# Introductory Chemistry

Lead Author(s): **Jennifer Donovan**

Student Price: **Contact us to learn more**

"Introductory chemistry features over 750 interactive questions and solution keys to include basic math review for intro level students. The course includes embedded videos, virtual and kitchen chemistry labs with related assessment of labs, automatic grading and can be customized for specific course use."

## Key features in this textbook

### Integrated questions

- Includes text-based, integrated homework, and lab-based questions

### Built-in assessments

- Over 760 built-in assessment questions are embedded throughout chapters
- These questions offer hints and solutions for math-based questions
- A discussion area is offered for peer-to-peer interaction

### Interactive learning

- Each chapter comes with auto-graded interactive questions, videos and eye-catching visuals
- Virtual and kitchen chemistry labs are provided, as well as related lab assessments

## Comparison of Introductory Chemistry Textbooks

Consider adding Top Hat’s *Introductory Chemistry* textbook to your upcoming course. We’ve put together a textbook comparison to make the decision easy for you in your upcoming evaluation.

### Top Hat

*Introductory Chemistry*

(only one edition needed)

### McGraw

*Introductory Chemistry: An Atoms Approach*

(1st edition)

### Pearson

*Introductory Chemistry: Concepts and Critical Thinking*

(7th edition)

### Pearson

*Introductory Chemistry*

(6th edition)

### Pricing

Average price of textbook across most common format

#### Up to 40-60% more affordable

Lifetime access on any device

#### Package: $242.67

Does not include labs or interactive practice problems

#### Package: $213.32

Does not include labs or interactive practice problems

#### Package: $258.13

With Mastering Chemistry access for course only, does not include labs

### Always up-to-date content

Constantly revised and updated by a community of professors with the latest content

### In-Book Interactivity

Includes embedded multi-media files and integrated software to enhance visual presentation of concepts directly in textbook

Only available with supplementary resources at additional cost

Only available with supplementary resources at additional cost

Only available with supplementary resources at additional cost

### Customizable

Ability to revise, adjust and adapt content to meet needs of course and instructor

### BUILT-IN INTERACTIVE ASSESSMENT QUESTIONS

Assessment questions with feedback embedded throughout textbook

### All-in-one Platform

Access to additional questions, test banks, and slides available within one platform

## Pricing

Average price of textbook across most common format

### Top Hat

*Introductory Chemistry*

(only one edition needed)

#### Up to 40-60% more affordable

Lifetime access on any device

### McGraw

*Introductory Chemistry: An Atoms Approach*

(1st edition)

#### Package: $242.67

Does not include labs or interactive practice problems

### Pearson

*Introductory Chemistry: Concepts and Critical Thinking*

(7th edition)

#### Package: $213.32

Does not include labs or interactive practice problems

### Pearson

*Introductory Chemistry*

(6th edition)

#### Package: $258.13

With Mastering Chemistry access for course only, does not include labs

## Always up-to-date content

Constantly revised and updated by a community of professors with the latest content

### Top Hat

*Introductory Chemistry*

(only one edition needed)

### McGraw

*Introductory Chemistry: An Atoms Approach*

(1st edition)

### Pearson

*Introductory Chemistry: Concepts and Critical Thinking*

(7th edition)

### Pearson

*Introductory Chemistry*

(6th edition)

## In-book Interactivity

Includes embedded multi-media files and integrated software to enhance visual presentation of concepts directly in textbook

### Top Hat

*Introductory Chemistry*

(only one edition needed)

### McGraw

*Introductory Chemistry: An Atoms Approach*

(1st edition)

### Pearson

*Introductory Chemistry: Concepts and Critical Thinking*

(7th edition)

### Pearson

*Introductory Chemistry*

(6th edition)

## Customizable

Ability to revise, adjust and adapt content to meet needs of course and instructor

### Top Hat

*Introductory Chemistry*

(only one edition needed)

### McGraw

*Introductory Chemistry: An Atoms Approach*

(1st edition)

### Pearson

*Introductory Chemistry: Concepts and Critical Thinking*

(7th edition)

### Pearson

*Introductory Chemistry*

(6th edition)

## Built-in Interactive Assessment Questions

Assessment questions with feedback embedded throughout textbook

### Top Hat

*Introductory Chemistry*

(only one edition needed)

