Transcript II. Units of Measurement

II. Units of Measurement
Number vs. Quantity
Observing and Collecting Data
•
data may be
• qualitative (descriptive)
• quantitative (numerical)

Quantity = number + unit
UNITS MATTER!!




Agreed upon single measurement system
Standard of measurement, constant value, easy
to preserve, reproduce, and practical in size
7 base units with standard abbreviations
Prefixes added to base units to represent
quantities that are larger or smaller than the
base
Quantity
Symbol
Base Unit
Abbrev.
Length
l
meter
m
Mass
m
kilogram
kg
Time
t
second
s
Temp
T
kelvin
K
Amount
n
mole
mol
Prefix
mega-
Symbol
M
Factor
106
kilo-
k
103
BASE UNIT
---
100
deci-
d
10-1
centi-
c
10-2
milli-
m
10-3
micro-

10-6
nano-
n
10-9
pico-
p
10-12
1. Find the difference between the exponents
of the two prefixes.
2. Move the decimal that many places.
To the left
or right?
move right
move left
Prefix
mega-
Symbol
M
Factor
106
kilo-
k
103
BASE UNIT
---
100
deci-
d
10-1
centi-
c
10-2
milli-
m
10-3
micro-

10-6
nanopico-
n
10-9
p
10-12
1) 20 cm =
______________
m
0.2
2) 0.032 L = ______________
mL
32
3) 45 m =
______________
45,000 nm
4) 805 dm = ______________
0.0805 km
K H D B d C M
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Derived SI Units
• Combinations of SI base units form derived units.
• pressure is measured in kg/m•s2, or pascals

Combination of units.

Volume amount of space occupied by an object
 length  length  length
 (m3 or cm3)
1 cm3 = 1 mL
1 m3 = 1 L
Density (kg/m3 or g/cm3)
mass per volume
M
D=
V

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 = 11,200 g
C. Johannesson

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
0.87 g/mL
V = 29 mL
C. Johannesson
 The unit m3 is used to express ________


One cubic centimeter is equivalent to ___
The relationship between the mass m of a
material, its volume V, and
its density D is __________


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
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Visual Concept
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Visual Concept
Conversion Factors
• A conversion factor is a ratio derived from the
equality between two different units that can be used
to convert from one unit to the other.
• example: How quarters and dollars are related
4 quarters
1
1 dollar
1 dollar
1
4 quarters
0.25 dollar
1
1 quarters
1 quarter
1
0.25 dollar
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Conversion Factors, continued
• Dimensional analysis is a mathematical technique
that allows you to use units to solve problems
involving measurements.
• quantity sought = quantity given × conversion factor
• example: the number of quarters in 12 dollars
number of quarters = 12 dollars × conversion factor
4 quarter
? quarters  12 dollars 
 48 quarters
1 dollar

Indicates accuracy of a measurement
experim ent
al  literature
% error
 100
literature
your value
accepted value

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
% error = 2.9 %
 100

A chemical reaction was carried out three
times. The mass of the product was 8.93 g for
the first trial, 8.94 g for the second trial, and
8.92 g for the third trial. Under the conditions
of the experiment, the reaction is known to
yield 8.60 g of product. The three mass values
measured are?
C. Johannesson


Indicate precision of a measurement.
Consists of all the digits known with
certainty plus one final digit, which is
somewhat uncertain or estimated
2.35 cm

Counting Sig Figs (p.45)
 Count
all numbers EXCEPT:
 Leading zeros -- 0.0025
 Trailing zeros without
a decimal point -- 2,500
1. 23.50
4 sig figs
2. 402
3 sig figs
3. 5,280
3 sig figs
4. 0.080
2 sig figs
Significant Figures, continued
Rounding

Multiply/Divide - The # with the
fewest sig figs determines the # of sig
figs in the answer.
(13.91g/cm3)(23.3cm3) = 324.103g
4 SF
3 SF
3 SF
324 g

Add/Subtract - The # with the lowest
decimal value determines the place of
the last sig fig in the answer.
3.75 mL
+ 4.1 mL
7.85 mL  7.9 mL
224 g
+ 130 g
354 g  350 g
 Exact
Numbers do not limit the # of
sig figs in the answer.
 Counting numbers: 12 students
 Exact conversions: 1 m = 100 cm
 “1” in any conversion: 1 in = 2.54 cm
(15.30 g) ÷ (6.4 mL)
4 SF
2 SF
= 2.390625 g/mL  2.4 g/mL
2 SF
18.9 g
- 0.84 g
18.06 g  18.1 g

WHY????
 Chemistry often deals with very large
and very small numbers.
 There are
602,000,000,000,000,000,000,000
molecules of water in 18 mL
 one electron has a mass of
0.000000000000000000000000000911 g
 We need a shorter way of writing these
numbers
65,000 kg  6.5 × 104 kg

Move decimal until there’s 1 digit to its
left. Places moved = exponent.

Large # (>1)  positive exponent
Small # (<1)  negative exponent

Only include sig figs.
7. 2,400,000 g
2.4 
8. 0.00256 kg
2.56 
9. 7  10-5 km
0.00007 km
10. 6.2  104 mm
62,000 mm
6
10
g
-3
10
kg
(5.44 × 107 g) ÷ (8.1 × 104 mol) =
Type on your calculator:
5.44
EXP
EE
7
÷
8.1
EXP
EE
4
EXE
ENTER
2 g/mol
=
6.7
×
10
= 671.6049383 = 670 g/mol
Using Scientific Measurements
Direct Proportions
• Two quantities are directly proportional to each
other if dividing one by the other gives a constant
value. y  x
• read as “y is proportional to x.”
Using Scientific Measurements
Inverse Proportions
• Two quantities are inversely proportional to each
other if their product is constant.
1
y
x
• read as “y is proportional to 1 divided by x.”
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