Transcript Chapter 2 PowerPoint - Barrington Public Schools

Section 2.1
Units and Measurements
Pages 32-39
International System of Units
(SI System)
In 1960, the metric system was
standardized in the form of the
International System of Units (SI).
These SI units were accepted by
the international scientific
community as the system for
measuring all quantities.
SI Base Units
are defined by an object or event in the physical world.
The foundation of the SI is seven independent quantities
and their SI base units. You must learn the first 5
quantities listed!
Quantity
Time
Length
Mass
Temperature
Amount of a
Substance
Electric Current
Luminous Intensity
Base Unit
second (s)
meter (m)
kilogram (kg)
Kelvin (K)
mole (mol)
ampere (A)
candela (cd)
SI Prefixes
SI base units are not always convenient to use so
prefixes are attached to the base unit, creating a more
convenient easier-to-use unit. You must memorize
these!
Prefix
Kilo
---Deci
Centi
Milli
Micro
Nano
Symbol
k
---d
c
m
u
n
Numerica Power of
l Value
10
1000
103
1
100
0.1
10-1
0.01
10-2
0.001
10-3
0.000001
10-6
0.000000001
10-9
Temperature
Temperature is a
measure of the average
kinetic energy of the
particles in a sample of
matter.
Kelvin  C  273
o
The Fahrenheit scale is not used in
chemistry.
SI Derived Units
•
•
In addition to the seven base units, other SI
units can be made from combinations of the
base units.
Area, volume, and density are examples of
derived units.
Volume (m3 or dm3 or cm3 )
length  length  length
1 cm3 = 1 mL
1 dm3 = 1 L
Density
Density (kg/m3 or g/cm3 or g/mL) is a
physical property of matter.
m
D=
V
m = mass
V = volume
Density
An object has a volume of 825 cm3 and a density
of 13.6 g/cm3. Find its mass.
GIVEN:
WORK:
V = 825 cm3
D = 13.6 g/cm3
m=?
m = DV
m
D
V
m = (13.6 g/cm3)(825cm3)
m = 11,220 g
m = 11,200 g
(correct sig figs)
Density
A liquid has a density of 0.87 g/mL. What volume
is occupied by 25 g of the liquid?
GIVEN:
WORK:
D = 0.87 g/mL
V=?
m = 25 g
V=m
D
m
D
V
V = 25 g
= 28.736 mL
0.87 g/mL
V = 29 mL
(correct sig figs)
Non SI Units
The volume unit, liter (L), and
temperature unit, Celsius (C), are
examples of non-SI units frequently
used in chemistry.
SI & English Relationships
• One meter is approximately 3.3 feet.
• One kilogram weighs approximately 2.2
pounds at the surface of the earth.
Remember: Mass (amount of material in
the object) is constant,but weight (force
of gravity on the object) may change.
• One liter or one dm3 is slightly more than a
quart, 1.06 quart to be exact.
Section 2.2
Scientific Notation
Pages 40-43
Scientific
Notation
Scientific Notation
In science, we deal with some very
LARGE numbers:
1 mole = 602000000000000000000000
In science, we deal with some very
SMALL numbers:
Mass of an electron =
0.000000000000000000000000000000091 kg
Imagine the difficulty of calculating
the mass of 1 mole of electrons!
0.000000000000000000000000000000091 kg
x 602000000000000000000000
???????????????????????????????????
Scientific Notation:
A method of representing very large or
very small numbers in the form:
M x 10n
• M is a number between 1 and 10
• n is an integer
2 500 000 000 .
9 8 7 6 5 4 3 2 1
Step #1: Insert an understood decimal point
Step #2: Decide where the decimal must end
up so that one number is to its left
Step #3: Count how many places you bounce
the decimal point
Step #4: Re-write in the form M x 10n
2.5 x
9
10
The exponent is the
number of places we
moved the decimal.
0.0000579
1 2 3 4 5
Step #2: Decide where the decimal must end
up so that one number is to its left
Step #3: Count how many places you bounce
the decimal point
Step #4: Re-write in the form M x 10n
5.79 x
-5
10
The exponent is negative
because the number we
started with was less
than 1.
PERFORMING
CALCULATIONS
IN SCIENTIFIC
NOTATION
ADDITION AND SUBTRACTION
Review:
Scientific notation expresses a
number in the form:
M x
1  M  10
n
10
n is an
integer
4 x 106
6
+ 3 x 10
7 x 106
IF the exponents are
the same, we simply
add or subtract the
numbers in front and
bring the exponent
down unchanged.
106
6
10
4 x
- 3 x
6
1 x 10
The same holds true
for subtraction in
scientific notation.
106
4 x
+ 3 x 105
If the exponents are
NOT the same, we
must move a decimal
to make them the
same.
6
10
4.00 x
4.00 x
6
5
+ .30 x 10
+ 3.00 x 10
6
4.30 x 10
Move the
decimal on
the smaller
number!