### McGraw

*Introductory Chemistry: An Atoms Approach*

(1st edition)

### Pearson

*Introductory Chemistry: Concepts and Critical Thinking*

(7th edition)

### Pearson

*Introductory Chemistry*

(6th edition)

## All-in-one Platform

Access to additional questions, test banks, and slides available within one platform

### Top Hat

*Introductory Chemistry*

(only one edition needed)

### McGraw

*Introductory Chemistry: An Atoms Approach*

(1st edition)

### Pearson

*Introductory Chemistry: Concepts and Critical Thinking*

(7th edition)

### Pearson

*Introductory Chemistry*

(6th edition)

## About this textbook

### Lead Author

#### Jennifer Donovan Ma.ED, M.S, Ph.D.Arizona State University

Jennifer Donovan is an innovative professor from Arizona State University. She has 19 years of experience working with at-risk and under-represented populations at both the high school and the university level. She has been an integral part of online curriculum for Arizona State University and always strives to keep updated on the best pedagogical practices to help reach students that struggle with math. Dr. Donovan currently serves as a Lecturer and has also published and presented on cutting-edge educational practices.

## Explore this textbook

Read the fully unlocked textbook below, and if you’re interested in learning more, get in touch to see how you can use this textbook in your course today.

# Chapter 1: Introduction to Numbers in Chemistry

Table of Contents

By the end of this chapter, you should be able to:

- Explain what the subject of chemistry can be used for
- Understand how numbers are used in chemistry
- Identify and apply the rules for significant figures
- Convert within the metric system
- Apply dimensional analysis to metric conversions
- Apply density to assigned problems and lab analysis

## 1.1 The subject of chemistry and what it can be used for

In the most basic terms, chemistry is the study of matter and matter is anything that has mass and takes up space. Chemistry is related to the subject of physics because physics is the study of energy and energy affects matter so they are interrelated. Chemistry has been described as the central science because it can encompass all other sciences. Why is chemistry important and how can it be used in your everyday life? The answers are enlightening.

Chemistry is essentially the study of everything. The air we breathe and the water we drink and the food we eat all involve chemistry. In particular, environmental chemistry looks at impacts that certain toxins may have on our air and water supply.

Foods and particular flavors of foods can be created and engineered in a lab through the use of chemistry. Ever wonder how certain drinks have flavors such as 'Riptide?' What exactly is that flavor? It is a flavor designed by a food chemist. Whenever you are creating or modifying a recipe, you are using chemistry..bet you didn't know that!

Have you ever used or viewed fireworks? That also uses chemistry. The creation of structures and building in particular regions of the world involve chemistry. The study of the weather and how it is impacted by how humans are changing the environment involves chemistry.

At this point, you may be asking yourself, "Exactly how do these involve chemistry?" The answers will be found within the pages of this text for your reference and you may soon see the value of this subject and its importance in your everyday life.

## 1.2 Measurement in Chemistry

For many students in chemistry, the thought is that it is entirely about numbers and math. While chemistry is focused upon numbers and quantities of items, these numbers come from measurements that are being performed in a lab setting. This is the reason why chemistry is often touted as being an applied math course. In reality, chemistry does not dwell only on numbers but upon many concepts that some may see as abstract until the concept is applied in every day life such as tasks as simple as boiling water.

The units of measurement used in the United States are based upon the standard or English system. Nearly every other country uses the metric system which is based upon the power of 10. As such, converting within the metric system can be relatively simple and as quick as moving a decimal point. It is important for chemists all across the world to communicate using the same language. In chemistry, this language is the international system which has mostly standard units from the metric system. Most students learn the old phrase 'King Henry died drinking chocolate milk' to apply to the metric system with the following prefixes: Kilo, Hecto, Deka, standard unit, deci, centi and milli.

**

### Metric Practice

However, in chemistry, unit prefixes much smaller than milli will be used. Have you ever heard of nanotechnology? The term 'nano' is a prefix of measurement and this type of technology refers to changing the size of particles and thus changing their physical properties.

