lec2 the numerical side of chemistry, measurement and chemical calculations

8/8/2019 Lec2 the Numerical Side of Chemistry, Measurement and Chemical Calculations

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Chemistry is the study of the properties of materials and

the changes that materials undergo.

Chemistry is central to our understanding of other

sciences.

Chemistry is also encountered in everyday life.

Why Study Chemistry



The Molecular Perspective of Chemistry Matter is the physical material of the universe.

Matter is made up of relatively few elements.

On the microscopic level, matter consists of atoms andmolecules.

Atoms combine to form molecules.

As we see, molecules may consist of the same type of

atoms or different types of atoms.

The Study of Chemistry



Molecular Perspective of Chemistry



States of Matter

Matter can be a gas, a liquid, or a solid.

These are the three states of matter.

Gases take the shape and volume of their container.

Gases can be compressed to form liquids.

Liquids take the shape of their container, but they dohave their own volume.

Solids are rigid and have a definite shape and volume.

Classification of M

atter



6

Scientific Method

The scientific method is

the process used by

scientists to explain

observations in nature.

Copyright © 2005 by Pearson Education, Inc.

Publishing as Benjamin Cummings



7

Scientific Method

The scientific method involves

Making Observations

Writing a Hypothesis

Doing Experiments

Proposing a Theory



8

Features of the Scientific Method

Observations

Facts obtained by observing and measuring events in nature.

Hypothesis

A statement that explains the observations.Experiments

Procedures that test the hypothesis.

Theory

A model that describes how the observations occur usingexperimental results.



9

Measurement in Chemistry

In chemistry we

Measure quantities.

Do experiments.

Calculate results.

Use numbers to report

measurements.

Compare results to

standards.



10

Stating a Measurement

In every measurement, a number is followed by a unit.

Observe the following examples of measurements:

Number and Unit35 m

0.25 L

225 lb

3.4 hr



11

Units in the Metric System

In the metric and SI systems, one unit is used for each

type of measurement:

Measurement Metric SILength meter (m) meter (m)

Volume liter (L) cubic meter (m3)

Mass gram (g) kilogram (kg)

Time second (s) second (s)Temperature Celsius (rC) Kelvin (K)



12

Length Measurement

Length

Is measured using a meter

stick.

Uses the unit of meter (m)in both the metric and SI

systems.



13

Inches and Centimeters

The unit of an inch

Is equal to exactly 2.54

centimeters in the metric

(SI) system.

1 in. = 2.54 cm



14

Volume Measurement

Volume

Is the space occupied by a

substance.

Uses the unit liter (L) inmetric system.

1 L = 1.06 qt

Uses the unit m3(cubic

meter) in the SI system.

Is measured using a

graduated cylinder.



15

For each of the following, indicate whether the unit

describes 1) length 2) mass or 3) volume.

____ A. A bag of tomatoes is 4.6 kg.

____ B. A person is 2.0 m tall.

____ C. A medication contains 0.50 g aspirin.

____ D. A bottle contains1.5 L of water.

Learning Check



16

For each of the following, indicate whether the unit describes

1) length 2) mass or 3) volume.

2 A. A bag of tomatoes is 4.6 kg.

1 B. A person is 2.0 m tall.

2 C. A medication contains 0.50 g aspirin.

3 D. A bottle contains 1.5 L of water.

Solution



17

Scientific Notation

Scientific notation

Is used to write very largeor very small numbers.

For the width of a humanhair (0.000 008 m) iswritten

8 x 10-6 m

For a large number such as

4 500 000 s is written

4.5 x 106 s



18

Writing Numbers in Scientific Notation

A number in scientific notation contains a coefficient and apower of 10.

coefficient power of ten coefficient power of ten

1.5 x 102 7.35 x 10-4

To write a number in scientific notation, the decimal point isplaced after the first digit.

The spaces moved are shown as a power of ten.52 000. = 5.2 x 104 0.00378 = 3.78 x 10-3

4 spaces left 3 spaces right



19

Some Powers of Ten

TABLE 1.2



20

Learning Check

Select the correct scientific notation for each.

A. 0.000 008

1) 8 x 1062) 8 x 10-6 3) 0.8 x 10-5

B. 72 000

1) 7.2 x 104 2) 72 x 103 3) 7.2 x 10-4



21

Learning Check

Write each as a standard number.