6
10
A Problem for you…
-6
10
2.37 x
-4
+ 3.48 x 10
Solution…
-6
002.37
2.37 x 10
-4
+ 3.48 x 10
Solution…
-4
0.0237 x 10
-4
+ 3.48
x 10
-4
3.5037 x 10
PERFORMING
CALCULATIONS
IN SCIENTIFIC
NOTATION
Multiplication and Division
Multiplication
4.0 x 106 Exponents do NOT have
to be the same.
X 3.0 x
MULTIPLY the
coefficients
and
then
11
12 x 10
ADD the exponents.
105
1.2 x 1012
Rewrite in proper
scientific notation.
Division
4.0 x 106 Exponents do NOT have
÷
3.0 x
105
1.3 x 101
to be the same.
DIVIDE the coefficients
and then SUBTRACT
the exponents.
Section 2.2
Dimensional Analysis
Pages 44-46
Dimensional Analysis
Dimensional Analysis
A tool often used in science for
converting units within a measurement
system
Conversion Factor
A numerical factor by which a quantity
expressed in one system of units may
be converted to another system
Dimensional Analysis
The “Factor-Label” Method
Units, or “labels” are canceled, or
“factored” out
g
cm 

g
3
cm
3
Dimensional Analysis
Steps to solving problems:
1. Identify starting & ending units.
2. Line up conversion factors so
units cancel.
3. Multiply all top numbers & divide
by each bottom number.
4. Check units & answer.
Conversion Factors
Fractions in which the numerator and
denominator are EQUAL quantities
expressed in different units
Example:
Factors:
1 in. = 2.54 cm
1 in.
2.54 cm
and
2.54 cm
1 in.
How many minutes are in 2.5
hours?
conversion factor
2.5 hr x 60 min
1 hr
1
cancel
= 150 min
By using dimensional analysis / factor-label
method, the UNITS ensure that you have
the conversion right side up, and the UNITS
are calculated as well as the numbers!
Convert 400 mL to Liters
400 mL
1
L
1000 mL
= .400 L
= 0.4 L
= 4x10-1 L
Convert 0.02 kilometers to m
0.02 km 1 000 m
1
km
= 20 m
= 2x101 m
Squared and Cubed Conversions
Convert 455.5 cm3 to dm3.
1dm=10cm
4 5 5 . 5 c 3m 1 d m 1 d m
1dm
X
X
X
 0 . 4 5 5 5 d 3m
1
10c m 10c m 10c m
Multiple Unit Conversions
Convert 568 mg/dL to g/L.
1 g = 1000 mg
1L = 10 dL
568mg
1g
10dL
g
X
X
 5.68
L
dL
1000mg 1L
Section 2.3
Uncertainty in Data
Pages 47-49
Types of Observations and
Measurements
We make QUALITATIVE
observations of reactions — changes
in color and physical state.
We also make QUANTITATIVE
MEASUREMENTS, which involve
numbers.
Nature of Measurement
Measurement – quantitative observation
consisting of two parts:
 Number
 Scale (unit)
Examples:
 20 grams
 6.63 × 10-34 joule·seconds
Accuracy vs. Precision
Accuracy - how close a measurement is
to the accepted value
Precision - how close a series of
measurements are to each other
ACCURATE = CORRECT
PRECISE = CONSISTENT
Accuracy vs. Precision
Precision and Accuracy in
Measurements
In the real world, we never know
whether the measurement we make
is accurate
We make repeated measurements,
and strive for precision
We hope (not always correctly) that
good precision implies good accuracy
Percent Error
Indicates accuracy of a measurement
experim ent
al  accepted
% error
 100
accepted
your value
given value
Percent Error
A student determines the density of a
substance to be 1.40 g/mL. Find the %
error if the accepted value of the density
is 1.36 g/mL.
% error
1.40 g/m L 1.36 g/m L
1.36 g/m L
0 .0 4
 1 0 0 3 %
1 .3 6
 100
(correct sig figs)
Section 2.3
Significant Figures or Digits
Pages 50-54
Uncertainty in Measurement
A digit that must be estimated
is called uncertain. A
measurement always has some
degree of uncertainty.
Why Is there Uncertainty?
 Measurements
are performed with
instruments
 No instrument can read to an
infinite number of decimal places
Significant Figures
Indicate precision of a measurement.
Recording Sig Figs
Sig figs in a measurement include the known
digits plus a final estimated digit
2.31 cm
Significant Figures
What is the length of the cylinder?
Significant figures
The cylinder is 6.3 cm…plus a little more
The next digit is uncertain; 6.36? 6.37?
We use three significant figures to express the
length of the cylinder.
When you are given a
measurement to work with in a
chemistry problem you may not
know the type of instrument that
was used to make the
measurement so you must apply a
set of rules in order to determine
the number of significant digits
that are in the measurement.
Rules for Counting Significant
Figures
Nonzero integers always count as
significant figures.
