Download Chapter 1_Part II Measurements

Fundamentals of General, Organic and
Biological Chemistry
6th Edition
Chapter Two
Measurements in
Chemistry
Outline
► 2.1 Physical Quantities
► 2.2 Measuring Mass
► 2.3 Measuring Length and Volume
► 2.9 Measuring Temperature
► 2.4 Measurement and Significant Figures
► 2.5 Scientific Notation
► 2.6 Rounding Off Numbers
► 2.7 Converting a Quantity from One Unit to Another
► 2.11 Density
Copyright © 2010 Pearson Education, Inc.
Chapter Two
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Goals
►1. How are measurements made, and what units
are used? Be able to name and use the metric and SI
units of measure for mass, length, volume, and
temperature.
►2. How good are the reported measurements? Be
able to interpret the number of significant figures in a
measurement and round off numbers in calculations
involving measurements.
►3. How are large and small numbers best
represented? Be able to interpret prefixes for units of
measure and express numbers in scientific notation.
Copyright © 2010 Pearson Education, Inc.
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Goals Contd.
►4. How can a quantity be converted from one unit
of measure to another? Be able to convert quantities
from one unit to another using conversion factors.
►5. What techniques are used to solve problems? Be
able to analyze a problem, use the factor-label method
to solve the problem, and check the result to ensure that
it makes sense chemically and physically.
►6. What are temperature,density, and specific
gravity? Be able to define these quantities and use
them in calculations.
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2.1 Physical Quantities
Physical properties such as height, volume, and
temperature that can be measured are called physical
quantities. Both a number and a unit of defined size
is required to describe physical quantity.
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► A number without a unit is meaningless.
► To avoid confusion scientists have agreed on a standard set of
units.
► Scientists use SI or the closely related metric units.
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► Scientists work with both very large and very
small numbers.
► Prefixes are applied to units to make saying and
writing measurements much easier.
► The prefix pico (p) means a trillionth of
► The radius of a lithium atom is 0.000000000152
meter (m). Try to say it.
► The radius of a lithium atom is 152 picometers
(pm). Try to say it.
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Frequently used prefixes are shown below.
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 Use prefixes on SI base units when number is
too large or too small for convenient usage
Ex. 1 mL = 10–3 L
 1 km = 1000 m
 1 ng = 10–9 g
 1,130,000,000 s = 1.13 × 109 s = 1.13 Gs
9
2.2 Measuring Mass
► Mass is a measure of the amount of matter in an
object. Mass does not depend on location.
► Weight is a measure of the gravitational force
acting on an object. Weight depends on location.
► A scale responds to weight.
► At the same location, two objects with identical
masses have identical weights.
► The mass of an object can be determined by
comparing the weight of the object to the weight
of a reference standard of known mass.
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a) The single-pan balance with sliding
counterweights. (b) A modern electronic balance.
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Relationships between metric units of mass and the
mass units commonly used in the United States are
shown below.
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2.3 Measuring Length and Volume
► The meter (m) is the standard measure of length or
distance in both the SI and the metric system.
► Volume is the amount of space occupied by an
object. A volume can be described as a length3.
► The SI unit for volume is the cubic meter (m3).
►Scientists use the International System of Units
(SI), which is based on the metric system.
The abbreviation SI comes from the French, phrase
Système International d’Unités.
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International System of Units (SI)
 Standard system of units used in scientific &
engineering measurements
 Metric
 7 Base Units
14
Learning Check
 What is the SI unit for velocity?
distance
Velocity (v) 
time
meters
m
Velocity units 