A. 2.0 x 10-2

1) 200 2) 0.0020 3) 0.020

B. 1.8 x 105

1) 180 000 2) 0.000 018 3) 18 000



22

Solution

Write each as a standard number.

A. 2.0 x 10-2

3) 0.020

B. 1.8 x 105

1) 180 000



23

Measured Numbers

A measuring tool

Is used to determine a

quantity such as height

or the mass of anobject.

Provides numbers for a

measurement called

measured numbers.





24

. l2. . . . l . . . . l3 . . . . l . . . . l4. . cm

The markings on the meter stick at the end of the blue

line are read as

The first digit 2 plus

the second digit 2.7

The last digit is obtained by estimating.

The end of the line might be estimated between 2.7

2.8 as half-way (0.5) or a little more (0.6), which gives

a reported length of 2.75 cm or 2.76 cm.

Reading a Meter Stick



25

Known + Estimated Digits

In the length reported as 2.76 cm,

The digits 2 and 7 are certain (k nown).

The final digit 6 was estimated (uncertain). All three digits (2.76) are significant including the

estimated digit.



26

Learning Check

. l8. . . . l . . . . l9. . . . l . . . . l10. . cm

What is the length of the red line?

1) 9.0 cm

2) 9.03 cm

3) 9.04 cm



27

Solution

. l8. . . . l . . . . l9. . . . l . . . . l10. . cm

The length of the red line could be reported as

2) 9.03 cm

or 3) 9.04 cm

The estimated digit may be slightly different. Both readingsare acceptable.



28

. l3. . . . l . . . . l4. . . . l . . . . l5. . cm

For this measurement, the first and second known digits

are 4.5.

Because the line ends on a mark, the estimated digit in the

hundredths place is 0.

This measurement is reported as 4.50 cm.

Zero as a Measured Number



29

Significant Figures

in Measured Numbers

Significant figures

Obtained from a measurement include

all of the known digits plus the

estimated digit.

Reported in a measurement depend on

the measuring tool.



30

Significant Figures

TABLE 1.4





31

All non-zero numbers in a measured number are

significant.

Measurement Number of Significant

Figures

38.15 cm 4

5.6 ft 2

65.6 lb 3

122.55 m 5

Counting Significant Figures



32

Sandwiched zeros

Occur between nonzero numbers.

Are significant.


Figures

50.8 mm 3

2001 min 4

0.0702 lb 3

0.40505 m 5

Sandwiched Zeros



33

Trailing zeros

Follow non-zero numbers in numbers without decimal

points.

Are usually place holders.

Are not significant.


Figures

25 000 cm 2

200 kg 1

48 600 mL 3

25 005 000 g 5

Trailing Zeros



34

Leading zeros

Precede non-zero digits in a decimal number.

Are not significant.


Figures

0.008 mm 1

0.0156 oz 3

0.0042 lb 2

0.000262 mL 3

Leading Zeros



35

Significant Figures in

Scientific Notation

In scientific notation

All digits including zeros in the coefficient are significant.

Scientific Notation Number of SignificantFigures

8 x 104 m 1

8.0 x 104 m 2

8.00 x 104 m 3



36

State the number of significant figures in each of the

following measurements:

A. 0.030 m

B. 4.050 L

C. 0.0008 g

D. 2.80 m

Learning Check



37

State the number of significant figures in each of the

following measurements:

A. 0.030 m 2

B. 4.050 L 4C. 0.0008 g 1

D. 2.80 m 3

Solution



38

A. Which answer(s) contains 3 significant figures?

1) 0.47602) 0.00476 3) 4.76 x 103

B. All the zeros are significant in1) 0.00307 2) 25.300 3) 2.050 x 103

C. The number of significant figures in 5.80 x 102 is

1) one 2) two 3) three

Learning Check



39

A. Which answer(s) contains 3 significant figures?

2) 0.00476 3) 4.76 x 103

B. All the zeros are significant in

2) 25.300 3) 2.050 x 103

C. The number of significant figures in 5.80 x 102 is

3) three

Solution



40

In which set(s) do both numbers contain the same

number of significant figures?

1) 22.0 and 22.00

2) 400.0 and 4.00 x 102

3) 0.000015 and 150 000

Learning Check



41

Solution

In which set(s) do both numbers contain the same

number of significant figures?

