Chapter 1 Chemistry and Measurements

Chapter 1 Chemistry and Measurements
1.1 Chemistry and Chemicals

What Is Chemistry? Chemistry
is the study of composition, structure, properties, and reactions of matter happens all around you everyday Antacid tablets undergo a chemical reaction when dropped in water.

Chemistry Matter is another word for all substances that make up our world. Antacid tablets are matter. Water is matter. Glass is matter. Air is matter.

Branches of Chemistry The field of chemistry is divided into branches, such as organic chemistry, the study of substances that contain carbon inorganic chemistry, the study of all substances except those that contain carbon general chemistry, the study of the composition, properties and reactions of matter

Chemistry + Other Sciences
Chemistry is often combined with other sciences: Geology + Chemistry = Geochemistry Biology + Chemistry = Biochemistry Physical Science + Chemistry = Physical Chemistry Biochemists analyze lab samples.

Chemicals Chemicals are
substances that have the same composition and properties wherever found often substances made by chemists that you use everyday Toothpaste is a combination of chemicals.

Chemicals Commonly Used in Toothpaste

Chemicals Used When Cooking
Many substances found in the kitchen are obtained using chemical reactions.

Learning Check Which of the following contains chemicals? A. sunlight
B. fruit C. milk

Solution Which of the following contains chemicals?
A. Sunlight is energy given off by the Sun and therefore does not contain chemicals. B. Fruit contains chemicals that have the same composition and properties wherever found. C. Milk contains chemicals that have the same composition and properties wherever found. Therefore, only B. fruit and C. milk contain chemicals.

Solution Which of the following activities should be included in your study plan for learning chemistry? A. Skipping lectures will not help you to understand the concepts. B. Forming a study group will be helpful for learning chemistry. C. Reviewing Learning Goals before reading will help you understand and remember the concepts. D. Becoming an active learner will help you understand the concepts.

1.2 A Study Plan for Learning Chemistry

Features in This Text Help You Study
1. Periodic Table - inside front cover 2. Tables - inside back cover 3. Looking Ahead - beginning of each chapter 4. Learning Goals - beginning of each section 5. Glossary and Index - end of text

Before Reading Before you begin to read the chapter
obtain an overview of the chapter by reading Looking Ahead look at the section title and rephrase it to be a question review the Learning Goal that tells you what to expect in that section

As You Read As you read the chapter
try to answer the question you made from the section title review Concept Checks that help you understand key ideas work through the Sample Problems and review visual Guide to Problem Solving try the Questions and Problems that allow you to apply problem solving to new problems

Throughout the Chapter
Throughout the chapter there are tools that help you connect the chemical concepts you are learning to real life. Chemistry Link to Health Chemistry Link to Industry Chemistry Link to the Environment Chemistry Link to History Macro-to-Micro Illustrations

Figures and Diagrams Many figures and diagrams use micro-to-macro illustrations to depict atomic level of organization to illustrate the concepts in the text to allow you to see the world in a microscopic way

End of Chapter At the end of the chapter there are study aids that complete the chapter, such as Concept Maps, which show connections between important concepts Chapter Reviews, which provide a summary Key Terms, which are listed with their definitions Understanding Concepts, which help you visualize concepts Additional Questions and Problems and Challenge Problems, which provide a means to assess your understanding

Active Learning Steps You can become an active learner and enhance your learning process by reading each Learning Goal for an overview forming a question from the section title and looking for answers as you read self-testing by working Concept Checks, Sample Problems, and Study Checks and checking answers

Study Check Which of the following activities should be included in your study plan for learning chemistry? A. skipping lectures B. forming a study group C. reviewing Learning Goals before reading D. becoming an active learner

Solution Which of the following activities should be included in your study plan for learning chemistry? A. Skipping lectures will not help you to understand the concepts. B. Forming a study group will be helpful for learning chemistry. C. Reviewing Learning Goals before reading will help you understand and remember the concepts. D. Becoming an active learner will help you understand the concepts.

