How Chemists Use Numbers in Science
Chapter 4: How Chemists Use Numbers
ICK
!
What is water,
ugly human ?
(A visceral way
to explain why
units)
WHY UNITS ????? (BORING….)
F
u
n
d
a
m
e
n
t
a
l
S
I
(
l
e
S
y
s
t
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m
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I
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t
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r
n
a
t
i
o
n
a
l
)
U
n
i
t
s
(
s
e
e
T
a
b
l
e
4
.
1
,
p
1
2
3
)
•
L
ength (meters, m)
•
M
ass (kilograms, kg)
•
t
ime (seconds, s)
•
T
emperature (Kelvin, K)
Basic
biggies to
know
•
count of stuff (moles, mol)
`
m
k
s
’
+
Chemistry
add-on
Area =
derived units
= combos of
fundamental
L,M, t, T
...
L
(m) x
L
(m)
m
2
Volume (
V
)=
L
(m) x
L
(m) x
L
(m)
m
3
Speed=
L
(m)
t
(s)
m
s
Energy=
M
(kg)*
L
(m) x
L
(m)
t
(s)*
t
(s)
Density=
M
(kg)
V
(m
3)
kg m
2
s
2
kg
m
3
DERIVED UNITS
Derived unit
•
Width
of a human
blood cell:
~0.000002 m
•
time
for
computer
to do a single operation:
~ 0.000000003 s
•
Nimitz class aircraft carrier weighs:
~ 100,000,000 kg
•
Distance
to Sun:
~
13,000,000,000 m
….
It’s hard to recognize/remember
how many zeroes….
The “problem’ with the
M
K
S
system…
Two ways to keep track of the zeroes
and the decimal place:
•
scientific notation
•
Prefixes
Example:
Width
of a human
blood cell in
scientific notation
0.000002 m
Review of scientific notation:
6 bunny hops to right starting from decimal to
form a number (
2
) which is between 1 and 9….
aka: Bunny hop arithmetic
0.000002 m
=
decimal
scientific notation
2 *10
-6
m
•
time
for
computer
to do a single operation:
~ 0.000000003 s
•
Nimitz class aircraft carrier weighs:
~ 100,000,000 kg
•
Distance
to Sun:
~
13,000,000,000 m
In-class board practice converting decimal to
scientific notation…count with me !
3*10
-9
s
1*10
+9
kg
1.3*10
+10
m
Can we `simplify’ scientific notation expressions even
more ??? (The 10
xx
thingie still requires remembering
sign and exponent…)
Prefixes are symbolic, `word’
versions of powers of 10
Example: 10
-3
= m= milli
get this table in your head by Monday (mini-quiz)
see also-
Text
table 4.2
p. 125
Board practice with:
•
prefix assignment
E
x
p
r
e
s
s
t
h
e
w
i
d
t
h
o
f
a
h
u
m
a
n
b
l
o
o
d
c
e
l
l
(
0
.
0
0
0
0
0
1
m
=
1
*
1
0
-
6
m
)
i
n
p
r
e
f
i
x
n
o
t
a
t
i
o
n
A.
1 mm
B.
1 Mm
C.
1 Gm
D.
1
m
E
x
p
r
e
s
s
t
h
e
t
i
m
e
f
o
r
a
s
i
n
g
l
e
c
o
m
p
u
t
e
r
o
p
e
r
a
t
i
o
n
0
.
0
0
0
0
0
0
0
0
3
s
i
n
p
r
e
f
i
x
n
o
t
a
t
i
o
n
(
r
e
c
a
l
l
0
.
0
0
0
0
0
0
0
0
3
=
3
*
1
0
-
9
)
A.
3 Gs
B.
0.3 ns
C.
0.003
s
D.
3 ns
Express the mass of a Nimitz class aircraft carrier in
the most reasonable prefixed unit. (It weighs
100,000,000 kg =100,000,000,000 g = 1*10
11
g
A.
100 Gg
B.
100000 Mg
C.
0.01 Tg
D.
1 Gg
(Unfortunately) there are many competing choices of
prefixes for a given quantity in chemistry (and physics and
biology)
EXAMPLE
Common prefix units used
to define wavelength,
:
•
m
•
nm
•
pm
•
m
m
(millimicron)
•
Å =10
-1
nm
“How do I convert
between these %%&!
prefix systems ?”
15
m = ??? pm
1) Algebraic (‘Marine’ way)
Doc’s story about his HS chem teacher
Divide and
conquer,
maggot !
2
w
a
y
s
t
o
c
o
n
v
e
r
t
b
e
t
w
e
e
n
m
e
t
r
i
c
u
n
i
t
s
15
m = ??? pm
1) Algebraic (‘Marine’ way)
Doc’s story about his HS chem teacher
Divide and
conquer,
maggot !