seconds
s
 What is the SI unit for volume of a cube?
Volume (V) = length × width × height
V = meter × meter × meter
V = m3
15
Your Turn!
The SI unit of length is the
A. millimeter
B. meter
C. yard
D. centimeter
E. foot
16
Some Useful Conversions
17
Relationships between metric units of length and
volume and the length and volume units commonly
used in the United States are shown below and on the
next slide.
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A m3 is the volume of a cube 1 m or 10 dm on edge.
Each m3 contains (10 dm)3 = 1000 dm3 or liters. Each
liter or dm3 = (10cm)3 =1000 cm3 or milliliters. Thus,
there are 1000 mL in a liter and 1000 L in a m3 .
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2.9 Measuring Temperature
► Temperature is commonly reported either in
degrees Fahrenheit (oF) or degrees Celsius (oC).
► The SI unit of temperature is the Kelvin (K).
► Temperature in K = Temperature in oC + 273.15
► Temperature in oC = Temperature in K - 273.15
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Freezing point of H2O
32oF
0oC
Boiling point of H2O
212oF
100oC
212oF – 32oF = 180oF covers the same range of
temperature as 100oC-0oC=100oC covers. Therefore,
a Celsius degree is exactly 180/100 = 1.8 times as
large as Fahrenheit degree. The zeros on the two
scales are separated by 32oF.
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Fahrenheit, Celsius, and Kelvin temperature scales.
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► Converting between Fahrenheit and Celsius scales
is similar to converting between different units of
length or volume, but is a little more complex.
The different size of the degree and the zero offset
must both be accounted for.
►
►
oF
= (1.8 x oC) + 32
oC = (oF – 32)/1.8
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Laboratory Measurements
 4 common
1.
2.
3.
4.
Length
Volume
Mass
Temperature
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Laboratory Measurements
1. Length
 SI Unit is meter (m)
 Meter too large for most
laboratory measurements
 Commonly use
 Centimeter (cm)
 1 cm = 10–2 m = 0.01 m
 Millimeter (mm)
 1 mm = 10–3 m = 0.001 m
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2. Volume (V)
 Dimensions of (length)3
 SI unit for Volume = m3
 Most laboratory
measurements use V in
liters (L)
 Chemistry glassware
marked in L or mL
 1 L = 1000 mL
 What is a mL?
 1 mL = 1 cm3
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3. Mass
 SI unit is kilogram (kg)
 Frequently use grams (g) in laboratory as more
realistic size
1
 1 kg = 1000 g
1 g = 0.1000 kg = 1000 g
 Mass is measured by comparing weight of sample
with weights of known standard masses
 Instrument used = balance
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4. Temperature
 Measured with thermometer
 3 common scales
A.Fahrenheit scale
 Common in US
 Water freezes at 32 °F and boils at 212 °F
 180 degree units between melting & boiling
points of water
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4. Temperature
B. Celsius scale
 Rest of world (aside from U.S.) uses
 Most common for use in science
 Water freezes at 0 °C
 Water boils at 100 °C
 100 degree units between melting & boiling
points of water
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4. Temperature
C. Kelvin scale
 SI unit of temperature is kelvin (K)
 Note: No degree symbol in front of K
 Water freezes at 273.15 K & boils at 373.15 K
 100 degree units between melting & boiling points
Absolute Zero
 Zero point on Kelvin scale
 Corresponds to nature’s lowest possible
temperature
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Temperature Conversions
oF = (1.8 x oC) + 32
►
oC = (oF – 32)/1.8
►
► Temperature in K = Temperature in oC + 273.15
► Temperature in oC = Temperature in K - 273.15
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Learning Check: T Conversions
1. Convert 100. °F to the Celsius scale.
= 38 °C
2. Convert 100. °F to the Kelvin scale.
 We already have in °C so…
TK = 311 K
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Learning Check: T Conversions
3. Convert 77 K to the Celsius scale.
= –196 °C
4. Convert 77 K to the Fahrenheit scale.
 We already have in °C so
= –321 °F
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Your Turn!
In a recent accident some drums of uranium
hexafluoride were lost in the English Channel. The
melting point of uranium hexafluouride is 64.53 °C.
What is the melting point of uranium hexafluoride