1.3 Units of Measurement

Units of Measurement Scientists use the metric system of measurement and have adopted a modification of the metric system called the International System of Units as a worldwide standard. International System of Units (SI) is an official system of measurement used throughout the world for units in length, volume, mass, temperature, and time.

Units of Measurement, Metric and SI

Length, Meter (m) and Centimeter (cm)
1 m = 100 cm 1 m = 1.09 yd 1 m = 39.4 in cm = 1 in.

Volume, Liter (L) and Milliliter (mL)
1 L = 1000 mL 1 L = 1.06 qt 946 mL = 1 qt We use graduated cylinders to measure small volumes.

Mass, Gram (g) and Kilogram (kg)
1 kg = 1000 g 1 kg = 2.20 lb 454 g = 1 lb The mass of a nickel is 5.01 g on an electronic scale.

Temperature, Celsius (oC) and Kelvin (K)
Water freezes: 32 oF 0 oC The Kelvin scale for temperature begins at the lowest possible temperature, 0 K. A thermometer is used to measure temperature.

Time, Second (s) The second is the correct metric and SI unit for time. The standard measure for 1 s is an atomic clock. A stopwatch is used to measure the time of a race.

Learning Check What are the SI units for the following? A. volume B. mass C. length D. temperature

Solution What are the SI units for the following? A. The SI unit for volume is the cubic meter, m3. B. The SI unit for mass is the kilogram, kg. C. The SI unit for length is the meter, m. D. The SI unit for temperature is Kelvin, K.

1.4 Scientific Notation People have an average of 1 x 105 hairs on their scalp. Each hair is about 8 x 10−6 m wide.

Writing a Number in Scientific Notation
Numbers written in scientific notation have three parts: coefficient power of unit To write 2400 m in correct scientific notation: the coefficient is 2.4 the power of 10 is 3 the unit is "m"

Writing a Number in Scientific Notation
2400. m = 2.4 x 1000 = 2.4 x 103 m  3 places coefficient x power of 10 unit g = = 8.6 x 10−4 g 4 places  coefficient x power of 10 unit

Some Powers of 10

Measurements in Scientific Notation
Diameter chickenpox virus = m = 3 x 10−7 m

Some Measurements Written in Scientific Notation

Scientific Notation and Calculators
Number to enter: 4 x 106 Enter: 4 EXP (EE) 6 Display: 4 06 or E06 Number to enter: 2.5 x 10−4 Enter: 2.5 EXP (EE) +/− 4 Display: 2.5 −04 or 2.5− E−04

Learning Check Write each of the following in correct scientific notation: A. 64,000 g B m C. 138 mL

Solution Write each of the following in correct scientific notation: A. 64,000 g 6.4 x 104 g B m 2.1 x 10−2 m C. 138 mL 1.38 x 102 mL

1.5 Measured Numbers and Significant Figures

Measured Numbers Measured numbers are the numbers obtained when you measure a quantity such as your height, weight, or temperature.

Writing Measured Numbers
To write a measured number, observe the numerical values of marked lines estimate value of number between marks the estimated number is the final number in your measured number

Writing Measured Numbers for Length
The lengths of the objects are measured as (a) 4.5 cm (b) 4.55 cm (c) 3.0 cm

A Number Is Significant When
A number is a significant figure (SF) if it is Example a. not a zero 4.5 g 2 SF b. a zero between digits 205 m 3 SF c. a zero at the end of a 50. L 2 SF decimal number d. in the coefficient of a 4.8 x 105 m 2 SF number written in scientific notation

A Number Is NOT Significant When
A number is not significant if it is Example a. at the beginning of a decimal number s 1 SF b. used as a placeholder in a large number without a decimal point m 2 SF

Learning Check Identify the significant and nonsignificant zeros in each of the following numbers: A m B g C L