2
w
a
y
s
t
o
c
o
n
v
e
r
t
b
e
t
w
e
e
n
m
e
t
r
i
c
u
n
i
t
s
2)
Factor-label (commonly taught by high school
teachers) Major stumbling block for many students
15
m = ??? pm
Done two ways
on blackboard
Guided practice Unit conversions
Convert 45.7 kg to g
Convert 0.73 mL to
L
Convert 7.2 kg/L to mg/
L
4.57*10
4
g
730
L =7.3*10
2
L
7.2 mg/
L
answers
Convert 100 ps to ns
100 ps =0.1 ns
Convert 100 pm to nm
A.
0.01 nm
B.
0.001 nm
C.
1 nm
D.
0.1 nm
E.
No clue…help !
Convert 5000 kg to Mg
A.
5 Mg
B.
50 Mg
C.
0.5 Mg
D.
500 Mg
E.
Still no clue…need nap
PRECISION AND ACCURACY :
what are they ?
Your thoughts…..
Why do we care about
Sig Figs
in Chemistry?
The
Sig Fig
count tells us the precision of measuremen
t
How long is the screw ?
5 cm
1
sig fig
How long is the screw now?
5.1 cm
2
sig fig
How many sig figs now ?
51.03
mm
Metric micrometer does even better
How long is the screw now in cm ?
5.103 cm
4 sig fig
Technological aside:
Higher verifiable precision
(more sig figs) correlates
with higher technical development
1492:
Columbus is
within
+
10,000
miles
of estimate for Earth’s
diameter
2016:
we can pin point the
position of anyone via GPS
to within ~
+
0.0001
miles
(within 12 inches)
In ~ 500 years human measurement
precision has increased by > 10 million
C
o
u
n
t
i
n
g
s
i
g
f
i
g
s
:
A
t
l
a
n
t
i
c
&
P
a
c
i
f
i
c
m
e
t
h
o
d
A
bsent
Decimal…
move from right
(
A
tlantic
side) and start
counting when first non-
zero digit encountered
10020
300
450070
4
1
5
# sig fig ?
C
o
u
n
t
i
n
g
s
i
g
f
i
g
s
:
A
t
l
a
n
t
i
c
&
P
a
c
i
f
i
c
m
e
t
h
o
d
P
ossesses
decimal
…move from left
(
P
acific
side) and start
counting when first
non-zero digit
encountered
1.002
0.030
0.00400
4
2
3
# sig fig ?
What is the sig fig count given a
scientific notation version of a
number ???
Example:
6.02
*10
23
exponent
Pre-exponent
The count of digits in the
pre-exponent
is
the sig fig count.
3 sig figs
2
2
3
5
2
# sig figs ?
In Chapter 4, chemists utilize numbers to quantify properties of matter. Understanding units, fundamental SI quantities, and derived units is crucial for precise measurements. Scientific notation and prefixes help simplify large and small values. Explore practical examples and in-class exercises to familiarize yourself with these concepts in chemistry.
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Presentation Transcript
WHY UNITS ????? (BORING.) What is water, ugly human ? (A visceral way to explain why units)
Fundamental SI (le Fundamental SI (le S Systeme Units (see Table Units (see Table 4.1, p 123) ysteme I International) nternational) 4.1, p 123) Length (meters, m) Mass (kilograms, kg) time (seconds, s) Temperature (Kelvin, K) Basic biggies to know `mks +Chemistry add-on count of stuff (moles, mol)
DERIVED UNITS derived units = combos of fundamental L,M, t, T... Derived unit m2 Area = L(m) x L(m) Volume (V)= L(m) x L(m) x L(m) m3 M(kg) V(m3) Density= kg m3 L(m) t(s) Speed= m s Energy= M(kg)*L(m) x L(m) t(s)*t(s) kg m2 s2
The problem with the MKS system Width of a human blood cell: ~0.000002 m time for computer to do a single operation: ~ 0.000000003 s Nimitz class aircraft carrier weighs: ~ 100,000,000 kg Distance to Sun: .It s hard to recognize/remember how many zeroes . ~13,000,000,000 m
Two ways to keep track of the zeroes and the decimal place: scientific notation Prefixes
Review of scientific notation: aka: Bunny hop arithmetic Example: Width of a human blood cell in scientific notation 0.000002 m 6 bunny hops to right starting from decimal to form a number (2) which is between 1 and 9 . 2 *10-6 m 0.000002 m= decimal scientific notation
In-class board practice converting decimal to scientific notation count with me ! time for computer to do a single operation: ~ 0.000000003 s 3*10-9 s Nimitz class aircraft carrier weighs: ~ 100,000,000 kg 1*10+9 kg Distance to Sun: ~13,000,000,000 m 1.3*10+10 m
