Download Rules for Counting Significant Figures

CHEMISTRY
Dr. Shyh-ching Yang
Chemistry, 6e


Steven S. Zumdahl
歐亞書局有限公司
楊
士
慶
Chapter 1(a)
Chemical
Foundations
Introduction: Chemistry is around you
all the time
Prof. Luis W. Alvarez solved the problem of the disappearing dinosaurs.
--- iridium 銥 77Ir
--- niobium 鈮 41 Nb
 Decline of Roman Empire
--- A sweet syrup called “ Sapa”
Boiling down grape juice in a lead-lined vessels, and cooled it down.
It is the reason for Sapa’s sweetness. It was “lead acetate”.
 Story of David & Susam
--- Porphyria 一種稀有的血液疾病
 Low cobalt level 27Co, could be result in personality disorder and
violent behavior.
 Lithium salts have been shown to be very effective in controlling the
effects of manic狂噪depressive憂鬱disease.

Chemistry: A Science for the 21st Century
• Health and Medicine
• Sanitation衛生 systems
• Surgery with
anesthesia麻醉
• Vaccines 疫苗and
antibiotics抗生素
•Energy and the Environment
• Fossil fuels
• Solar energy
• Nuclear energy
1.1
Chemistry: A Science for the 21st Century
• Materials and Technology
• Polymers, ceramics, liquid crystals
• Room-temperature superconductors?
• Molecular computing?
• Food and Agriculture
• Genetically modified crops
• “Natural” pesticides殺蟲劑
• Specialized fertilizers肥料
1.1
（1.1). Chemistry: An Overview



What is matter made of ? – Atoms
Very recently for the first time we can “see”
individual atoms—via STM (Scanning
Tunneling Microscope)
One of the main challenges of chemistry is to
understand the connection between the
macroscopic world that we experience and
the microscopic world of atoms and
molecules.
Figure 1.01a: The surface of a
single grain of table salt.
Figure 1.01b: An oxygen atom on a
gallium 31Ga鎵arsenide 33As砷 surface.
Figure 1.01c: Scanning tunneling microscope image
showing rows of ring-shaped clusters(串) of benzene
molecules on a rhodium 45Rh銠surface.
Figure 1.2 A
charged
mercury atom
shows up as a
tiny white dot.
Figure 1.3: Sand on a beach looks uniform from a
distance, but up close the irregular sand grains are
visible.
Igniting soap
bubbles
filled with a
mixture of
hydrogen and
oxygen.
(1.2) Steps in the Scientific Method(P.6)
1.
Observations
quantitative( involves both a number and a unit)
qualitative（does not involve a number)
2. Formulating hypotheses
possible explanation for the observation
3. Performing experiments
gathering new information to decide whether
the hypothesis is valid
Outcomes(結果） Over the LongTerm
Theory (Model)

A set of tested hypotheses that give an
overall explanation of some natural
phenomenon.
Natural Law


The same observation applies to many
different systems
Example - Law of Conservation of mass
Law（定律） v. Theory

A law summarizes what happens;

A theory (model) is an attempt to
explain why it happens.
Figure 1.4:
The
fundamental
steps of the
scientific
method.
Figure 1.5:
The various
parts of the
scientific
method.
Nature of Measurement

Measurement - quantitative observation
consisting of 2 parts
*Part 1 –number
*Part 2 - scale (unit)