Solution Identify the significant and nonsignificant zeros in each of the following numbers: A m The zeros preceding 2 are not significant. The digits 2, 6, 5 are significant. The zero in last decimal place is significant SF B g The zeros between nonzero digits or at the end of decimal numbers are significant SF

Solution Identify the significant and nonsignificant zeros in each of the following numbers: C L The zeros between nonzero digits are significant. The zeros at end of a number with no decimal are not significant SF

Exact Numbers Exact numbers are numbers obtained by counting 8 cookies
in definitions that compare two units 6 eggs in the same measuring system 1 qt = 4 cups 1 kg = 1000 g

Learning Check Identify the numbers below as measured or exact and give the number of significant figures in each measured number: A. 3 coins B. the diameter of a circle is cm C. 60 min = 1 h

Solution Identify the numbers below as measured or exact and give the number of significant figures in each measured number: A. 3 coins is a counting number and therefore is an exact number. B. The diameter of a circle is cm. This is a measured number and the zero is significant, so it contains 4 SF. C. 60 min = 1 h is a definition and therefore an exact number.

1.6 Significant Figures in Calculations

Rules for Rounding Off 1. If the first digit to be dropped is 4 or less, then it and all the following digits are dropped from the number. 2. If the first digit to be dropped is 5 or greater, then the last retained digit of the number is increased by 1.

Examples of Rounding

Learning Check Select the correct value when g is rounded to: A. three significant figures B. two significant figures

Solution Select the correct value when 3.1457 g is rounded to:
A. To round to three significant figures, drop the final digits, 57 increase the last remaining digit by 1. The answer is 3.15 g. B. To round g to two significant figures, drop the final digits 457. do not increase the last number by 1 since the first of these digits is 4. The answer is 3.1 g.

Rules for Multiplication and Division
In multiplication or division, the final answer is written so it has the same number of significant figures as the measurement with the fewest significant figures (SFs). Example 1: Multiply the following measured numbers: cm x 0.35 cm = (calculator display) = 8.6 cm2 (2 significant figures) Multiplying 4 SFs by 2 SFs gives us an answer with 2 SFs.

Multiplication and Division with SFs
Example 2: Multiply and divide the following measured numbers: 21.5 cm x 0.30 cm = 1.88 cm Put the following into your calculator: 21.5 x 0.30 ÷ 1.88 = = 3.4 cm (2 significant figures) Multiplying 4 SFs by 2 SFs gives us an answer with 2 SFs.

Multiplication and Division with SFs
Example 3: Multiply and divide the following measured numbers: 6.0 g = 2.00 g Put the following into your calculator: 6.0 ÷ 2.00 = 3 (calculator display) = 3.0 g (2 significant figures) Add one zero to give 2 significant figures.

Learning Check Perform the following calculation of measured numbers. Give the answer in the correct number of significant figures cm x cm = 2.00 cm

Solution Perform the following calculation of measured numbers. Give the answer in the correct number of significant figures cm x cm = 2.00 cm (3 SF x 4 SF ÷ 3 SF ) = 8.52 cm calculator display and correct significant figures.

Addition and Subtraction
In addition or subtraction, the final answer is written so it has the same number of decimal places as the measurement with the fewest decimal places. Example 1: Add the following measured numbers: g three decimal places g two decimal places g one decimal place g (calculator display) = 66.1 g answer rounded to one decimal place

Addition and Subtraction with SFs
Example 2: Subtract the following measured numbers: g two decimal places − 3.0 g one decimal place g (calculator display) = 62.1 g answer rounded to one decimal place

Learning Check Add the following measured numbers: mg mg

Solution Add the following measured numbers: mg three decimal places mg one decimal place mg (calculator display) = mg answer rounded to one decimal place

1.7 Prefixes and Equalities

Prefixes A special feature of the SI as well as the metric system is that a prefix can be placed in front of any unit to increase or decrease its size by some factor of ten. For example, the prefixes milli and micro are used to make the smaller units: milligram (mg) microgram (μg)