on the Fahrenheit scale?
A. 67.85 °F
B. 96.53 °F
C. 116.2 °F
D. 337.5 °F
E. 148.2 °F
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2.4 Measurement and Significant
Figures
► Every experimental
measurement has a
degree of uncertainty.
► The volume, V, at right
is certain in the 10’s
place, 10mL<V<20mL
► The 1’s digit is also
certain, 17mL<V<18mL
► A best guess is needed
for the tenths place.
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► To indicate the precision of a measurement, the
value recorded should use all the digits known
with certainty, plus one additional estimated digit
that usually considered uncertain by plus or
minus 1.
► No further, insignificant, digits should be
recorded.
► The total number of digits used to express such a
measurement is called the number of significant
figures.
► All but one of the significant figures are known
with certainty. The last significant figure is only
the best possible estimate.
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Below are two measurements of the mass of the
same object. The same quantity is being described
at two different levels of precision or certainty.
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Rules for Significant Figures
1. All non-zero numbers are significant.
Ex. 3.456
has 4 sig. figs.
2. Zeros between non-zero numbers
are significant.
Ex. 20,089
or
2.0089 × 104
has 5 sig. figs
3. Trailing zeros always count as significant if
number has decimal point
Ex. 500.
or
has 3 sig. figs
5.00 × 102
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Rules for Significant Figures
4. Final zeros on number without decimal point
are NOT significant
Ex. 104,956,000
or
1.04956 × 108
has 6 sig. figs.
5. Final zeros to right of decimal point are
significant
Ex. 3.00
has 3 sig. figs.
6. Leading zeros, to left of 1st nonzero digit, are
never counted as significant
Ex. 0.00012
or
1.2 × 10–4
has 2 sig. figs.
39
Learning Check
How many significant figures does each of the
following numbers have?
scientific notation # of Sig. Figs.
1. 413.97
2. 0.0006
4.1397 × 102
5
6 × 10–4
1
3. 5.120063
4. 161,000
5.120063
7
1.61 × 105
3
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Your Turn!
How many significant figures are in 19.0000?
A. 2
B. 3
C. 4
D. 5
E. 6
41
2.5 Scientific Notation
► Scientific Notation is a convenient way to
write a very small or a very large number.
► Numbers are written as a product of a number
between 1 and 10, times the number 10 raised
to power.
► 215 is written in scientific notation as:
215 = 2.15 x 100 = 2.15 x (10 x 10) = 2.15 x 102
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Two examples of converting standard notation to
scientific notation are shown below.
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Two examples of converting scientific notation back to
standard notation are shown below.
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Learning Check
Round each of the following to 3 significant
figures. Use scientific notation where needed.
1. 37.549
37.5 or 3.75 × 101
2. 5431978
5.43 × 106
3. 132.7789003
133 or 1.33 × 102
4. 0.00087564
8.76 × 10–4
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2.6 Rounding off Numbers
► Often when doing arithmetic on a pocket
calculator, the answer is displayed with more
significant figures than are really justified.
► How do you decide how many digits to keep?
► Simple rules exist to tell you how.
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Rules for Rounding
• When rounding to the correct number of
significant figures,
• round down if the last (or leftmost) digit dropped is
four or less;
• round up if the last (or leftmost) digit dropped is
five or more.
Rules for Rounding
• Round to two significant figures:
5.37 rounds to 5.4
5.34 rounds to 5.3
5.35 rounds to 5.4
5.349 rounds to 5.3
• Notice in the last example that only the last (or
leftmost) digit being dropped determines in
which direction to round—ignore all digits to the
right of it.
Significant Figures in Calculations
Multiplication and Division
 Number of significant figures in answer = least
number of significant figures
Ex. 10.54 × 31.4 × 16.987 = 5620 = 5.62×103
4 sig. figs. × 3 sig. figs. × 5 sig. figs = 3 sig. figs.
2
=
700
=
7×10
Ex. 5.896 ÷ 0.008
4 sig. figs. ÷ 1 sig. fig. = 1 sig. fig.
49
Your Turn!
Give the value of the following calculation to the
correct number of significant figures.
 635.4  0.0045 


