Measurement and Problem Solving techniques While Performing Experim

Introductory Chemistry, : Roy Kennedy Massachusetts Bay Community College Wellesley Hills, MA Introductory Chemistry, Chapter 2 Measurement and Problem Solving 2009, Prentice Hall

What Is a Measurement? : Tro's "Introductory Chemistry", Chapter 2 2 What Is a Measurement? Quantitative = quantity and it must have a unit Comparison to an agreed upon standard. accuracy

Scientists have measured the average global temperature rise over the past century to be 0.6 °C : 3 Scientists have measured the average global temperature rise over the past century to be 0.6 °C Quantity is 0.6 the unit is °C Comparison to an agreed upon standard is Celsius temperature scale. Accuracy: The confidence in the measurement is determined by looking at the last digit, here it is in the 1/10th’s position, so the certain is plus and minus 1/10 or between 0.5 and 0.7 °C.

Scientific Notation : Tro's Introductory Chemistry, Chapter 2 4 Scientific Notation A way of writing large and small numbers.

Big and Small Numbers : Tro's "Introductory Chemistry", Chapter 2 5 Big and Small Numbers We commonly measure objects that are many times larger or smaller than our standard of comparison. Writing large numbers of zeros is tricky and confusing. Not to mention there’s the 8-digit limit of your calculator! The sun’s diameter is 1,392,000,000 m.

Exponents : Tro's "Introductory Chemistry", Chapter 2 6 Exponents When the exponent on 10 is positive, it means the number is that many powers of 10 larger. Sun’s diameter = 1.392 x 109 m = 1,392,000,000 m. When the exponent on 10 is negative, it means the number is that many powers of 10 smaller. Average atom’s diameter = 3 x 10-10m = 0.0000000003m

Scientific Notation : Tro's "Introductory Chemistry", Chapter 2 7 Scientific Notation To compare numbers written in scientific notation: First compare exponents on 10. If exponents are equal, then compare decimal numbers 1.23 x 105 > 4.56 x 102 4.56 x 10-2 > 7.89 x 10-5 7.89 x 1010 > 1.23 x 1010

Writing a Number in Scientific Notation, Continued : Tro's "Introductory Chemistry", Chapter 2 8 12340 1. Locate the decimal point. 12340. 2. Move the decimal point to obtain a number between 1 and 10. 1.234 3. Multiply the new number by 10n . Where n is the number of places you moved the decimal point. 1.234 x 104 4. If you moved the decimal point to the left, then n is +; if you moved it to the right, then n is − . 1.234 x 104 Writing a Number in Scientific Notation, Continued

Writing a Number in Scientific Notation, Continued : Tro's "Introductory Chemistry", Chapter 2 9 Writing a Number in Scientific Notation, Continued 0.00012340 1. Locate the decimal point. 0.00012340 2. Move the decimal point to obtain a number between 1 and 10. 1.2340 3. Multiply the new number by 10n . Where n is the number of places you moved the decimal point. 1.2340 x 104 4. If you moved the decimal point to the left, then n is +; if you moved it to the right, then n is − . 1.2340 x 10-4

Writing a Number in Standard Form : Tro's "Introductory Chemistry", Chapter 2 10 Writing a Number in Standard Form 1.234 x 10-6 Since exponent is -6, make the number smaller by moving the decimal point to the left 6 places. When you run out of digits to move around, add zeros. Add a zero in front of the decimal point for decimal numbers. 000 001.234 0.000 001 234

Practice—Write the Following in Scientific Notation, Continued : Tro's "Introductory Chemistry", Chapter 2 11 Practice—Write the Following in Scientific Notation, Continued 123.4 = 1.234 x 102 145000 = 1.45 x 105 25.25 = 2.525 x 101 1.45 = 1.45 x 100 8.0012 = 8.0012 x 100 0.00234 = 2.34 x 10-3 0.0123 = 1.23 x 10-2 0.000 008706 = 8.706 x 10-6