Prefixes and Equalities
The relationship of a prefix to a unit can be expressed by replacing the prefix with its numerical value. For example, when the prefix kilo in kilometer is replaced with its value of 1000, we find that a kilometer is equal to meters. kilometer = 1000 meters kilogram = 1000 grams

Prefixes That Increase Unit Size

Prefixes That Decrease Unit Size

Learning Check Fill in the blanks with the correct prefix:
A m = 1 ___m B. 1 x 10−3 g = 1 ___g C m = 1 ___m

Solution Fill in the blanks with the correct prefix:
A m = 1 ___m The prefix for 1000 is kilo; 1000 m = 1 km B. 1 x 10−3 g = 1 ___g The prefix for 1 x 10−3 is milli; 1 x 10−3 g = 1 mg C m = 1 ___m The prefix for 0.01 is centi; 0.01 m = 1 cm

Measuring Length Each of the following equalities describes the same length in a different unit. 1 m = 100 cm = 1 x 102 cm 1 m = 1000 mm = 1 x 103 mm 1 cm = 10 mm = 1 x 101 mm

Measuring Length The metric length of 1 meter is the same as 10 dm, 100 cm, or 1000 mm.

Measuring Volume Examples of Some Volume Equalities 1 L = 10 dL = 1 x 101 dL 1 L = 1000 mL = 1 x 103 mL 1 dL = 100 mL = 1 x 102 mL

The Cubic Centimeter The cubic centimeter (abbreviated as cm3 or cc) is the volume of a cube whose dimensions are 1 cm on each side. A cubic centimeter has the same volume as a milliliter, and the units are often used interchangeably. 1 cm3 = 1 cc = 1 mL

1 cm3 = 1 cc = 1 mL 10 cm x 10 cm x 10 cm = 1000 cm3 = 1000 mL = 1 L
The Cubic Centimeter 1 cm3 = 1 cc = 1 mL 10 cm x 10 cm x 10 cm = 1000 cm3 = 1000 mL = 1 L

Measuring Mass Examples of Some Mass Equalities 1 kg = 1000 g = 1 x 103 g 1 g = 1000 mg = 1 x 103 mg 1 g = 100 cg = 1 x 102 cg 1 mg = 1000 μg = 1 x 103 μg

Learning Check Identify the larger unit in each of the following: A. mm or cm B. kilogram or centigram C. mL or μL

Solution Identify the larger unit in each of the following: A. mm or cm A mm is m, smaller than a cm, 0.01 m. B. kilogram or centigram A kilogram is 1000 g, larger than a centigram or 0.01 g. C. mL or μL A milliliter is L, larger than a μL, L.

1.8 Writing Conversion Factors

Equalities Equalities
use two different units to describe the same measured amount are written for relationships between units of the metric system, U.S. units, or between metric and U.S. units For example, 1 m = mm 1 lb = oz 2.20 lb = 1 kg

Exact and Measured Numbers in Equalities
Equalities between units in the same system of measurement are definitions that use exact numbers different systems of measurement (metric and U.S.) use measured numbers that have significant figures Exception: The equality 1 in. = 2.54 cm has been defined as an exact relationship and therefore 2.54 is an exact number.

Some Common Equalities

Equalities on Food Labels
The contents of packaged foods in the U.S. are listed in both metric and U.S. units indicate the same amount of a substance in two different units

Conversion Factors A conversion factor is
obtained from an equality and written in the form of a fraction with a numerator and denominator Equality: 1 in. = 2.54 cm inverted to give two conversion factors for every equality 1 in. and cm 2.54 cm in.