2.3589


A. 1.21213
B. 1.212
C. 1.212132774
D. 1.2
E. 1
50
Significant Figures in Calculations
Addition and Subtraction
 Answer has same number of decimal places as
quantity with fewest number of decimal
places.
Ex.
4 decimal places
12.9753
Ex.
319.5
+ 4.398
336.9
1 decimal place
3 decimal places
1 decimal place
397
– 273.15
124
0 decimal places
2 decimal places
0 decimal place
51
Your Turn!
When the expression,
412.272 + 0.00031 – 1.00797 + 0.000024 + 12.8
is evaluated, the result should be expressed as:
A. 424.06
B. 424.064364
C. 424.1
D. 424.064
E. 424
52
Exact Numbers
 Number that come from definitions
 12 in. = 1 ft
 60 s = 1 min
 Numbers that come from direct count
 Number of people in small room
 Have no uncertainty
 Assume they have infinite number of significant
figures.
 Do not affect number of significant figures in
multiplication or division
53
Learning Check
For each calculation, give the answer to the correct
number of significant figures.
1.10.0 g + 1.03 g + 0.243 g = 11.3 g or
1.13 × 101 g
2.19.556 °C – 19.552 °C =
3.327.5 m × 4.52 m =
0.004 °C or
4 × 10–3 °C
1.48 × 103 m
4.15.985 g ÷ 24.12 mL =
0.6627 g/mL
or 6.627 g/mL
54
Learning Check
For the following calculation, give the answer to the
correct number of significant figures.
(71.359 m  71.357 m)
(0.002 m)

(3.2 s × 3.67 s)
(11.744 s 2 )
1.
= 2 × 10–4 m/s2
2.
(13.674 cm × 4.35 cm × 0.35 cm )
(856 s + 1531.1 s)
3
(20.818665 cm )
= 0.87 cm3/s

(2387.1 s)
55
Your Turn!
For the following calculation, give the answer to
the correct number of significant figures.
(14.5 cm  12.334 cm)
(2.223 cm  1.04 cm)
A. 179 cm2
B. 1.18 cm
(178.843 cm2 )
(1.183 cm)
C. 151.2 cm
D. 151 cm
E. 178.843 cm2
56
2.7 Problem Solving: Converting a
Quantity from One Unit to Another
► Factor-Label Method: A quantity in one unit is
converted to an equivalent quantity in a different
unit by using a conversion factor that expresses the
relationship between units.
(Starting quantity) x (Conversion factor) = Equivalent quantity
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Writing 1 km = 0.6214 mi as a fraction restates it in
the form of a conversion factor. This and all other
conversion factors are numerically equal to 1.
The numerator is equal to the denominator.
Multiplying by a conversion factor is equivalent to
multiplying by 1 and so causes no change in value.
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When solving a problem, the idea is to set up an
equation so that all unwanted units cancel, leaving
only the desired units.
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Conversion Factors
Ex. How to convert a person’s height from 68.0 in
to cm?
 Start with fact
2.54 cm = 1 in.
60
 multiply original number by conversion factor that
cancels old units & leaves new
Given
× Conversion = Desired
Quantity
Factor
Quantity
2.54 cm
68.0 in. 
= 173 cm
1 in.
 Factor-Label Method can tell us when we have
done wrong arithmetic
1 in.
68.0 in. 
2.54 cm
= 26.8 in2/cm
 Units not correct
61
Ex. Convert 0.097 m to mm.
 Relationship is
1 mm = 1 × 10–3 m
 Can make 2 conversion factors
1 mm
1  10 3 m
1 mm
1  10  3 m
 Since going from m to mm use one on left.
0.097 m 
1 mm
1  10
3
m
= 173 cm
62
Non-metric to Metric Units
Convert speed of light from 3.00×108 m/s to mi/hr
 Use Factor-Label Method
 1 min = 60 s
 1 km = 1000 m
60 min = 1 hr
1 mi = 1.609 km
3.00  10 8 m 60 s 60 min


