Download 22 Sept 08 - Seattle Central College

Plan for Mon, 22 Sept 08
• Sign-in sheet…make sure to write your email
extra legibly
• Introduction to the course, syllabus
• Today’s Lecture:
– Uncertainty in measurement and sig figs (1.4-5)
– Density (1.8)
– Classification of matter (1.9)
• Other sections you should review:
– 1.3 (units of measurement), 1.6 (dimensional
analysis), 1.7 (temperature conversions)
Uncertainty in Measurement
or, The Reason You Have to Learn Sig Fig Rules
The accuracy of a
measurement depends
on the device.
45 mL
46.3 mL
Imagine measuring
~40-50 mL of water
using a…
100-mL beaker
100-mL graduated cylinder
2 sig figs: one
certain digit, one
estimated digit
3 sig figs: two
certain digits, one
estimated digit
Significant Figure Rules
1. All nonzero digits are significant.
3.45
3 significant figures
2. Zeros.
a. Leading Zeros appear before nonzero digits. These are not significant figures.
0.00040
2 significant figures
b. Captive Zeros appear between nonzero digits. These are always significant.
3.05
3 significant figures
c. Trailing Zeros appear at the right end of a number. These are significant only if
the number contains a decimal point.
0.400
4.0
40,000
40,000.
4.00 x 104
3 significant figures
2 significant figures
1 significant figure
5 significant figures
3 significant figures
3. Exact Numbers that are determined by counting or by definition are
considered to have infinite significant figures.
Sig Figs in Calculated Values
• Since there is a limit to the accuracy of measured values,
there must also be a limit to the accuracy of calculations
performed using measured values.
• In general, we can say that a calculated value can be no
more accurate than the least accurate measurement used
in the calculation.
• However, exactly how the least-accurate measurement
determines the number of significant figures in the
calculated result depends on the operation performed.
Sig Figs in Calculated Values (cont)
• Multiplication/Division: The result of a multiplication or division must
have the same number of significant figures as the measurement
with the fewest number of significant figures.
• For example, let's say you want to determine the area of a rectangular
room using the lengths of two walls, 3.55 m and 11.65 m:
3.55 m  11.65 m  41.3575 m 2  41.4 m 2
measured value
3 sig figs
measured value
4 sig figs
calculator answer
6 digits
correct answer
3 sig figs
• Reporting 41.3575 m2 implies that the calculated area was more
accurate than either of the wall measurements, which is impossible.
• Since your least accurate value has two certain digits and one
estimated digit, your calculated digit simply can't do any better, so it
cannot have more than three significant figures.
Sig Figs in Calculated Values (cont)
• Addition/Subtraction: The result of an addition or subtraction must
have the same number of decimal places as the measurement with
the fewest number of decimal places.
• Let's say that in addition to the area, you were also interested in
determining the perimeter of the room:
11.65 m + 11.65 m + 3.55 m + 3.55 m = 30.4 m = 30.40 m
measured values
2 decimal places each
4 sig figs each
measured values
2 decimal places each
3 sig figs each
calculator answer
1 decimal place
3 digits
correct answer
two decimal places
4 sig figs
• Reporting 30.4 m would imply that this calculated value is somehow
less accurate than either of the wall measurements.
• We have an estimate for the hundredths place in our measured
values. We can include information about the hundredths place in our
calculated value by adding a zero to the end, to give two decimal
places and four significant figures.
Sig Figs in Calculated Values (cont)
• Now, consider the difference between two masses,
weighed on scales with different accuracy:
Mass from
first scale
81.65 kg 
measured value
2 decimal places
4 sig figs
Mass from
second scale
4.5 kg = 77.15 kg = 77.2 kg
measured value
1 decimal place
2 sig figs
calculator answer
2 decimal places
4 digits
correct answer
1 decimal place
3 sig figs
• Reporting 77.15 kg implies that the second scale is more
accurate than it really is.
• The result is limited by the accuracy of the second scale.