The base units in the metric system are as follows: grams to measure mass, meters to measure length, and liters to measure volume. Prefixes are then applied to these base measurements. For example, a kilogram is much larger than a milligram and a kilometer is much larger than a millimeter. For those who may have run track, you already have some background knowledge on these measurements. For example, the traditional 5K race is 5 kilometers which is equivalent to 3.1 miles.

Here are the following prefixes commonly used :

## 1.3 Converting within the Metric System

Let's take a look at some examples for converting within the metric system:

**Converting from Larger to Smaller Units**

Converting between measurements in the metric system requires you to determine which unit you have, what unit to convert to and then moving decimal places. An example of this is shown below.

__Metric Conversions__ are changing a basic unit into a different size. An example of metric conversion is changing a millimeter into a centimeter.

You must use the ladder to change the size of the unit.

Example:

K H D U D ** C ** M

Convert:

2000 mg = _________ grams

On the ladder, *grams* are 3 decimal places to the right of *milligrams*. Therefore, you should move the decimal 3 places to the right to find the measurement in grams.

2000. mg = 2.00 grams

See these conversions and their answers below:

K H D U D **C** M

104 km = 104000 m (moved decimal three spaces to right)

480 cm = 4.80 m (moved decimal two spaces to the left)

5.6 kg= 5600 g (moved decimal three spaces to right)

8 mm= .8 cm (moved decimal one space to the left)

5 L = 5000 mL (moved decimal three spaces to the right)

120 mg= .120 g (moved decimal three spaces to the left)

65 g = 65000 mg (moved decimal three spaces to the right)

There is also a different method for converting between metric units. See example below:

Convert 3.59 kg into g. Do not include units in your answer.

Convert from 2000.4 mm to km. Do not include units in your answer.

Convert 62 picometers to millimeters. Do not use units or scientific notation in your answer.

Convert 5.45 micrograms to femtograms. Do not include units in your answer and do not use scientific notation.

Convert 35 centigrams to grams. Do not include units in your answer.

Convert .067 microliters to liters. Do not include units in your answer.

### 1.4 Significant Figures: Why do we use them?

The use of significant figures is particularly important in the subject of chemistry as the number of digits that a number exhibits can tell us just how accurate the measuring device to determine that number actually was. To compare this to the real world, how accurate must the timing be for swimmers during the Olympics? World class Olympians may need to be measured by the hundredths of a second because of how close these races can be. Measuring in seconds alone would result in many ties. This same concept applies in the chemistry lab. Analog or more traditional devices require an amount of estimation and are not very precise. Digital devices which are now used more often may not require estimation and may be more accurate. An example of an analog measuring device would be measuring tape.

Think about an item to be measured with the tape above that fell between two of those lines. The last digit of that would be estimated. Digital measurements can be more or less precise.

This leads to the discussion of accuracy versus precision and both are needed for a reliable and fair experiment. Precision is based upon how close two measurements are to one another. Using the example above, if you weigh a given substance six times, and get 4.2 mg each time, then your measurement is very precise. Precision is independent of accuracy. You can be very precise but inaccurate, as described above. For an experiment to be accurate, the results must be repeatable.

In Figure 1.11 above, a (a) is neither precise nor accurate. (b) is precise and accurate. (c) is precise but inaccurate. Lastly, the number of digits represented in a lab measurement must be the same in order to analyze results. As an example, if a substance was measured as having 0.04 g and another substance was measured as having 0.0456 g, which is being measured more precisely and how can a scientist effectively compare these two values for analysis? The answer to that is through the use of significant figures. Ideally, all numbers in an experiment should have the same numbers of significant figures. There are specific rules to follow for this that must be applied to the equations used within the course of chemistry. This becomes important because the correct mathematical answer to a problem may not be the correct answer to a problem in chemistry. Let's look at these rules in the next section.