3) 0.000015 and 150 000

Both numbers contain two (2) significant figures.



42

Examples of Exact Numbers

An exact number is obtained

When objects are counted

Counting objects

2 soccer balls4 pizzas

From numbers in a defined relationship.

Defined relationships

1 foot = 12 inches1 meter = 100 cm



43

Exact Numbers

TABLE 1.5





44

Learning Check

Classify each of the following as exact (E) or

measured (M) numbers.

A.__Gold melts at 1064°C.

B.__1 yard = 3 feet

C.__The diameter of a red blood cell is 6 x 10-4 cm.

D.__There are 6 hats on the shelf.

E.__A can of soda contains 355 mL of soda.



45

Classify each of the following as exact (E) or

measured (M) numbers.

A. M A measuring tool is required.

B. E This is a defined relationship.

C. M A measuring tool is used to determine

length.

D. E The number of hats is obtained by counting.

E. M The volume of soda is measured.

Solution



46

Calculated Answers

In calculations,

Answers must have the same

number of significant figures as

the measured numbers. Calculator answers must often

be rounded off.

Rounding rules are used to

obtain the correct number of significant figures.





47

Rounding Off Calculated Answers

When the first digit dropped is 4 or less,

The retained numbers remain the same.

To round 45.832 to 3 significant figures

drop the digits 32 = 45.8

When the first digit dropped is 5 or greater,

the last retained digit is increased by 1.

To round 2.4884 to 2 significant figures

drop the digits 884 = 2.5 (increase by 0.1)



48

Adding Significant Zeros

Sometimes a calculated answer requires more significantdigits. Then one or more zeros are added.

Calculated answer Zeros added togive 3 significant figures

4 4.00

1.5 1.50

0.2 0.200

12 12.0



49

Learning Check

Adjust the following calculated answers to give

answers with three significant figures:

A. 824.75 cm

B. 0.112486 g

C. 8.2 L



50

Solution

Adjust the following calculated answers to give

answers with three significant figures:

A. 825 cm First digit dropped is greater than 4.

B. 0.112 g First digit dropped is 4.

C. 8.20 L Significant zero is added.



51

When multiplying or dividing use

The same number of significant figures as the

measurement with the fewest significant figures.

Rounding rules to obtain the correct number of significant

figures.

Example:110.5 x 0.048 = 5.304 = 5.3 (rounded)

4 SF 2 SF calculator 2 SF

Multiplication and Division



52

Give an answer for the following with the correct

number of significant figures:

A. 2.19 x 4.2 =

1) 9 2) 9.2 3) 9.198

B. 4.311 ÷ 0.07 =

1) 61.59 2) 62 3) 60

C. 2.54 x 0.0028 =0.0105 x 0.060

1) 11.3 2) 11 3) 0.041

Learning Check



53

A. 2.19 x 4.2 = 2) 9.2

B. 4.311 ÷ 0.07 = 3) 60

C. 2.54 x 0.0028 = 2) 11

0.0105 x 0.060

On a calculator, enter each number followed by the

operation key.

2.54 x 0.0028 z 0.0105 z 0.060 = 11.28888889

= 11 (rounded )

Solution



54

When adding or subtracting use

The same number of decimal places as the measurement

with the fewest decimal places.

Rounding rules to adjust the number of digits in the

answer.

25.2 one decimal place

+ 1.34 two decimal places26.54calculated answer

26.5 answer with one decimal place

Addition and Subtraction



55

For each calculation, round the answer to give the

correct number of significant figures.

A. 235.05 + 19.6 + 2 =

1) 257 2) 256.7 3) 256.65

B. 58.925 - 18.2 =

1) 40.725 2) 40.73 3) 40.7

Learning Check



56

A. 235.05

+19.6

+ 2

256.65 rounds to 257 Answer (1)

B. 58.925

-18

.240.725 round to 40.7 Answer (3)

Solution



57

Prefixes

A prefix

In front of a unit increases or decreases the size of that unit.

Make units larger or smaller than the initial unit by one or

more factors of 10.

Indicates a numerical value.

prefix value

1 kilometer = 1000 meters

1 kilogram = 1000 grams



58

Metric and SI Prefixes

TABLE 1.6


Publishing as Benjamin Cmings





59

Equalities

Use two different units to describe the same measured

amount.