3456 has
4 significant figures
Rules for Counting Significant
Figures
Zeros
- Leading zeros do not count as
significant figures.
0.0486 has
3 significant figures
Rules for Counting Significant
Figures
Zeros
-
Captive zeros always count as
significant figures.
16.07 has
4 significant figures
Rules for Counting Significant
Figures
Zeros
Trailing zeros are significant only
if the number contains a decimal
point.
9.300 has
4 significant figures
9,300 has
2 significant figures
Rules for Counting Significant
Figures
Exact Numbers do not limit the # of sig
figs in the answer. They have an infinite
number of sig figs.
Counting numbers: 12 students
Exact conversions: 1 m = 100 cm
“1” in any conversion: 1 in = 2.54 cm
Sig Fig Practice #1
How many significant figures in each of the following?
1.0070 m 
5 sig figs
17.10 kg 
4 sig figs
100,890 L 
5 sig figs
3.29 x 103 s 
3 sig figs
0.0054 cm 
2 sig figs
3,200,000 
2 sig figs
Significant Numbers in Calculations
• A calculated answer cannot be more precise
than the measuring tool.
• A calculated answer must match the least
precise measurement.
• Significant figures are needed for final
answers from
1) multiplying or dividing
2) adding or subtracting
Rules for Significant Figures in
Mathematical Operations
Multiplication and Division
Use the same number of significant figures in the
result as the data with the fewest significant
figures.
1.827 m x 0.762 m = 1.392174 m2 (calculator)
= 1.39 m2 (three sig. fig.)
453.6 g / 21 people = 21.6 g/person (calculator)
= 21.60 g/person (four sig. fig.)
(Question: why didn’t we round to 22 g/person?)
Rounding Numbers in Chemistry
• If the digit to the right of the last sig fig is less
than 5, do not change the last sig fig.
2.532  2.53
• If the digit to the right of the last sig fig is
greater than 5, round up the last sig fig.
2.536  2.54
• If the digit to the right of the last sig fig is a 5
followed by a nonzero digit, round up the last sig
fig.
2.5351  2.54
• If the digit to the right of the last sig fig is a 5
followed by zero or no other number, look at the
last sig fig. If it is odd round it up; if it is even
do not round up.
2.5350  2.54
2.5250  2.52
Sig Fig Practice #2
Calculation
Calculator says:
Answer
3.24 m x 7.0 m
22.68 m2
100.0 g ÷ 23.7 cm3
4.219409283 g/cm3 4.22 g/cm3
23 m2
0.02 cm x 2.371 cm 0.04742 cm2
0.05 cm2
710 m ÷ 3.0 s
236.6666667 m/s
240 m/s
1818.2 lb x 3.23 ft
5872.786 lb·ft
5870 lb·ft
1.030 g ÷ 2.87 mL
2.9561 g/mL
2.96 g/mL
Rules for Significant Figures in
Mathematical Operations
Addition and Subtraction: The number of
decimal places in the result equals the
number of decimal places in the least
precise measurement. Use the same
number of decimal places in the result as
the data with the fewest decimal places.
49.146 m + 72.13 m – 9.1434 m = ?
= 112.1326 m (calculator)
= 112.13 m (2 decimal places)
Adding and Subtracting with
Trailing Zeros
The answer has the same number of trailing
zeros as the measurement with the greatest
number of trailing zeros.
110
one trailing zero
2500
two trailing zeros
+ 230.3
2840.3
answer 2800
two trailing zeros
Sig Fig Practice #3
Calculation
Calculator says:
Answer
3.24 m + 7.0 m
10.24 m
10.2 m
100.0 g - 23.73 g
76.27 g
76.3 g
0.02 cm + 2.371 cm
2.391 cm
2.39 cm
713.1 L - 3.872 L
709.228 L
709.2 L
1818.2 g + 3.37 g
1821.57 g
1821.6 g
2.030 mL - 1.870 mL
0.16 mL
0.160 mL
Learning Check
A. Which answers contain 3 significant
figures?
1)
0.4760
2) 0.00476
3) 4760
B. All the zeros are significant in
1)
0.00307
2) 25.300
3) 2.050 x 103
C. 534,675 rounded to 3 significant figures is
1) 535
2) 535,000
3) 5.35 x 105
Learning Check
In which set(s) do both numbers
contain the same number of
significant figures?
1) 22.0 and 22.00
2) 400.0 and 40
3) 0.000015 and 150,000
Learning Check
In each calculation, round the answer to the
correct number of significant figures.
A. 235.05 +
1) 256.75
B.
58.925
1) 40.725
19.6 + 2.1 =
2) 256.8
3) 257
- 18.2 =
2) 40.73
3) 40.7
Learning Check
A.
2.19 X 4.2 =
1) 9
2) 9.2
B.
4.311 ÷ 0.07
1) 61.58
=
C.
2.54 X 0.0028 =
0.0105 X 0.060
1) 11.3
2) 11
2) 62
3)
9.198
3)
60
3) 0.041