Learning Check Write conversion factors from the equality for each of the following: A. L and mL B. hours and minutes C. meters and kilometers

Solution Write conversion factors from the equality for each of the following: A. 1 L = 1000 mL L and mL 1000 mL L B. 1 h = 60 min h and min 60 min h C. 1 km = 1000 m km and m 1000 m km

Conversion Factors in a Problem
A conversion factor may be obtained from information in a word problem is written for that problem only Example 1: The price of one pound (1 lb) of red peppers is $2.39. 1 lb red peppers and $ $ lb red peppers Example 2: The cost of one gallon (1 gal) of gas is $2.89. 1 gal gas and $2.89 $ gal gas

Percent as a Conversion Factor
A percent factor gives the ratio of the parts to the whole % = parts x 100 whole uses the same unit in the numerator and denominator uses the value of 100 can be written as two factors Example: A food contains 30% (by mass) fat: 30 g fat and g food 100 g food g fat

Percent Factor in a Problem
The thickness of the skin fold at the waist indicates 11% body fat. What factors can be written for percent body fat (in kg)? Percent factors using kg: 11 kg fat and 100 kg mass 100 kg mass 11 kg fat

Smaller Percents: ppm and ppb
Small percents are given as ppm and ppb. Parts per million (ppm) = mg part kg whole Example: The EPA allows 15 ppm cadmium in food colors. 15 mg of cadmium = 1 kg of food color Parts per billion (ppb) = μg part Example: The EPA allows 10 ppb arsenic in public water. 10 μg of arsenic = 1 kg of water

Learning Check Write the conversion factors for 10 ppb arsenic in public water from the equality. 10 μg of arsenic = 1 kg of water

Solution Write the conversion factors for 10 ppb arsenic in public water from the equality. 10 μg of arsenic = 1 kg of water Conversion Factors 10 μg arsenic and 1 kg water 1 kg water 10 μg arsenic

Study Tip: Conversion Factors
An equality is written as a fraction (ratio) provides two conversion factors that are the inverse of each other

Learning Check Write the equality and conversion factors for each of the following. A. meters and centimeters B. jewelry that contains 18% gold C. one gallon of gas is $3.40

Solution A. meters and centimeters: 1 m = 100 cm 1m and 100 cm 100 cm 1m B. jewelry that contains 18% gold: 100 g of jewelry = 18 g of gold 18 g gold and 100 g jewelry 100 g jewelry 18 g gold C. one gallon of gas is $3.40: 1 gal gas = $ gal gas and $3.40 $ gal gas

Risk-Benefit Assessment
A measurement of toxicity is LD50 or “lethal dose” the concentration of the substance that causes death in 50% of the test animals in milligrams per kilogram (mg/kg or ppm) of body mass in micrograms per kilogram (g/kg or ppb) of body mass

Learning Check The LD50 for aspirin is 1100 ppm. How many grams of aspirin would be lethal in 50% of persons with a body mass of 85 kg? A. 9.4 g B. 94 g C g

Solution The LD50 for aspirin is 1100 ppm. How many grams of aspirin would be lethal in 50% of persons with a body mass of 85 kg? 85 kg x 1100 mg x 1 g = 94 g of aspirin 1 kg 1000 mg

1.9 Problem Solving

Given and Needed Units To solve a problem, identify the given unit
identify the needed unit Example: A person has a height of 2.0 meters. What is that height in inches? The given unit is the initial unit of height. given unit = meters (m) The needed unit is the unit for the answer. needed unit = inches (in.)

Study Tip: Problem Solving Using GPS
The steps in the Guide to Problem Solving (GPS) are useful in setting up a problem with conversion factors.

Setting Up a Problem How many minutes are in 2.5 hours? Solution:
Step 1 State the given and needed quantities. Given unit: hours Needed unit: min Step 2 Write a unit plan. Plan: hours min

Solving a Problem How many minutes are in 2.5 hours?
Step 3 State equalities and conversion factors to cancel units. 60 min = 1 h 60 min and h 1 h min Step 4 Set up problem to cancel units. Given Conversion Needed unit unit factor 2.5 h x 60 min = 150 min (2 SF) 1 h

Learning Check A rattlesnake is 2.44 m long. How many centimeters long is the snake?