Practice—Write the Following in Standard Form, Continued : Tro's "Introductory Chemistry", Chapter 2 12 Practice—Write the Following in Standard Form, Continued 2.1 x 103 = 2100 9.66 x 10-4 = 0.000966 6.04 x 10-2 = 0.0604 4.02 x 100 = 4.02 3.3 x 101 = 33 1.2 x 100 = 1.2

Numbers : Tro's "Introductory Chemistry", Chapter 2 13 Numbers Exact Measured: Significant Figures

Exact Numbers vs. Measurements : Tro's "Introductory Chemistry", Chapter 2 14 Exact Numbers vs. Measurements Exact: Sometimes you can determine an exact value for a quality of an object. Often by counting. Pennies in a pile. Sometimes by definition 1 ounce is exactly 1/16th of 1 pound. Measured: Whenever you use an instrument to compare a quality of an object to a standard, there is uncertainty in the comparison.

Exact Numbers : Tro's "Introductory Chemistry", Chapter 2 15 Exact Numbers Exact numbers have an unlimited number of significant figures. A number whose value is known with complete certainty is exact. From counting individual objects. From definitions. 1 cm is exactly equal to 0.01 m. 20@ $.05 = $1.0000000000000 12 inches = 1.000000000000000000000000 ft

4 fundamental measuring instruments : 4 fundamental measuring instruments Length Mass Time Temperature Tro's "Introductory Chemistry", Chapter 2 16

How do we make a Measurement : Tro's "Introductory Chemistry", Chapter 2 17 How do we make a Measurement Measurements are written to indicate the uncertainty in the measurement. The system of writing measurements we use is called significant figures. When writing measurements, all the digits written are known with certainty except the last one, which is an estimate. 45.872

Reading a Measuring Instrument/Device : Reading a Measuring Instrument/Device For any Digital Device record ALL the digits 18

Reading a Measuring Instrument/Device : Reading a Measuring Instrument/Device Record all the numbers you can see Make ONE Guess! 19

Skillbuilder 2.3—Reporting the Right Number of Digits : Tro's "Introductory Chemistry", Chapter 2 20 Skillbuilder 2.3—Reporting the Right Number of Digits A thermometer used to measure the temperature of a backyard hot tub is shown to the right. What is the temperature reading to the correct number of digits?

Skillbuilder 2.3—Reporting the Right Number of Digits : Tro's "Introductory Chemistry", Chapter 2 21 Skillbuilder 2.3—Reporting the Right Number of Digits A thermometer used to measure the temperature of a backyard hot tub is shown to the right. What is the temperature reading to the correct number of digits? 103.4 °F

What is the Length? : 22 What is the Length? We can see the markings between 1.6-1.7cm We can’t see the markings between the .6-.7 We must guess between .6 & .7 We record 1.67 cm as our measurement

Slide 23 : What is the length of the wooden stick? 1) 4.5 cm 2) 4.54 cm 3) 4.547 cm

Slide 24 : 24 8.00 cm or 3 (2.2/8) ?

Counting Significant Figures : Tro's "Introductory Chemistry", Chapter 2 25 Counting Significant Figures All non-zero digits are significant. 1.5 has 2 significant figures. Interior zeros are significant. 1.05 has 3 significant figures. Trailing zeros after a decimal point are significant. 1.050 has 4 significant figures.

Counting Significant Figures, Continued : Tro's "Introductory Chemistry", Chapter 2 26 Counting Significant Figures, Continued Leading zeros are NOT significant. 0.001050 has 4 significant figures. 1.050 x 10-3 Zeros at the end of a number without a written decimal point are NOT significant If 150 has 2 significant figures, then 1.5 x 102, but if 150 has 3 significant figures, then 1.50 x 102.

