Transcript File - CCAChemistry

Conversions and
Significant Figures
Kelley Kuhn
Center for Creative Arts
Dimensional Analysis
► One
unit can be converted to another by
using a conversion factor.
►(Unit
A)(conversion factor) = Unit B
►Conversion factors are created by using the
expression that expresses the relationship between
the two units. For example:
 1 foot = 12 inches, so the conversion factor
will be 1foot or 12 inches
12 in
1 foot
The correct choice shall be the one that allows for
the cancellation of the units.
Practice Conversions
► Convert
the following quantities from one
unit to another using the following
relationships.
►
1 m = 1.094 yd 1 mile = 1760 yd
►30
m to mil
►1500 yd to mil
►206 mil to m
►34 kg to lbs
►34 lb to kg
1 kg = 2.205 lbs
Density
Density is an important physical characteristic in
Chemistry. It is often used to aid in the
identification of unknown solids and liquids.
Density = mass/volume
Because liquids are frequently used in the lab
setting, a volume measured in graduated cylinder
can be used to determine the mass using density.
Mass = (density)(volume)
“Certainty” in Measurement
► When
visually reading the measurement
using a lab tool such as a graduated
cylinder or meter stick, there is always a
certain degree of uncertainty in the
recorded quantity. The reading may fall
between two divisions on the scale and an
estimate must be made in order to record
the final digit.
Example of Uncertainty
 When reading a graduated cylinder, the lowest
point on the curve of the liquid is read as the
volume. What is the volume of this liquid?
20
15
meniscus
Because the eye can discriminate the approximate distance between the 17th
and 18th mls, this number must be recorded and is said to be uncertain. The
actual volume would be recorded as 17.3 mls +/- .2 mls.
Are Significant Figures Important? A Fable
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A student once needed a cube of metal which had to have a mass of 83 grams. He
knew the density of this metal was 8.67 g/mL, which told him the cube's volume.
Believing significant figures were invented just to make life difficult for chemistry
students and had no practical use in the real world, he calculated the volume of the
cube as 9.573 mL. He thus determined that the edge of the cube had to be 2.097
cm. He took his plans to the machine shop where his friend had the same type of
work done the previous year. The shop foreman said, "Yes, we can make this
according to your specifications - but it will be expensive."
"That's OK," replied the student. "It's important." He knew his friend has paid $35,
and he had been given $50 out of the school's research budget to get the job
done.
He returned the next day, expecting the job to be done. "Sorry," said the foreman.
"We're still working on it. Try next week." Finally the day came, and our friend got
his cube. It looked very, very smooth and shiny and beautiful in its velvet case.
Seeing it, our hero had a premonition of disaster and became a bit nervous. But he
summoned up enough courage to ask for the bill. "$500, and cheap at the price.
We had a terrific job getting it right -- had to make three before we got one right."
"But--but--my friend paid only $35 for the same thing!"
"No. He wanted a cube 2.1 cm on an edge, and your specifications called for 2.097.
We had yours roughed out to 2.1 that very afternoon, but it was the precision
grinding and lapping to get it down to 2.097 which took so long and cost the big
money. The first one we made was 2.089 on one edge when we got finshed, so we
had to scrap it. The second was closer, but still not what you specified. That's why
the three tries."
"Oh!"
Significant Figures
► The
certain and uncertain numbers that
must be recorded are called significant
figures.
► Significant figures (sigfigs) are important for
accurately conveying experimental data.
► Sigfig rules help to identify which numbers
have meaning and which are simply
placeholders.
Significant Figure Rules
All non-zero integers are counted as significant figures.
► Leading zeros are those that precede all of the non-zero
integers and are NEVER counted as significant figures.
► Captive zeros are those that fall between non-zero digits
and are ALWAYS counted as sigfigs.
► Trailing zeros are those at the end of a number and ONLY
significant if the number is written with a decimal.
► EXACT numbers have an unlimited number of significant
figures. (Exact numbers are those which are a result of
counting or by definition, such as 1kg = 2.205 lbs.)
► In scientific notation, the 10x part is NEVER significant.
►
Using Sigfigs in Calculations
► When
multiplying or dividing, limit the
answer to the same number of significant
figures that appear in the original data with
the fewest number of sigfigs.
► When adding or subtracting, limit the
answer to the same number of decimal
places that appear in the original data with
the fewest number of decimal places.
Let’s Try It!
► How
many sigfigs in these numbers?
 0.00970, 130400, 0.203040, 7.650 x 10-8
 3, 4, 6, 4
Record the answer to the following in
correct sigfigs.
10.045 + .33
.00976 – 0.0100
(34.00)(0.001)
76.2/0.1000