Can we `simplify scientific notation expressions even more ??? (The 10xx thingie still requires remembering sign and exponent )
Prefixes are symbolic, `word versions of powers of 10 Example: 10-3 = m= milli
get this table in your head by Monday (mini-quiz) Prefix symbol T Prefix name Tera Power of 10 equivalent 1012 109 106 103 10-1 10-2 10-3 10-6 10-9 10-12 see also- Text table 4.2 p. 125 G giga M mega k kilo d deci c centi m milli micro n nano p pico
Board practice with: prefix assignment
Express the width of a human blood cell Express the width of a human blood cell (0.000001 m=1*10 (0.000001 m=1*10- -6 6 m) in prefix notation m) in prefix notation A. 1 mm B. 1 Mm C. 1 Gm D. 1 m
Express the time for a single computer operation Express the time for a single computer operation 0.000000003 s in prefix notation in prefix notation (recall 0.000000003=3*10 (recall 0.000000003=3*10- -9 9) ) A. 3 Gs B. 0.3 ns C. 0.003 s D. 3 ns
Express the mass of a Nimitz class aircraft carrier in the most reasonable prefixed unit. (It weighs 100,000,000 kg =100,000,000,000 g = 1*1011 g A. 100 Gg B. 100000 Mg C. 0.01 Tg D. 1 Gg 0% 0% 0% 0% 1 Gg 100 Gg 0.01 Tg 100000 Mg
(Unfortunately) there are many competing choices of prefixes for a given quantity in chemistry (and physics and biology) How do I convert between these %%&! prefix systems ? EXAMPLE Common prefix units used to define wavelength, : m nm pm m m (millimicron) =10-1 nm
2 ways to convert between metric units 2 ways to convert between metric units 1) Algebraic ( Marine way) Doc s story about his HS chem teacher Divide and conquer, maggot !
2 ways to convert between metric units 2 ways to convert between metric units 1) Algebraic ( Marine way) Doc s story about his HS chem teacher Divide and conquer, maggot !
2) Factor-label (commonly taught by high school teachers) Major stumbling block for many students
15 m = ??? pm Done two ways on blackboard
Guided practice Unit conversions answers 4.57*104 g Convert 45.7 kg to g Convert 0.73 mL to L 730 L =7.3*102 L Convert 100 ps to ns 100 ps =0.1 ns Convert 7.2 kg/L to mg/ L 7.2 mg/ L
Convert 100 pm to nm A. 0.01 nm B. 0.001 nm C. 1 nm D. 0.1 nm E. No clue help ! 20% 20% 20% 20% 20% 0.1 nm 1 nm 0.01 nm 0.001 nm No clue help !
Convert 5000 kg to Mg A. 5 Mg B. 50 Mg C. 0.5 Mg D. 500 Mg E. Still no clue need nap 20% 20% 20% 20% 20% 5 Mg 0.5 Mg 50 Mg 500 Mg Still no clue need nap
PRECISION AND ACCURACY : what are they ? Your thoughts ..
Why do we care about Sig Figs in Chemistry? The Sig Fig count tells us the precision of measurement 1 sig fig How long is the screw ? 5 cm 2 sig fig How long is the screw now? 5.1 cm
Metric micrometer does even better https://encrypted-tbn2.gstatic.com/images?q=tbn:ANd9GcRu9WN1XxxcSOTsTy-DltBINC5f_qxjtpTZ1oDPoSYOHFtu_Bhm 51.03mm How long is the screw now in cm ? 5.103 cm 4 sig fig How many sig figs now ?
Technological aside: Higher verifiable precision (more sig figs) correlates with higher technical development 2016: we can pin point the position of anyone via GPS to within ~ + 0.0001 miles (within 12 inches) 1492: Columbus is within + 10,000 miles of estimate for Earth s diameter In ~ 500 years human measurement precision has increased by > 10 million
Counting sig figs Counting sig figs: : Atlantic Atlantic & & Pacific Pacific method method Absent Decimal move from right (Atlantic side) and start counting when first non- zero digit encountered 10020 300 450070 4 1 5 # sig fig ?
Counting sig figs Counting sig figs: : Atlantic Atlantic & & Pacific Pacific method method Possesses decimal move from left (Pacific side) and start counting when first non-zero digit encountered 4 2 3 1.002 0.030 0.00400 # sig fig ?
What is the sig fig count given a scientific notation version of a number ??? 3 sig figs exponent Example: 6.02*1023 Pre-exponent The count of digits in the pre-exponent is the sig fig count.
# sig figs ? value 0.0051 510 5.10 5.0010 5.0*1060 # sig figs = 2 2 3 5 2