Example 2.4—Determining the Number of Significant Figures in a Number, Continued : Tro's "Introductory Chemistry", Chapter 2 27 Example 2.4—Determining the Number of Significant Figures in a Number, Continued How many significant figures are in each of the following numbers? 0.0035 2 significant figures—leading zeros are not significant. 1.080 4 significant figures—trailing and interior zeros are significant. 2371 4 significant figures—All digits are significant. 2.97 × 105 3 significant figures—Only decimal parts count as significant. 1 dozen = 12 Unlimited significant figures—Definition 100,000 1, no decimal

Determine the Number of Significant Figures, : Tro's "Introductory Chemistry", Chapter 2 28 Determine the Number of Significant Figures, 12000 120. 12.00 1.20 x 103 0.0012 0.00120 1201 1201000 2 3 4 3 2 3 4 4

: How many sig figs? 45.8736 .000239 .00023900 48000. 48000 3.982106 1.00040 6 3 5 5 2 4 6 All digits count Leading 0’s don’t Trailing 0’s do 0’s count in decimal form 0’s don’t count w/o decimal All digits count 0’s between digits count as well as trailing in decimal form

Rounding : Tro's "Introductory Chemistry", Chapter 2 30 Rounding When rounding to the correct number of significant figures, if the number after the place of the last significant figure is: 0 to 4, round down. Drop all digits after the last significant figure and leave the last significant figure alone. 5 to 9, round up. Drop all digits after the last significant figure and increase the last significant figure by one.

Examples of Rounding : Examples of Rounding For example you want a 4 Sig Fig number 4965.03   780,582   1999.5 0 is dropped, it is <5 8 is dropped, it is >5; Note you must include the 0’s 5 is dropped it is = 5; note you need a 4 Sig Fig 4965 780,600 2000.

Multiplication and Division with Significant Figures : Tro's "Introductory Chemistry", Chapter 2 32 Multiplication and Division with Significant Figures When multiplying or dividing measurements with significant figures, the result has the same number of significant figures as the measurement with the fewest number of significant figures. 5.02 × 89,665 × 0.10 = 45.0118 = 45 3 sig. figs. 5 sig. figs. 2 sig. figs. 2 sig. figs. 5.892 ÷ 6.10 = 0.96590 = 0.966 4 sig. figs. 3 sig. figs. 3 sig. figs.

Determine the Correct Number of Significant Figures for Each Calculation and : Tro's "Introductory Chemistry", Chapter 2 33 Determine the Correct Number of Significant Figures for Each Calculation and 1.01 × 0.12 × 53.51 ÷ 96 = 0.067556 = 0.068 56.55 × 0.920 ÷ 34.2585 = 1.51863 = 1.52 3 sf 2 sf 4 sf 2 sf Result should have 2 sf. 7 is in place of last sig. fig., number after is 5 or greater, so round up. 4 sf 3 sf 6 sf Result should have 3 sf. 1 is in place of last sig. fig., number after is 5 or greater, so round up.

Addition/Subtraction : Addition/Subtraction 25.5 32.72 320 +34.270 ‑ 0.0049 + 12.5 59.770 32.7151 332.5 59.8 32.72 330

Addition and Subtraction with Significant Figures : Tro's "Introductory Chemistry", Chapter 2 35 Addition and Subtraction with Significant Figures When adding or subtracting measurements with significant figures, the result has the same number of decimal places as the measurement with the fewest number of decimal places. 5.74 + 0.823 + 2.651 = 9.214 = 9.21 2 dec. pl. 3 dec. pl. 3 dec. pl. 2 dec. pl. 4.8 - 3.965 = 0.835 = 0.8 1 dec. pl 3 dec. pl. 1 dec. pl.

Determine the Correct Number of Significant Figures for Each Calculation and Round and Report the Result, Continued : Tro's "Introductory Chemistry", Chapter 2 36 Determine the Correct Number of Significant Figures for Each Calculation and Round and Report the Result, Continued 0.987 + 125.1 – 1.22 = 124.867 = 124.9 0.764 – 3.449 – 5.98 = -8.664 = -8.66 3 dp 1 dp 2 dp Result should have 1 dp. 8 is in place of last sig. fig., number after is 5 or greater, so round up. 3 dp 3 dp 2 dp Result should have 2 dp. 6 is in place of last sig. fig., number after is 4 or less, so round down.