### 1.5 Significant Figures Rules and Examples

See the list below for a list of rules for significant figures:

•**Any digit is significant if it is …**

1) A non-zero

24.7 _________ 2458 __________

2) A zero between non-zeros

7003 _______ 1.503 __________

3) A zero at the end of a number **and** after a decimal (these show *degrees of* *accuracy*)

43.00 __________ 1.010 _____________

4) Part of an exact or counted number

60 minutes = 1 hour 24 students in the class

•**Digits are not significant if they are…**

5) To the left of non-zeros (these are *place holders*)

0.0071 _____ 0.0420 ______

6) At the end of a number **and** there is no written decimal (show *degree* *of accuracy*)

4100 _________ 300 _________

**Exception: If a decimal is written, the zeros **are** significant

4100. ________

**Types of Zeroes:**

•Leading zeros ---> Never significant

•Captive zeros ---> Always significant

•Trailing zeros ---> Sometimes significant, depends on decimal

How many significant figures are in the following number? 100

1

3

0

How many significant figures are in the following number? 0.00090

2

5

1

How many significant figures does the following number have? 1.000803

7

3

4

How many significant figures does the following number have? 0.0000000001

1

0

10

How many significant figures does the following number have? 5.6709

5

4

3

**Adding and Subtracting with Sig Figs**

Example: 13.50 + 7.2 + 23.452

Step 1: Determine the “real” answer ---> 44.152

Step 2: Determine the number of Decimal Places in original numbers

13.50 ---> 2 decimal places

7.2 ---> 1 decimal place

23.452---> 3 decimal places

Step 3: Round answer to the least number of decimal places

Answer has 1 decimal place

44.152 becomes 44.2

Solve to the correct number of sig figs (decimal places) 12 cm + 0.031 cm + 7969 cm = enter your answer as exact numbers only.

Please answer the following problem using the correct number of sig figs (decimal places) 3.419 g + 3.912 g + 7.0518 g + 0.00013 g = Enter your answer as a number only.

Please answer the following problem using the correct number of sig figs (decimal places) 143.00 cm + 289.25 cm + 68.45 cm - 6.00 cm = Enter your answer as a number only.

Please answer the following problem using the correct number of sig figs (decimal places) 0.085 cm + 0.062 cm + 0.14 cm Enter your answer as a number only. Start with 0.

Please answer the following problem using the correct number of sig figs (decimal places) 30.5 g - 16.82 g + 41.07 g + 85.219 g = Enter your answer as a number only. Start with 0.

**Multiplication & Division with Sig Figs**

Step 1: Determine the “real” answer ---> 41.634

Step 2: Determine the number of Significant Figures in original numbers

7.71 ---> 3 significant figures

5.4 ---> 2 significant figures

Step 3: Round answer to the least number of significant figures

Answer has 2 significant figures

41.634 becomes 42

For tougher examples, be sure to follow the order of operations:

PEMDAS or Please Excuse My Dear Aunt Sally for Parentheses, exponents, multiplication, division, addition, and subtraction

26.972−3.5 /4.06+1.8+0.95

Assume parentheses! (26.972−3.5) /(4.06+1.8+0.95)

Calculate top and bottom halves separately and round to appropriate decimal place (addition and subtraction rules)

23.472 /6.81 becomes 23.5 /6.8

Then divide and round to lowest # sigfigs (multiplication and division rules)

23.5 /6.8 = 3.45 Round to 3.5

Here's another example:

(23.1 + 5.61 + 1.008) × 7.6134 × 8.431=?

Calculate addition first and round to tenths

Multiply it with the other two and round to the lowest # sigfigs

(29.7) x 7.6134 x 8.431 = 1906.400589 ---> 1910

Please answer the following problem using the correct number of sig figs 5.08 x 1.2= Enter your answer as a number only.

Please answer the following problem using the correct number of sig figs 0.000180 x 4.00006= Enter your answer as a number only.

Please answer the following problem using the correct number of sig figs 4.819/9.8= Enter your answer as a number only.

Please answer the following problem using the correct number of sig figs 5.08 x 1.2/ 1.90+ 2.0-3.0001= Enter your answer as a number only.

Please answer the following problem using the correct number of sig figs 1.123/6.0+2.001+5.6/5.3 (9.9)= Enter your answer as a number only.

Now, in chemistry, we often deal with very small numbers.

How should we write these? The answer is scientific notation. Rules for this are as follows:

**Scientific Notation Rules**

3,600,000 = 3.6 x 10_{6 }

1) Write Only the Sig Figs

2)Only one # to the left of the decimal

3) Exponent = # of decimal jumps

Exponent is + if # > 1.

Exponent is - if #< 1.