 1.08 × 1012 m/hr
s
1 min
1 hr
12
1.08  10
hr
m
1 km
1 mi



1000 m 1.609 km
6.71 × 108 mi/hr
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2.11 Density
Density relates the mass of an object to its volume.
Density is usually expressed in units of grams per cubic
centimeter (g/cm3) for solids, and grams per milliliter
(g/mL) for liquids.
Density =
Copyright © 2010 Pearson Education, Inc.
Mass (g)
Volume (mL or cm3)
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Learning Check
 A student weighs a piece of gold that has a
volume of 11.02 cm3 of gold. She finds the mass
to be 212 g. What is the density of gold?
m
d
V
d
212 g
11.02 cm 3
 19.3 g/cm3
65
Density
 Most substances expand slightly when heated
 Same mass
 Larger volume
 Less dense
 Density  slightly as T 
 Liquids & Solids
 Change is very small
 Can ignore except in very precise calculations
 Density useful to transfer between mass &
volume of substance
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Learning Check
1. Glass has a density of 2.2 g/cm3. What is the
volume occupied by 22 g of glass?
m
22 g
V

 10. g/cm3
d 2.2 g/cm 3
2. What is the mass of 400 cm3 of glass?
m  d  V  2.2 g/cm3  400. cm3  880 g
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Your Turn!
Titanium is a metal used to make artificial joints. It
has a density of 4.54 g/cm3. What volume will a
titanium hip joint occupy if its mass is 205 g?
A. 9.31 × 102 cm3
B. 4.51 × 101 cm3
C. 2.21 × 10–2 cm3
V
205 g
4.54 g cm 3

D. 1.07 × 10–3 cm3
E. 2.20 × 10–1 cm3
68
Your Turn!
A sample of zinc metal (density = 7.14 g cm-3) was
submerged in a graduated cylinder containing water.
The water level rose from 162.5 cm3 to 186.0 cm3
when the sample was submerged. How many grams
did the sample weigh?
mass  density  volume
A. 1.16 × 103 g
B. 1.33 × 103 g
C. 23.5 g
D. 1.68 × 102 g
volume  ( 186.0 cm3  162.5 cm3 )
 23.5 cm 3
mass  7.14 g cm 3  23.5 cm3
E. 3.29 g
69
Specific Gravity
 Ratio of density of substance to density of water
density of substance
specific gravity 
density of water
 Unitless
 Way to avoid having to tabulate densities in all
sorts of different units
70
Learning Check
Liquid hydrogen has a specific gravity of
7.08 × 10–2. If the density of water is 1.05 g/cm3 at
the same temperature, what is the mass of hydrogen in
a tank having a volume of 36.9 m3?
dsulfuric acid  specific gravity sulfuric acid  dH2O
A. 7.43 × 10–2 g
B. 2.74 g
C. 274 g
D. 2.74 × 106 g
E. 2.61 × 106 g
dsulfuric  7.08  10 2  1.05 g/cm 3
acid
= 7.43 × 10–2 g/cm3
m sulfuric acid  7.43  10 2 g/cm 3
 100 cm 
 36.9m  

 1m 
3
3
71
Chapter Summary
► Physical quantities require a number and a unit.
► Preferred units are either SI units or metric units.
► Mass, the amount of matter an object contains, is
measured in kilograms (kg) or grams (g).
► Length is measured in meters (m). Volume is
measured in cubic meters in the SI system and in
liters (L) or milliliters (mL) in the metric system.
► Temperature is measured in Kelvin (K) in the SI
system and in degrees Celsius (°C) in the metric
system.
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Chapter Summary Contd.
► The exactness of a measurement is indicated by
using the correct number of significant figures.
► Significant figures in a number are all known with
certainty except for the final estimated digit.
► Small and large quantities are usually written in
scientific notation as the product of a number
between 1 and 10, times a power of 10.
► A measurement in one unit can be converted to
another unit by multiplying by a conversion factor
that expresses the exact relationship between the
units.
Copyright © 2010 Pearson Education, Inc.
Chapter Two
73