Are written for relationships between units of the metricsystem, U.S. units, or between metric and U.S. units.

For example,

1 m = 1000 mm

1 lb = 16 oz

2.20 lb = 1 kg

Equalities



60

Exact and Measured Numbers in

Equalities

Equalities between units of

The same system are definitions and use exact numbers.

Different systems (metric and U.S.) use measurednumbers and count as significant figures.



61

Some Common Equalities

TABLE 1.9





62

A conversion factor

Is a fraction obtained from an equality.

Equality: 1 in. = 2.54 cm

Is written as a ratio with a numerator and denominator.

Can be inverted to give two conversion factors for every

equality.

1 in. and 2.54 cm2.54 cm 1 in.

Conversion Factors



63

Write conversion factors for each pair of units:

A. liters and mL

B. hours and minutes

C. meters and kilometers

Learning Check



64

Write conversion factors for each pair of units:

A. liters and mL Equality: 1 L = 1000 mL

1 L and 1000 mL

1000 mL 1 L

B. hours and minutes Equality: 1 hr = 60 min

1 hr and 60 min

60 min 1 hr

C. meters and kilometers Equality: 1 km = 1000 m

1 km and 1000 m

1000 m 1 km

Solution



65

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 $2.39

$2.39 1 lb red peppers

Example 2: The cost of one gallon (1 gal) of gas is $2.94.

1 gallon of gas and $2.94

$2.94 1 gallon of gas

Conversion Factors in a Problem



66

To solve a problem

Identify the initial unit.

Identify the final unit.

Problem: A person has a height of 2.0 meters.

What is that height in inches?

The initial unit is the given unit of height.

initial unit = meters (m)

The final unit is the unit for the answer.

final unit = inches (in.)

Initial and Final Units



67

Write the initial and final units.

Write a unit plan to convert the initial unit to the final unit.

Write equalities and conversion factors.

Use conversion factors to cancel the initial unit and providethe final unit.

Unit 1 x Unit 2 = Unit 2

Unit 1Initial x Conversion = Final

unit factor unit

Problem Setup



69

Often, two or more conversion factors are required toobtain the unit needed for the answer.

Unit 1 Unit 2 Unit 3

Additional conversion factors are placed in the setup tocancel each preceding unit

Initial unit x factor 1 x factor 2 = Final unit

Unit 1 x Unit 2 x Unit 3 = Unit 3

Unit 1 Unit 2

Using Two or More Factors



71

Be sure to check your 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 1 hr

24 hr 60 min

Units = day2/min is not the uni t needed Units dont cancel properly.

Check the Unit Cancellation



72

Guide to Problem Solving

What is 165 lb in kg?

STEP 1 Initial 165 lb Final: kg

STEP 2 Plan lb kg

STEP 3 Equalities/Factors1 kg = 2.20 lb

2.20 lb and 1 kg

1 kg 2.20 lb

STEP4 Set Up Problem

165 lb x 1 kg = 74.8 kg

2.20 lb



7

3

A bucket contains 4.65 L of water. How manygallons of water is that?

Unit plan: L qt gallon

Equalities: 1.06 qt = 1 L

1 gal = 4 qt

Learning Check



7

4

Initial : 4.65 L Final: gallons

Plan: L qt gallon

Equalities: 1.06 qt = 1 L; 1 gal = 4 qt

Set Up Problem:

4.65 L x x 1.06 qt x 1 gal = 1.23 gal

1 L 4 qt3 SF 3 SF exact 3 SF

Solution



77

Density

Compares the mass of an object to its volume.

Is the mass of a substance divided by its volume.

Density expression

D = mass = g or g = g/cm3

volume mL cm3

Note: 1 mL = 1 cm3

Density



78

Densities of Common Substances

TABLE 1.10





79

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) 2.25 g/cm3

2) 22.5 g/cm3

3) 111 g/cm3

Learning Check



80

Given: mass = 50.0 g volume = 22.2 cm3

Plan: Place the mass and volume of the osmium

metal in the density expression.

D = mass = 50.0 g

volume 2.22 cm3

calculator = 22.522522 g/cm3

final answer (2) = 22.5 g/cm3

Solution



81

Volume by Displacement

A solid completely

submerged in water

displaces its own

volume of water.

