a mass of 17. 8 g and a volume of 2. 35 cm 3. What is the density of this mineral? Return to TOC Copyright © Cengage Learning. All rights reserved

Section 2. 8 Density Example #2 What is the mass of a 49. 6 m. L sample of a liquid, which has a density of 0. 85 g/m. L? OR g Return to TOC

Section 2. 8 Density Exercise If an object has a mass of 243. 8 g and occupies a volume of 0. 125 L, what is the density of this object in g/cm 3? a) 0. 513 b) 1. 95 c) 30. 5 d) 1950 Return to TOC

Section 2. 8 Density Using Density as a Conversion Factor How many lbs of sugar is in 945 gallons of 60. 0 Brix (% sugar) orange concentrate if the density of the concentrate is 1. 2854 g/m. L? 1 L 1000 m. L 1. 2854 g. T 60. 0 g. S 1 lbs 945 gal 4 qt 1 gal 1. 06 qt 1 L 1 m. L 100 g. T 454 g. S = 6057. 865514 lbs = 6. 06 x 103 lbs sugar lbs of what? Coffee? Cocaine? Return to TOC

Section 2. 8 Density Using Density as a Conversion Factor Using the Formula How many lbs of sugar is in 256 L of 60. 0 Brix (% sugar) orange concentrate if the density of the concentrate is 1. 2854 g/m. L? M D= Solve for Mass DV = M V (1. 2854 g/m. L)(256, 000 m. L) = 329062. 4 g. T = 3. 29 x 105 g. T 1 lb. T 60. 0 lbs. S 454 g. T 100 lbs. T = 434. 8017621 lbs. S = 4. 35 x 102 lbs. S = 435 lbs. S Return to TOC

Section 2. 8 Density Concept Check Copper has a density of 8. 96 g/cm 3. If 75. 0 g of copper is added to 50. 0 m. L of water in a graduated cylinder, to what volume reading will the water level in the cylinder rise? a) 8. 4 m. L b) 41. 6 m. L c) 58. 4 m. L d) 83. 7 m. L 8. 37 m. L Cu + 50. 0 m. L water = 58. 4 m. L Return to TOC