Examples:
* 20 grams
* 6.63   Joule seconds
(1.3) Unit of Measurement

International System
Based on metric system and units
derived （取得）from metric system.
Chemistry In Action
On 9/23/99, $125,000,000 Mars Climate Orbiter entered Mar’s
atmosphere 100 km lower than planned and was destroyed by
heat.
1 lb = 1 N
1 lb = 4.45 N
“This is going to be the
cautionary tale that will be
embedded （深留腦中）into
introduction to the metric
system in elementary school,
high school, and college
science courses till the end of
time.”
1.7
1.7
Figure
1.6:
Measurement of
volume
Figure 1.7: Common types of laboratory
equipment used to measure liquid volume.
Figure 1.8:
An
electronic
analytical
balance.
Figure 1.9:
Measurement of
volume using a
buret. The volume is
read at the bottom
of the liquid curve
(called the
meniscus(新月).
(1.4) Uncertainty in Measurement
 A digit
that must be estimated is
called uncertain. A measurement
always has some degree of
uncertainty.
Figure 1.10: The
results of several
dart throws show the
difference between
precise （精確）and
accurate（準確）.
Accuracy – how close a measurement is to the true value
Precision – how close a set of measurements are to each other
accurate
&
precise
precise
but
not accurate
not accurate
&
not precise
1.8
Scientific Notation
The number of atoms in 12 g of carbon:
602,200,000,000,000,000,000,000
6.022 x 1023
The mass of a single carbon atom in grams:
0.0000000000000000000000199
1.99 x 10-23
N x 10n
N is a number
between 1 and 10
n is a positive or
negative integer
1.8
Scientific Notation
568.762
0.00000772
move decimal left
move decimal right
n>0
n<0
568.762 = 5.68762 x 102
0.00000772 = 7.72 x 10-6
Addition or Subtraction
1. Write each quantity with
the same exponent n
2. Combine N1 and N2
3. The exponent, n, remains
the same
4.31 x 104 + 3.9 x 103 =
4.31 x 104 + 0.39 x 104 =
4.70 x 104
1.8
Scientific Notation
Multiplication
1. Multiply N1 and N2
2. Add exponents n1 and n2
Division
1. Divide N1 and N2
2. Subtract exponents n1 and n2
(4.0 x 10-5) x (7.0 x 103) =
(4.0 x 7.0) x (10-5+3) =
28 x 10-2 =
2.8 x 10-1
8.5 x 104 ÷ 5.0 x 109
=
(8.5 ÷ 5.0) x 104-9 =
1.7 x 10-5
1.8
Precision（精密度）and Accuracy
（準確度）

Accuracy refers to the agreement of a
particular value with the true value.

Precision refers to the degree of
agreement among several elements of the
same quantity.
Types of Error

Random Error (Indeterminate不能確定
的 Error) - measurement has an equal
probability of being high or low.

Systematic Error (Determinate Error) Occurs in the same direction each time
(high or low), often resulting from poor
technique.
(1.5) Significant Figures and Caculations:
Rules for Counting Significant Figures Overview






1.
Nonzero integers
2.
Zeros
 leading zeros( does not count as
significant figures) ex. 0.0025 ( 2 sig.)
 captive (中間）zeros
(yes) ex. 1.008 ( 4sig.)
 trailing(尾數）zeros
ex. 100 (1 sig.); 100.(3 sig.)
1.00*10**2 (3 sig.)
3.
Exact numbers(精確數字）
Rules for Counting Significant
Figures - Details

Nonzero integers always count as
significant figures.
 3456
has
 4 sig figs.
Rules for Counting Significant
Figures - Details

Zeros


–
Leading zeros do not count as
significant figures.
0.0486 has
 3 sig figs.

Rules for Counting Significant
Figures - Details


Zeros
 Captive zeros always count as
–
significant figures.


16.07 has
4 sig figs.
Rules for Counting Significant
Figures - Details


Zeros

–
Trailing zeros are significant only
if the number contains a decimal
point（小數點）.


9.300 has
4 sig figs.
Rules for Counting Significant
Figures - Details

Exact numbers have an infinite
number of significant figures.
1
inch = 2.54 cm, exactly
Significant Figures
•Zeros between nonzero digits are significant
•Any digit that is not zero is significant
1.234 kg
4 significant figures
606 m
3 significant figures
•Zeros to the left of the first nonzero digit are not significant
0.08 L
1 significant figure
•If a number is greater than 1, then all zeros to the right of the decimal point
are significant
2.0 mg
2 significant figures
•If a number is less than 1, then only the zeros that are at the end and in the
middle of the number are significant
0.00420 g
3 significant figures
1.8
How many significant figures are in
each of the following measurements?
3001 g
4 significant figures
0.0320 m3
3 significant figures
6.4 x 104 molecules
2 significant figures
560 kg
2 significant figures
24 mL
2 significant figures
1.8
Significant Figures
Addition or Subtraction
The answer cannot have more digits to the right of the decimal
point than any of the original numbers.
89.332
+1.1
90.432
3.70
-2.9133
0.7867
one significant figure after decimal point
round off to 90.4
two significant figures after decimal point
round off to 0.79
1.8
Significant Figures
Multiplication or Division
The number of significant figures in the result is set by the original number that
has the smallest number of significant figures
4.51 x 3.6666 = 16.536366 = 16.5
3 sig figs
round to
3 sig figs
6.8 ÷ 112.04 = 0.0606926 = 0.061
2 sig figs
round to
2 sig figs
1.8
Significant Figures
Exact Numbers(精確數字）
Numbers from definitions or numbers of objects are considered
to have an infinite number of significant figures
The average of three measured lengths; 6.64, 6.68 and 6.70?
6.64 + 6.68 + 6.70
= 6.67333 = 6.67 = 7
3
Because 3 is an exact number
1.8
Rules for Significant Figures in
Mathematical Operations