The volume of the solid

is calculated from the

volume difference.

45.0 mL - 35.5 mL

= 9.5 mL

= 9.5 cm3



82

Density Using Volume Displacement

The density of the zinc object isthen calculated from its massand volume.

mass = 68.60 g = 7.2 g/cm3

volume 9.5 cm3



83

What is the density (g/cm3) of 48.0 g 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

25.0 mL 33.0 mL

object

Learning Check



84

Given: 48.0 g Volume of water = 25.0 mL

Volume of water + metal = 33.0 mL

Need: Density (g/mL)

Plan: Calculate the volume difference. Change to cm

3

,and place in density expression.

33.0 mL - 25.0 mL = 8.0 mL

8.0 mL x 1 cm3 = 8.0 cm3

1 mLSet up Problem:

Density = 48.0 g = 6.0 g = 6.0 g/cm3

8.0 cm3 1 cm3

Solution



85

Sink or Float

In water,

Ice floats because

the density of ice is

less than thedensity of water.

Aluminum sinks

because its density

is greater than the

density of water.



86

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 writtenfor density.

Conversion 3.8 g and 1 mL

factors 1 mL 3.8 g

Density as a Conversion Factor



87

If olive oil has a density of 0.92 g/mL, how many liters

of olive oil are in 285 g of olive oil?

1) 0.26 L

2) 0.31 L

3) 310 L

Learning Check



88

2) 0.31 L

Given: D = 0.92 g/mL mass = 285 g

Need: volume in liters

Plan: g mL L

Equalities: 1 mL = 0.92 g 1 L = 1000 mL

Set Up:

285 g x 1 mL x 1 L = 0.31 L

0.92 g 1000 mLdensity metric factor factor

Solution



89

A group of students collected 125 empty aluminum

cans to take to the recycling center. If 21 cans make 1.0

lb aluminum, how many liters of aluminum (D=2.70

g/cm3) are obtained from the cans?

1) 1.0 L 2) 2.0 L 3) 4.0 L

Learning Check



90

1) 1.0 L

125 cans x 1.0 lb x 454 g x 1 cm3 x 1 mL x 1 L

21 cans 1 lb 2.70 g 1 cm3 1000 mL

= 1.0 L

Solution



91

Temperature

Temperature

Is a measure of how hot or cold an

object is compared to another

object.

Indicates that heat flows from the

object with a higher temperature to

the object with a lower

temperature.

Is measured using a thermometer.



92

Temperature Scales

Temperature scales

Are Fahrenheit,Celsius, and Kelvin.

Have reference

points for theboiling and freezingpoints of water.





93

On the Fahrenheit scale, there are 180°F between the

freezing and boiling points and on the Celsius scale, there are

100°C.

180°F = 9°F = 1.8°F

100°C 5°C 1°C

In the formula for the Fahrenheit temperature, adding 32

adjusts the zero point of water from 0°C to 32°F.

TF

= 9/5 TC

+ 32r

or TF

= 1.8 TC + 32r

Fahrenheit Formula



94

Solving A Temperature Problem

A person with hypothermia has a

body temperature of 34.8°C. What is

that temperature in °F?

TF = 1.8 TC + 32r

TF

= 1.8 (34.8°C) + 32°

exact tenth's exact

= 62.6 + 32°= 94.6°F tenths





95

The normal temperature of a chickadee is 105.8°F. What

is that temperature on the Celsius scale?

1) 73.8°C

2) 58.8°C

3) 41.0°C

Learning Check



96

3) 41.0 °C

TC = (TF

- 32°)

1.8

= (105.8 - 32°)

1.8

= 73.8°F = 41.0°C

1.8°

Solution



97

On a cold winter day, the temperature is 15°C.

What is that temperature in °F?

1) 19°F

2) 59°F

3) 5°F

Learning Check



98

3) 5°F

TF

= 1.8 TC + 32r

TF

= 1.8( 15°C) + 32°

= 27 + 32°

= 5°F

Note: Be sure to use the change sign key on your

calculator to enter the minus sign.1.8 x 15 +/ = 27

Solution



100

What is normal body temperature of 37°C in kelvins?

1) 236 K

2) 310. K3) 342 K

Learning Check

lec2 the numerical side of chemistry, measurement and chemical calculations

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