0.000081 = 8.1 x 10^{-5}

Let's look at more examples below:

0.0000634---> 6.34 x 10^{-4}

0.000023 ---> 2.3 x 10^{-5}

0.010 --->1.0 x 10^{-2}

45.01---> 4.501 x 10^{1}

1,000,000 ---> 1 x 10^{6}

4.50 ---> 4.50 x 10^{0}

0.000023 ---> 2.3 x 10^{-5}

2.30 x 10^{4} ---> 23,000

1.76 x 10^{-3--->}^{ }0.00176

1.901 x 10^{-7--->} 0.0000001901

5.40 x 10^{1--->} 54.0

1.76 x 10^{0--->} 1.76

72,000---> 7.2 x 10^{4}

See quick video below for how to input scientific notation into your calculator. Always use the EE or EXP key for scientific notation input.

Choose the correct answer. What is the standard notation for 7.4 x $10 ^ {-5}$ ?

740000

0.0000074

0.000740

7400000

What is the standard notation for the following number? 6.34 x $10 ^ {12}$

6340000000000

0.000000000634

634

Write 534.67 in scientific notation.

5.3467 x $10 ^ { -2}$

53.467 x $10 ^ {-1}$

5.3467 x $10 ^ {2}$

53.467 x $10 ^ {1}$

Write 0.000000091 in scientific notation.

9.1 x $10 ^{-8}$

9.1 x $10 ^{ 8}$

91 x $10^{ -8}$

91 x $10^{ 8}$

Write 1 million in scientific notation.

1 x $10^ {6}$

1 x $10^{ -6}$

10 x $10^{ 6}$

10 x$10^{ -6}$

Lastly, it is hard to understand numbers in a vacuum. How are significant figures really used in chemistry? How is scientific notation used? Why do these numbers matter? This leads into one of the most important and basic concepts in all of chemistry: the concept of dimensional analysis which will be used to converts units that we are familiar and eventually, units that we will soon become familiar with. In chemistry, some of these units will involve very small numbers indeed as we analyze matter in ways that you may never have imagined. Stay tuned for the next section.

## 1.6 Using Dimensional Analysis

Nearly all of the math involved in introductory chemistry will involve the use of dimensional analysis which is also known by some as the factor- label method. This method is a step by step method guaranteed to ensure chemistry problems are properly set up so that answers can be obtained. By now, your eyes may have glossed over and you are about to stop reading...but wait, people use dimensional analysis everyday. We just did not realize it. Have you ever had to convert from gallons to liters or visited another country to find the signs are posted in kilometers per hour and not miles per hour. If you have an imported vehicle, you may have to use metric wrenches. Have you ever seen a temperature in Celsius and wondered why it was so low when it was so hot out? Have you ever had to convert US dollars to another currency? These are some very basic examples of when dimensional analysis and the conversion of one unit to another is needed.

The steps are as follows:

**1**- Write down your given

**2**- Locate your conversion factors

An example of some conversion factors are as follows:

7 days in a week

60 seconds in a minute

12 inches in a foot

Here is a some common conversion factors that may come in handy:

**Common Conversion Factors**

**Mass**

1 kilogram= 2.205 pounds

1 pound = 453.59 grams

1 ounce= 28.35 grams

**Volume**

1 liter= 1.057 quarts

1 US gallon= 3.785 liters

**Length**

1 kilometer= 0.6214 miles

1 meter= 39.37 inches

1 meter= 1.094 yards

1 foot= 30.48 centimeters

1 inch= 2.54 centimeters

**3**- Convert from your given to the units you are interested in making sure your units cancel out diagonally(this may be more than one step)

**4**- Do the math

**5**- Put answer in correct units and with correct sig figs

Doesn't make sense yet? Let's try an example:

Here is a helpful conversion factor: 2.54 cm = 1 inch

**Convert 5 inches into centimeters.**

**1**- Write down your given- 5 inches

**2**- Locate your conversion factors- 2.54 cm = 1 inch

**3**- Convert

5 inches x 2.54 cm

1 inch =

**4**- Do the math 5 inches x 2.54 cm divided by 1 inch is 12.7 cm. Our units of inches cancel out diagonally.

**5**- 12.7 cm is the correct sig fig since 5 has only 1 sig fig and an answer cannot ever have 1 sig fig so the answer should have 3 sig figs.