Sig Fig Examples
0.004708 x 0.050 = 0.0002354 = 0.00024
15.004 – 0.0009 = 15.0031 = 15.003
2.0270/10.3333 = 0.19616192 = 0.19616
(3.40 + 1.1)/0.00874 = 4.5/0.00874 = 514.87414
= 510
Density: how much mass can we
cram into a given volume?
For solids and liquids, the volume of a sample is directly proportional to the
mass of the sample. (For gases the situation is a little more complicated).
m=d*v
We can define a proportionality constant
called “density” and write a expression
for this relationship...
Fig. 3-9, p. 81
Density and Phase
In most compounds, the density of the solid is greater
than that of the liquid.
But solid water is actually less dense than liquid
water...this is why any of us are ALIVE.
Petrucci, Fig. 13.30
ice
liquid
paraffin
water
solid
paraffin
Why does ice float in water?
Density Examples
1. A block has a volume of 25.3 cm3. Its
mass is 21.7 g. What is the density of the
block? 0.858 g/cm3
2. A cube of magnesium (Mg) is needed
that has the mass 60.5 g. What must be
the length of the cube’s edge in cm? The
density of Mg is 1.74 g/cm3. 3.26 cm
Chemistry involves the study of matter
on the molecular/atomic scale
Just how small are we talking?
http://micro.magnet.fsu.edu/primer/java/scienceopticsu/powersof10/
Matter has mass and
takes up space.
Matter can exist in
three different states,
or phases.
Chemical vs. Physical
Properties of Matter
• All substances have physical properties such as odor, color, shape,
density, boiling point, melting point, electrical conductivity, etc.
• A physical change in a substance involves a change in one or more
of these physical properties, but the chemical composition remains the
same.
– e.g., density of liquid vs solid water
• A chemical change in a substance means the chemical composition
is altered (new substances are formed), which can be accompanied by
changes in physical properties.
– e.g., color change, temperature change, odor (think rotten milk)
Physical Change
During a physical
change, the
composition of the
molecules stays the
same, but one or
more physical
properties change.
When the state of
matter changes, the
association
between neighboring
molecules changes.
ice
water
steam
Chemical Change
liquid water
oxygen gas
hydrogen gas
Applying an electrical current
to a sample of liquid water
causes the water molecules
to break apart and form
hydrogen gas and oxygen
gas.
This is a chemical change,
the composition of the
molecules changes.
Example of a Chemical Change:
Spontaneous Combustion
White Phosphorus, P4
A suspension of P4 in alcohol, a solvent
that evaporates quickly.
When P4 is exposed to O2, it undergoes
spontaneous combustion.
http://genchem.chem.wisc.edu/demonstrations/Gen_Chem_Pages/06thermopage/spont
aneous_combustion_of_.htm
Chemical of Physical Change?
1. Baking bread C
2. Grinding sugar into
powder P
3. Burning wood C
4. Evaporation of water P
5. Dissolving sugar in
warm water P
P
C
Classification of Matter
There are 3 broad classes of matter:
• Element:
– composed entirely of atoms (all identical)
– cannot be decomposed into other pure, stable substances
• Compound:
– composed entirely of molecules (all identical)
– can be decomposed into constituent elements or other compounds
• Mixture:
– composed of different kinds of atoms or molecules, mixed together.
– can be separated into constituent elements and/or compounds
Some pictures of elements
Fluorine (F2): gas at Chlorine (Cl2): gas
Bromine (Br2): liq/gas Iodine (I2): solid/gas at
rm. temp.
at rm. temp.
rm. temp.
at rm. temp.
Osmium (Os) metal.
Carbon (C) nanotubes
Sulfur, S8
The densest element!!
d = 22.61 g/cm3
Some pictures of compounds
amorphous solid
Obsidian, volcanic glass.
crystalline solid
70–75% SiO2, plus MgO, Fe3O4
Potassium
bromide, KBr
Copper sulfate,
CuSO4
Carbon
dioxide (CO2)
Alloy (a
mixture) of
gallium,
indium, and
tin...three
different
elements
Gallium
metal, an
element
Target Check 2.5: Elements or
Compounds?
•
•
•
•
Na2S compound
Br2 element
Potassium
Hydroxide compound
Fluorine element
compound
element