Solution A rattlesnake is 2.44 m long. How many centimeters long is the snake? Step 1 State the given and needed quantities. Given unit: m Needed unit: cm Step 2 Write a unit plan. Plan: meters centimeters

Solution A rattlesnake is 2.44 m long. How many centimeters long is the snake? Step 3 State equalities and conversion factors to cancel units. 1 m = 102 cm 102 cm and m 1 m cm Step 4 Set up problem to cancel units. Given Conversion Needed unit unit factor 2.44 m x 102 cm = 244 cm (3 SF) 1 m

Learning Check How many minutes are in 1.4 days?

Solution How many minutes are in 1.4 days?
Step 1 State the given and needed quantities. Given unit: days Needed unit: minutes Step 2 Write a unit plan. Factor Factor 2 Plan: days h min

Step 3 State equalities and conversion factors to cancel units. 1 day = 24 hours 24 hours and day 1 day hours 1 hour = 60 minutes 60 min and h 1 h min

Step 4 Set up problem to cancel units. Given Conversion Conversion Needed unit unit factor factor 1.4 days x 24 h x 60 min = 2.0 x 103 min 1 day h (rounded) 2 SF Exact Exact = 2 SF

Study Tip: Check Unit Cancellation
Be sure to check the unit cancellation in the setup. The units in the conversion factors must cancel to give the correct unit for the answer. What is wrong with the following setup? 1.4 day x 1 day x h 24 h min = day2/min is not the unit needed. Units don’t cancel properly.

Learning Check If your pace on a treadmill is 65 meters per minute, how many minutes will it take for you to walk a distance of 7.5 kilometers?

Solution If your pace on a treadmill is 65 meters per minute, how many minutes will it take for you to walk a distance of 7.5 kilometers? Step 1 State the given and needed quantities. Given units: 7.5 km, 65 meters per minute Needed unit: minutes Step 2 Write a unit plan. Factor 1 Factor 2 Plan: kilometers meters min

Solution If your pace on a treadmill is 65 meters per minute, how many minutes will it take for you to walk a distance of 7.5 kilometers? Step 3 State equalities and conversion factors to cancel units. 1 kilometer = 103 meters 103 meters and 1 kilometer 1 kilometer meters 65 meters = 1 minute meters and 1 minute 1 minute meters

Solution If your pace on a treadmill is 65 meters per minute, how many minutes will it take for you to walk a distance of 7.5 kilometers? Step 4 Set up problem to cancel units. Given Conversion Conversion Needed unit unit factor factor 7.5 kilometers x 103 meters x 1 minute = 120 minutes 1 kilometer 65 meters (rounded) 2 SF Exact 2 SF = 2 SF

Percent Factor in a Problem
If the thickness of the skin fold at the waist indicates 11% body fat, how much fat is in a person with a mass of 86 kg? Percent factor: kg fat 100 kg mass percent factor 86 kg mass x 11 kg fat = 9.5 kg of fat

Learning Check How many pounds of sugar are in 120 g of candy if the candy is 25% (by mass) sugar?

Solution How many pounds of sugar are in 120 g of candy if the candy is 25% (by mass) sugar? Step 1 State the given and needed quantities. Given units: g of candy 25% by mass sugar Needed unit: pounds sugar Step 2 Write a unit plan. Conversion Percent factor factor Plan: grams pounds candy pounds sugar

Solution How many pounds of sugar are in 120 g of candy if the candy is 25% (by mass) sugar? Step 3 State equalities and conversion factors to cancel units. 1 pound = 454 grams 454 g and lb 1 lb g 25 pounds of sugar = 100 pounds of candy 25 lb sugar and lb candy 100 lb candy lb sugar

Solution How many pounds of sugar are in 120 g of candy if the candy is 25% (by mass) sugar? Step 4 Set up problem to cancel units. Given Conversion Percent unit factor factor 120 g candy x 1 lb candy x 25 lb sugar 454 g candy lb candy = lb of sugar