Addition and Subtraction : __ ___ __ Addition and Subtraction .56 + .153 = .713 82000 + 5.32 = 82005.32 10.0 - 9.8742 = .12580 10 – 9.8742 = .12580 .71 82000 .1 0 Look for the last important digit

Both Multiplication/Division and Addition/Subtraction with Significant Figures : Tro's "Introductory Chemistry", Chapter 2 38 Both Multiplication/Division and Addition/Subtraction with Significant Figures When doing different kinds of operations with measurements with significant figures, evaluate the significant figures in the intermediate answer, then do the remaining steps. Follow the standard order of operations. Please Excuse My Dear Aunt Sally. 3.489 × (5.67 – 2.3) = 2 dp 1 dp 3.489 × 3.37 = 12 4 sf 1 dp & 2 sf 2 sf

Example 1.6—Perform the Following Calculations to the Correct Number of Significant Figures, Continued : Tro's "Introductory Chemistry", Chapter 2 39 Example 1.6—Perform the Following Calculations to the Correct Number of Significant Figures, Continued b)

Basic Units of Measure : Tro's "Introductory Chemistry", Chapter 2 40 Basic Units of Measure

Units : Tro's "Introductory Chemistry", Chapter 2 41 Units Units tell the standard quantity to which we are comparing the measured property. Without an associated unit, a measurement is without meaning. Scientists use a set of standard units for comparing all our measurements. So we can easily compare our results. Each of the units is defined as precisely as possible.

The Standard Units : 42 The Standard Units Scientists generally report results in an agreed upon International System. The SI System Aka Système International

Volume : Volume 1 mL = 1 cm3

Related Units in the SI System : Tro's "Introductory Chemistry", Chapter 2 44 Related Units in the SI System All units in the SI system are related to the standard unit by a power of 10. The power of 10 is indicated by a prefix.

Common Prefixes in the SI System : Common Prefixes in the SI System

Measurements and SI : Measurements and SI 46

Measurements and SI : Measurements and SI Tro's "Introductory Chemistry", Chapter 2 47 (m = .001)L mL = .001L or 1000 mL = L

Prefixes Used to Modify Standard Unit : Tro's "Introductory Chemistry", Chapter 2 48 Prefixes Used to Modify Standard Unit kilo = 1000 times base unit = 103 k=1000 or k = 103 1 kg = 103g nano = 10-9 times the base unit n=.000000001 or n = 10-9 1 nL = 10-9L

Units : Tro's "Introductory Chemistry", Chapter 2 49 Units Always write every number with its associated unit. Always include units in your calculations. You can do the same kind of operations on units as you can with numbers. cm × cm = cm2 cm + cm = 2cm cm ÷ cm = 1 Using units as a guide to problem solving is called dimensional analysis.

Problem Solving and Dimensional Analysis, Continued : Tro's "Introductory Chemistry", Chapter 2 50 Problem Solving and Dimensional Analysis, Continued Arrange conversion factors so the starting unit cancels. Arrange conversion factor so the starting unit is on the bottom of the conversion factor. May string conversion factors. So we do not need to know every relationship, as long as we can find something else the starting and desired units are related to :

Problem Solving and Dimensional Analysis : Tro's "Introductory Chemistry", Chapter 2 51 Problem Solving and Dimensional Analysis Many problems in chemistry involve using relationships 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 have the same number of significant figures. Conversion factors generated from equivalence statements. e.g., 1 inch = 2.54 cm can give or

Systematic Approach : Tro's "Introductory Chemistry", Chapter 2 52 Systematic Approach 1. Write down the given amount and unit. 2. Write down what you want to find and unit. 3. Write down needed conversion factors or equations. a. Write down equivalence statements for each relationship. b. Change equivalence statements to conversion factors with starting unit on the bottom.

Systematic Approach, Continued : Tro's "Introductory Chemistry", Chapter 2 53 Systematic Approach, Continued 4. Design a solution map for the problem. Order conversions to cancel previous units or arrange equation so the find amount is isolated. 5. Apply the steps in the solution map. Check that units cancel properly. Multiply terms across the top and divide by each bottom term. 6. Determine the number of significant figures to report and round. 7. Check the answer to see if it is reasonable. Correct size and unit.