Let's see some more examples:

Before we try some on our own, let's have some fun with this concept. See the 'related' example below:

How many seconds old are you?

Conversion factors: 1 year= 12 months, 1 month = 4 weeks ( on average) 1 week = 7 days, 1 day= 24 hours, 1 hour= 60 minutes, 1 minute= 60 seconds

43 years x 12 months x 4 weeks x 7 days x 24 hours x 60 minutes x 60 seconds = 1 year 1 month 1 week 1 day 1 hour 1 minute

That equals a very large number indeed! In scientific notation 1.2 x 10 9 power-that's a lot of seconds!

Convert 3.50 inches to centimeters using the following conversion factor: 2.54 cm = 1 inch. Use correct sig figs.

8.89 centimters

8.9 centimeters

9 centimeters

1.38 centimeters

2 centimters

Convert 7.8 km to miles. Use the following conversion factor: 1km= 0.6214 miles Use correct sig figs and units in your answer.

4.8 miles

4.84692 miles

13 miles

12.5 miles

## 1.7 Density

Density is a unit type of measurement in that it is considered a 'derived' form of measurement. It measures the two main characteristics of matter (mass and volume) and since chemistry is the study of matter, density is a fundamental unit used for many uses in the subject. For example, think about the following question: if you are given a large container of 50 mL of clear liquid and another container of 100mL of a clear liquid - are both liquids the same ? Even though mass and volume are individual properties - for a given type of matter they are related.

Density is used every day. For example, helium gas in hot air balloons has less density than air which allows it to float.

Boats also use density to stay afloat because they have ballast tanks that contain air which provide large volumes for small mass to decrease the boat's density. This also helps to explain why scuba divers can dive below the surface by emptying their ballast tanks.

Our density also allows us to float on water. This is also seen with buoyancy since people are more buoyant in salt water pools than in chlorine pools. This also means that swimming in deeper salt water is easier than in chlorine pools because the combination of salt density and deep water can contribute to this increased buoyancy.

How do we measure density?

Ratio of mass:volume

Solids = g/cm^{3}

1 cm^{3} = 1 mL

Liquids = g/mL

Gases = g/L

Volume of a solid can be determined by water displacement – Archimedes Principle

In the above video, we see how to measure volume of a solid object using the water displacement method according to Archimedes' Principle. While volume can be measured mathematically as well, this is a quick laboratory method designed to get the volume of a solid object. Typically, a plastic graduated cylinder would be filled with water to a certain volume. In order to determine the volume , you would subtract the final water volume from the initial water volume.

Can you determine the volume of the ring shown in the above Figure 1.16?

If you came up with the answer of 4, then you now understand the water displacement method.

Remember to always read the graduated cylinder to the bottom of the meniscus (curve of liquid) as shown below:

Density : solids > liquids >>> gases

except ice is less dense than liquid water!

What is the density of a plastic ring that weighs 7.84 grams and takes up 2.3 cubic centimeters of space? Use correct units and sig figs in your answer.

3.4 grams per cubic centimeter

3.41 grams per liter

18 grams per cubic centimeter

18.03 grams per liter

The volume of a rock displaces 22.7 mL of water, and the mass in 39.943 g. What is the density of the rock? Make sure to have correct sig figs and units in the answer you choose.

1.76 g/cubic centimeters

1.7596 g/cubic centimeters

906 g/cubic centimeters

906.7 g/cubic centimeters

The density of silver is 10.49 $g/cm^{3}$. If a sample of silver has a volume of 12.993 $cm ^{3}$, what is the mass? Make sure the answer has the correct number of sig figs.

136.3 grams

136.296 grams

1.239 grams

1.2386 grams

A woman wants to determine if her engagement ring is platinum. 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 $cm^{3}$of water. Is the ring made of platinum? (Density Pt = 21.4 $g/cm^3)$

No

Yes

- Scientific notation is used to express very small or large quantities.
- Prefixes are attached to units to express very small or large scales.
- Significant figures relate to the precision of a measurement.
- Dimensional analysis utilizes conversion factors to express one unit in terms of another.
- Density is the ratio of a substance’s mass to its volume.