1.10 Density Objects that sink in water are more dense than water; objects that float in water are less dense.

Density Density compares the mass of an object to its volume
is the mass of a substance divided by its volume Density Expression Density = mass = g or g or g/cm3 volume mL cm3 Note: 1 mL = 1 cm3

Densities of Common Substances

Calculating Density

Learning Check Osmium is a very dense metal. What is its density in g/cm3 if 50.0 g of osmium has a volume of 2.22 cm3? 1) g/cm3 2) g/cm3 3) g/cm3

Solution Step 1 State the given and needed quantities.
Given: g; 22.2 cm Need: density, g/cm3 Step 2 Write the density expression. D = mass volume Step 3 Express mass in grams and volume in mL or cm3. Mass = 50.0 g Volume = 22.2 cm3 Step 4 Substitute mass and volume into the density expression and calculate. D = g = g/cm3 2.22 cm3 = g/cm3 (rounded to 3 SFs)

Volume by Displacement
A solid completely submerged in water displaces its own volume of water has a volume calculated from the volume difference 45.0 mL − 35.5 mL = 9.5 mL = 9.5 cm3

Density Using Volume Displacement
The density of the zinc object is calculated from its mass and volume. Density = mass = g = 7.2 g/cm3 volume cm3

Learning Check 33.0 mL 25.0 mL object
What is the density (g/cm3) of a 48.0-g sample of a metal if the level of water in a graduated cylinder rises from 25.0 mL to 33.0 mL after the metal is added? 1) 0.17 g/cm3 2) 6.0 g/cm3 3) 380 g/cm3 33.0 mL 25.0 mL object

Solution Step 1 State the given and needed quantities. Given: 48.0 g Volume of water = 25.0 mL Volume of water + metal = 33.0 mL Need: Density Step 2 Write the density expression. Density = mass of metal volume of metal

Solution Step 3 Express mass in grams and volume in mL or cm3. Mass = 48.0 g Volume of the metal is equal to the volume of water displaced. Volume of water + metal = 33.0 mL − Volume of water = 25.0 mL Volume of metal = 8.0 mL

Solution Step 4 Substitute mass and volume into the density expression and calculate the density. Density = 48.0 g = 6.0 g = 6.0 g/mL 8.0 mL 1 mL

Sink or Float Ice floats in water because the density of ice is less than the density of water. Aluminum sinks because its density is greater than the density of water.

Learning Check Which diagram correctly represents the liquid layers in the cylinder? Karo syrup (K) (1.4 g/mL); vegetable oil (V) (0.91 g/mL); water (W) (1.0 g/mL) K W V V W K V W K

Solution vegetable oil 0.91 g/mL V W K 1) water 1.0 g/mL
Karo syrup 1.4 g/mL V W K

Problem Solving Using Density
Density can be written as an equality. For a substance with a density of 3.8 g/mL, the equality is 3.8 g = 1 mL From this equality, two conversion factors can be written for density. Conversion 3.8 g and mL factors 1 mL g

Problem Solving Using Density

Learning Check The density of octane, a component of gasoline, is g/mL. What is the mass, in kg, of 875 mL of octane? A kg B kg C kg

Solution The density of octane, a component of gasoline, is g/mL. What is the mass, in kg, of 875 mL of octane? Step 1 State the given and needed quantities. Given: Density of octane = g/mL Volume = 875 mL Needed: Mass of octane Step 2 Write a plan to calculate the needed quantity. Density Conversion factor Plan: milliliters grams kilograms

Solution The density of octane, a component of gasoline, is g/mL. What is the mass, in kg, of 875 mL of octane? Step 3 Write equalities and their conversion factors including density. density g = 1 mL and 1 kg = 1000 g Step 4 Set up problem to calculate the needed quantity. 875 mL x g x 1 kg = kg 1 mL 1000 g Answer is A, kg.

Chapter 1 Chemistry and Measurements

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