2/24/09
Dimensional
Analysis
Chemistry
11
•  Dimensional
analysis
(or
factor
label
method)
is
a
tool
that
can
be
used
to
determine
how
to
manipulate
formulas
by
analyzing
the
units.
•  It
also
allows
us
to
convert
between
different
units
of
measurement.
Conversion
Factors
•  This
skill
is
ABSOLUTELY
NECESSARY
for
the
remainder
of
your
senior
science
courses...
so enjoy!!!!
•  This
is
a
fraction
which
is
written
so
that
the
numerator
and
denominator
are
equivalent
values
with
different
units.
•  For
Example:
•  1
inch
is
exactly
the
same
length
as
2.54
centimeters.
Therefore:
For
any
type
of
dimensional
analysis
question,
you
have
two
things
to
consider:
Which of the two forms of the
conversion factor will allow you
to cancel the given unit, and
convert it into the unit you
want? •  One
step
metric
conversions
involve
a
BASE
UNIT
(metres,
litres,
grams,
or
seconds)
being
converted
to
a
PREFIXED
METRIC
UNIT
or
vice
versa.
What other conversion factors
will you need to complete the
task? 1
2/24/09
Examples:
•  Convert
9.4
nM
into
metres.
•  Convert
16
s
into
ks.
•  Convert
75000
mL
into
L.
•  These
require
the
use
of
two
conversion
factors.
•  Two
factors
will
always
be
required
any
time
there
are
TWO
PREFIXES
in
the
question.
•  In
a
two
step
metric
conversion,
you
may
want
to
convert
to
the
base
unit
first
(for
now).
Examples:
•  Convert
6.32
µm
into
km.
•  Convert
457
ks
into
ms.
•  Convert
5.6
x
10‐4
Mm
into
dm.
Examples:
•  Convert
55.o
km/h
into
m/s.
•  A
DERIVED
UNIT
is,
itself,
composed
of
greater
than
one
unit
(km/h,
m/s,
g/ml).
•  Derived
unit
conversions
will
require
CANCELATIONS
IN
TWO
DIRECTIONS
(from
denominator
to
numerator
as
well
as
the
usual
numerator
to
denominator).
Homework:
•  Dimensional
Analysis
W.S.
#1,
5,
6,
8‐11
•  Convert
2.67
g/mL
to
kg/L.
•  Convert
35
mi/h
into
m/s.
2
2/24/09
How
does
this
work?
•  A
derived
unit
(often
a
rate
or
a
density)
may
be
used
to
CONVERT
A
UNIT
WHICH
MEASURES
ONE
THING,
INTO
A
UNIT
WHICH
MEASURES
SOMETHING
ELSE.
•  For
example,
a
rate
may
be
used
to
convert
a
distance
into
a
time
or
vice
versa.
The
speed
of
sound
is
330
m/s.
Assuming
a
sound
could
travel
indefinitely
at
this
speed,
how
long
would
it
take
a
noise
to
travel
115,000
km?
Express
your
answer
in
days.
In
this
problem
we
are
converting
a
unit
of
DISTANCE
into
a
unit
of
TIME.
•  The
key
to
this
type
of
conversion
problem
is
determining
which
form
of
the
conversion
factor
to
use.
Examples:
As
the
value
provided
is
a
distance,
which
of
the
two
forms
of
the
factor
will
allow
a
conversion
to
time?
•  The
density
of
lead
is
11.2
g/mL.
What
is
the
volume,
in
L,
of
a
15.6
kg
piece
of
lead?
•  The
speed
of
light
is
3.0
x
1010
cm/s.
Sunlight
takes
8.29
minutes
to
travel
from
the
surface
of
the
sun
to
the
Earth.
What
is
the
distance
from
the
Earth
to
the
sun?
Here
is
a
hint…
Examples:
•  These
are
pretty
straight
forward.
Treat
the
words
as
units.
•  The
process
is
the
same
as
in
the
other
conversions.
•  At
a
pet
swap,
4
dogs
are
worth
1
cat,
and
3
cats
are
worth
9
birds.
You
have
18
birds.
How
many
dogs
can
you
get?
•  At
a
lab
sale,
4
test
tubes
=
1
beaker;
2
beakers
=
1
graduated
cylinder;
1
graduated
cylinder
=
3
Bunsen
burners;
2
Bunsen
burners
=
8
watch
glasses.
Bill
has
6
test
tubes.
How
many
watch
glasses
can
he
get?
3
2/24/09
Examples:
•  If
a
unit
is
squared
or
cubed,
it
may
be
cancelled
in
two
ways:
•  Convert
4.3
dm3
into
cm3.
•  Atmospheric
pressure
is
14.7
lb/in2.
Convert
this
pressure
to
the
metric
unit
g/cm2.
1.  The
conversion
may
be
written
more
than
once:
(m3
=
m
•
m
•
m)
2.  It
may
be
placed
in
brackets
with
the
exponent
applied
to
the
NUMBER
and
THE
UNIT
inside
the
brackets.
Homework:
•  Dimensional
Analysis
W.S.
(the
rest…).
•  Study
for
quiz.
What
is
on
the
exam?
•  Metric
unit
conversions:
• 
• 
• 
• 
Prefix
to
base
unit.
Base
unit
to
prefix.
Prefix
to
prefix.
Know
your
metric
prefixes!
•  Dimensional
Analysis:
•  6
types
of
conversions.
•  Show
all
work.
•  Making
Measurements:
•  Accuracy,
Precision,
Uncertainty.
•  Significant
Figures:
•  Finding
number
of.
•  Operations
(+,
‐,
∙,
÷).
•  Using
Scientific
Notation.
STUDY!!!
•  Reading
a
scale.
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