Conversion Factors : Tro's "Introductory Chemistry", Chapter 2 54 Conversion Factors Convert inches into centimeters. 1. Find relationship equivalence: 1 in = 2.54 cm 2. Write solution map. in cm 3. Change equivalence into conversion factors with starting units on the bottom.

Slide 55 : Tro's "Introductory Chemistry", Chapter 2 55 Example 2.8: Convert 7.8 km to miles

Example:Convert 7.8 km to miles. : Tro's "Introductory Chemistry", Chapter 2 56 Example:Convert 7.8 km to miles. Write down the given quantity and its units. Given: 7.8 km

Example:Convert 7.8 km to miles. : Tro's "Introductory Chemistry", Chapter 2 57 Write down the quantity to find and/or its units. Find: ? miles Information Given: 7.8 km Example:Convert 7.8 km to miles.

Example:Convert 7.8 km to miles. : Tro's "Introductory Chemistry", Chapter 2 58 Collect needed conversion factors: 1 km = 0.6214 mile Information Given: 7.8 km Find: ? mi Example:Convert 7.8 km to miles.

Example:Convert 7.8 km to miles. : Tro's "Introductory Chemistry", Chapter 2 59 Write a solution map for converting the units: Information Given: 7.8 km Find: ? mi Conversion Factor: 1 km = 0.6214 mile Example:Convert 7.8 km to miles. km mi

Example:Convert 7.8 km to miles. : Tro's "Introductory Chemistry", Chapter 2 60 Apply the solution map: Information Given: 7.8 km Find: ? mi Conversion Factor:1 km = 0.6214 mile Solution Map: km  mi Example:Convert 7.8 km to miles. = 4.84692 mi = 4.8 mi Significant figures and round: 2 significant figures 2 significant figures

Practice—Convert 30.0 g to Ounces(1 oz. = 28.35 g) : Tro's "Introductory Chemistry", Chapter 2 61 Practice—Convert 30.0 g to Ounces(1 oz. = 28.35 g)

Convert 30.0 g to Ounces : Convert 30.0 g to Ounces Units and magnitude are correct. Check: Check. Round: Significant figures and round. Solution: Follow the solution map to Solve the problem. Solution Map: Write a Solution Map. 1 oz = 28.35 g Conversion Factor: Write down the appropriate Conversion Factors. oz. Find: Write down the quantity you want to Find and unit. 30.0 g Given: Write down the Given quantity and its unit. 3 sig figs 3 sig figs = 1.06 oz

Slide 63 : Tro's "Introductory Chemistry", Chapter 2 63 Example 2.10: An Italian recipe for making creamy pasta sauce calls for 0.75 L of cream. Your measuring cup measures only in cups. How many cups should you use?

An Italian recipe for making creamy pasta sauce calls for 0.75 L of cream. Your measuring cup measures only in cups. How many cups should you use? : Tro's "Introductory Chemistry", Chapter 2 64 An Italian recipe for making creamy pasta sauce calls for 0.75 L of cream. Your measuring cup measures only in cups. How many cups should you use? Write down the given quantity and its units. Given: 0.75 L

An Italian recipe for making creamy pasta sauce calls for 0.75 L of cream. Your measuring cup measures only in cups. How many cups should you use? : Tro's "Introductory Chemistry", Chapter 2 65 Write down the quantity to find and/or its units. Find: ? cups Information Given: 0.75 L An Italian recipe for making creamy pasta sauce calls for 0.75 L of cream. Your measuring cup measures only in cups. How many cups should you use?

An Italian recipe for making creamy pasta sauce calls for 0.75 L of cream. Your measuring cup measures only in cups. How many cups should you use? : Tro's "Introductory Chemistry", Chapter 2 66 Collect needed conversion factors: 4 cu = 1 qt 1.057 qt = 1 L Information Given: 0.75 L Find: ? cu An Italian recipe for making creamy pasta sauce calls for 0.75 L of cream. Your measuring cup measures only in cups. How many cups should you use?

