Lec2 the Numerical Side of Chemistry, Measurement and Chemical Calculations
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Transcript of 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
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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
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Molecular Perspective of Chemistry
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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
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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
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Scientific Method
The scientific method involves
Making Observations
Writing a Hypothesis
Doing Experiments
Proposing a Theory
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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.
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Measurement in Chemistry
In chemistry we
Measure quantities.
Do experiments.
Calculate results.
Use numbers to report
measurements.
Compare results to
standards.
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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
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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)
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Length Measurement
Length
Is measured using a meter
stick.
Uses the unit of meter (m)in both the metric and SI
systems.
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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
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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.
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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
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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
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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
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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
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Some Powers of Ten
TABLE 1.2
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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
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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
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Solution
Write each as a standard number.
A. 2.0 x 10-2
3) 0.020
B. 1.8 x 105
1) 180 000
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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.
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. 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
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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.
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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
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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.
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. 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
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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.
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Significant Figures
TABLE 1.4
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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
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Sandwiched zeros
Occur between nonzero numbers.
Are significant.
Measurement Number of Significant
Figures
50.8 mm 3
2001 min 4
0.0702 lb 3
0.40505 m 5
Sandwiched Zeros
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Trailing zeros
Follow non-zero numbers in numbers without decimal
points.
Are usually place holders.
Are not significant.
Measurement Number of Significant
Figures
25 000 cm 2
200 kg 1
48 600 mL 3
25 005 000 g 5
Trailing Zeros
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Leading zeros
Precede non-zero digits in a decimal number.
Are not significant.
Measurement Number of Significant
Figures
0.008 mm 1
0.0156 oz 3
0.0042 lb 2
0.000262 mL 3
Leading Zeros
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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
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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
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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
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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
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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
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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
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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.
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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
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Exact Numbers
TABLE 1.5
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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.
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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
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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.
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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)
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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
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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
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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.
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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
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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
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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
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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
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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
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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
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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
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Metric and SI Prefixes
TABLE 1.6
Copyright © 2005 by Pearson Education, Inc.
Publishing as Benjamin Cmings
Copyright © 2007 by Pearson Education, Inc.
Publishing as Benjamin Cummings
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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
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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.
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Some Common Equalities
TABLE 1.9
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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
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Write conversion factors for each pair of units:
A. liters and mL
B. hours and minutes
C. meters and kilometers
Learning Check
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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Densities of Common Substances
TABLE 1.10
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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
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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
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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
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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
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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
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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
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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.
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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
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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
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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
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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
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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
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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.
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Temperature Scales
Temperature scales
Are Fahrenheit,Celsius, and Kelvin.
Have reference
points for theboiling and freezingpoints of water.
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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
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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
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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
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3) 41.0 °C
TC = (TF
- 32°)
1.8
= (105.8 - 32°)
1.8
= 73.8°F = 41.0°C
1.8°
Solution
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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
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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
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What is normal body temperature of 37°C in kelvins?
1) 236 K
2) 310. K3) 342 K
Learning Check