Multiplication and Division: # sig figs in
the result equals the number in the least
precise measurement used in the
calculation.
 2.0 =
 12.76  13 (2 sig figs)
 6.38
Rules for Significant Figures in
Mathematical Operations

Addition and Subtraction: # sig figs
in the result equals the number of
decimal(小數點) places in the least
precise measurement.
6.8 + 11.934 =
18.734  18.7 (3 sig figs)


(1.6)Dimensional Analysis
Proper use of “unit factors” leads to
proper units in your answer.
(1.7)Temperature
 Celsius
scale =C
 Kelvin scale =K
 Fahrenheit scale
=F
Figure 1.11: The three major
temperature scales.
Figure 1.12: Normal body temperature on the
Fahrenheit, Celsius, and Kelvin scales.
Temperature
(1.8)Density
Density is the mass of substance per
unit
 volume of the substance:

Matter（物質）:
Anything occupying
space and having
mass.
(1.9) Classification of Matter
 Three
States of Matter:
–
Solid: rigid - fixed volume and shape
–
Liquid: definite volume but assumes
the shape of its container
–
Gas: no fixed volume or shape –
assumes the shape of its container
Figure 1.13: The three states of water (where
red spheres represent oxygen atoms and blue
spheres represent hydrogen atoms).
Types of Mixtures

Mixtures have variable composition.

A homogeneous mixture(均勻混合物）is a
solution(for example, vinegar食用醋)

A heterogeneous mixture （不均勻混合物
is, to the naked eye, clearly not uniform (for
example, a bottle of dressing)
Pure Substances
 Can
be isolated by separation
methods:






Chromatography
Filtration
Distillation
Figure 1.14: Simple laboratory
distillation apparatus.
Figure 1.15a:
Paper
chromatography
of ink.
(a) A line of the
mixture to be
separated is
placed at one end
of a sheet of
porous paper.
Figure 1.15b:
Paper
chromatography
(層析）of ink.
(b) The paper acts
as a wick（燈心）
to draw up the
liquid.
Figure 1.15c:
Paper
chromatography of
ink.
(c) The component
with the weakest
attraction for the
paper travels faster
than the
components that
cling（吸住） to the
paper.
Compound(化合物）: A substance（物質） with
a constant composition that can be broken down
into elements by chemical processes.
Element（元素）: A substance that cannot be
decomposed into simpler substances by
chemical means.
The element mercury (top left) combines with the
element iodine (top right) to form the compound
mercuric iodide (bottom). This is an example of a
chemical change.
Figure 1.16: The organization of matter.
25. How many significant figures are in
each of the following?
a.12
b.1098
c.2001
d .2.001103
e.0.0000101
f .1.01105
g .1000.
h.22.04030
26. How many significant figures are in
each of the following?
a.100
b.1.0 102
c.1.00 103
d .100.
e.0.0048
f .0.00480
g.4.80 103
h.4.800 103
27. Round off each of the following numbers
to three significant figures, and write the
answer in standard exponential notation.
a.312.54
b.0.00031254
c.31, 254, 000
d .0.31254
e.31.254 10
3
28. Use exponential notation to
express the number 480 to




one significant figure.
two significant figures.
Three significant figures.
four significant figures.
29. Perform the following mathematical
operations, and express each result to the
correct number of significant figures.
 A.
97.381+4.2502+0.99195
 B. 171.5+72.915-8.23
 C. 1.00914+0.87104+1.2012
 D. 21.901-13.21-4.0215
30. Perform the following mathematical
operations, and express each result to the
correct number of significant figures.
0.102  0.0821 273
a.
1.01
b.0.14  6.022 1023
c.4.0 104  5.021103  7.34993 102
2.00 106
d.
7
3.00 10
66. Classify each of the following as
homogeneous or heterogeneous.






A. Soil
B. the atmosphere
C. a carbonated soft drink
D. gasoline
E. gold
F. a solution of ethanol and water
68. Classify each of the following as a
mixture or a pure substance









A. Water
B. Blood
C. The Ocean
D. Iron
E. Brass
F. Uranium
G. Wine
H. Leather
I. Table Salt