An Italian recipe for making creamy pasta sauce calls for 0.75 L of cream. Your measuring cup measures only in cups. How many cups should you use? : Tro's "Introductory Chemistry", Chapter 2 67 Write a solution map for converting the units: Information Given: 0.75 L Find: ? cu Conversion Factors: 4 cu = 1 qt; 1.057 qt = 1 L L qt An Italian recipe for making creamy pasta sauce calls for 0.75 L of cream. Your measuring cup measures only in cups. How many cups should you use? cu

An Italian recipe for making creamy pasta sauce calls for 0.75 L of cream. Your measuring cup measures only in cups. How many cups should you use? : Tro's "Introductory Chemistry", Chapter 2 68 Apply the solution map: = 3.171 cu = 3.2 cu Significant figures and round: Information Given: 0.75 L Find: ? cu Conversion Factors: 4 cu = 1 qt; 1.057 qt = 1 L Solution Map: L  qt  cu An Italian recipe for making creamy pasta sauce calls for 0.75 L of cream. Your measuring cup measures only in cups. How many cups should you use? 2 significant figures 2 significant figures

Slide 69 : Tro's "Introductory Chemistry", Chapter 2 69 Example 2.12: A circle has an area of 2,659 cm2. What is the area in square meters?

Example:A circle has an area of 2,659 cm2. What is the area in square meters? : Tro's "Introductory Chemistry", Chapter 2 70 Example:A circle has an area of 2,659 cm2. What is the area in square meters? Write down the given quantity and its units. Given: 2,659 cm2

Example:A circle has an area of 2,659 cm2. What is the area in square meters? : Tro's "Introductory Chemistry", Chapter 2 71 Write down the quantity to find and/or its units. Find: ? m2 Information Given: 2,659 cm2 Example:A circle has an area of 2,659 cm2. What is the area in square meters?

Example:A circle has an area of 2,659 cm2. What is the area in square meters? : Tro's "Introductory Chemistry", Chapter 2 72 Collect needed conversion factors: 1 cm = 0.01m Information Given: 2,659 cm2 Find: ? m2 Example:A circle has an area of 2,659 cm2. What is the area in square meters?

Example:A circle has an area of 2,659 cm2. What is the area in square meters? : Tro's "Introductory Chemistry", Chapter 2 73 Write a solution map for converting the units: cm2 m2 Information Given: 2,659 cm2 Find: ? m2 Conversion Factor: 1 cm = 0.01 m Example:A circle has an area of 2,659 cm2. What is the area in square meters?

Example:A circle has an area of 2,659 cm2. What is the area in square meters? : Tro's "Introductory Chemistry", Chapter 2 74 Apply the solution map: = 0.265900 m2 = 0.2659 m2 Significant figures and round: Information Given: 2,659 cm2 Find: ? m2 Conversion Factor:1 cm = 0.01 m Solution Map: cm2  m2 Example:A circle has an area of 2,659 cm2. What is the area in square meters? 4 significant figures 4 significant figures

Practice—Convert 30.0 cm3 to ft3(1 cm = 1 x 10-2 m) (in class) : Tro's "Introductory Chemistry", Chapter 2 75 Practice—Convert 30.0 cm3 to ft3(1 cm = 1 x 10-2 m) (in class)

Convert 30.0 cm3 to m3 : Convert 30.0 cm3 to m3 Units and magnitude are correct. Check: Check. 30.0 cm3 = 3.00 x 10−5 m3 Round: Significant figures and round. Solution: Follow the solution map to Solve the problem. Solution Map: Write a Solution Map. (1 cm = 0.01 m)3 Conversion Factor: Write down the appropriate Conversion Factors. ? m3 Find: Write down the quantity you want to Find and unit. 30.0 cm3 Given: Write down the Given quantity and its unit. 3 sig figs 3 sig figs

Density : Tro's "Introductory Chemistry", Chapter 2 77 Density Inverse relationship between mass and volume. Solids = g/cm3 1 cm3 = 1 mL Liquids = g/mL Gases = g/L Volume of a solid can be determined by water displacement—Archimedes Principle. Density : solids > liquids > gases Except ice is less dense than liquid water!

Platinum has become a popular metal for fine jewelry and costs more than gold. A man gives a woman an engagement ring and tells her that it is made of platinum. Noting that the ring felt a little light, the woman decides to perform a test to determine the ring’s density before giving him an answer about marriage. She places the ring on a balance and finds it has a mass of 5.84 grams. She then finds that the ring displaces 0.556 cm3 of water. Is the ring made of platinum? (Density Pt = 21.4 g/cm3) : 78 Platinum has become a popular metal for fine jewelry and costs more than gold. A man gives a woman an engagement ring and tells her that it is made of platinum. Noting that the ring felt a little light, the woman decides to perform a test to determine the ring’s density before giving him an answer about marriage. She places the ring on a balance and finds it has a mass of 5.84 grams. She then finds that the ring displaces 0.556 cm3 of water. Is the ring made of platinum? (Density Pt = 21.4 g/cm3)

Data: She places the ring on a balance and finds it has a mass of 5.84 grams. She then finds that the ring displaces 0.556 cm3 of water. Is the ring made of platinum? (Density Pt = 21.4 g/cm3) : Tro's "Introductory Chemistry", Chapter 2 79 Data: She places the ring on a balance and finds it has a mass of 5.84 grams. She then finds that the ring displaces 0.556 cm3 of water. Is the ring made of platinum? (Density Pt = 21.4 g/cm3) Given: Mass = 5.84 grams Volume = 0.556 cm3 Find: Density in grams/cm3 Equation: Solution Map: m and V  d m, V d

Slide 80 : Tro's "Introductory Chemistry", Chapter 2 80 Apply the Solution Map: Since 10.5 g/cm3  21.4 g/cm3, the ring cannot be platinum.

Practice—What Is the Density of Metal if a 100.0 g Sample Added to a Cylinder of Water Causes the Water Level to Rise from 25.0 mL to 37.8 mL? : Tro's "Introductory Chemistry", Chapter 2 81 Practice—What Is the Density of Metal if a 100.0 g Sample Added to a Cylinder of Water Causes the Water Level to Rise from 25.0 mL to 37.8 mL?

Find Density of Metal if 100.0 g Displaces Water from 25.0 to 37.8 mL : Find Density of Metal if 100.0 g Displaces Water from 25.0 to 37.8 mL Units and magnitude are correct. Check: Check. 7.8125 g/cm3 = 7.81 g/cm3 Round: Significant figures and round. Solution: V = 37.8-25.0 = 12.8 mL Follow the solution map to Solve the problem. Solution Map: Write a Solution Map. CF & Equation: d, g/cm3 Find: Write down the quantity you want to Find and unit. m =100.0 g displaces 25.0 to 37.8 mL Given: Write down the Given quantity and its unit. 3 sig figs 3 significant figures 1 mL = 1 cm3 Write down the appropriate Conv. Factor and Equation.

Density as a Conversion Factor : Tro's "Introductory Chemistry", Chapter 2 83 Density as a Conversion Factor Can use density as a conversion factor between mass and volume! Density of H2O = 1 g/mL \ 1 g H2O = 1 mL H2O Density of Pb = 11.3 g/cm3 \ 11.3 g Pb = 1 cm3 Pb How much does 4.0 cm3 of lead weigh?

Measurement and Problem Solving:Density as a Conversion Factor : Tro's "Introductory Chemistry", Chapter 2 84 Measurement and Problem Solving:Density as a Conversion Factor The gasoline in an automobile gas tank has a mass of 60.0 kg and a density of 0.752 g/cm3. What is the volume? Given: 60.0 kg Find: Volume in cm3 Conversion factors: 0.752 g/cm3 1000 grams = 1 kg

Measurement and Problem Solving:Density as a Conversion Factor, Continued : Tro's "Introductory Chemistry", Chapter 2 85 Measurement and Problem Solving:Density as a Conversion Factor, Continued