Chemistry is like a class in the foreign language department. In order to understand what the
chemist is saying you have to know the terminology. The class begins with a lot of
memorization of simple vocabulary terms. This forms the backbone of all the knowledge to
come during the year. Thus, just like you learned what to do when you see this:
You should be able to recognize a similar sign:
and realize that it is asking you to do the same thing – but in a different language.
Many of these concepts you should have seen or heard of before – perhaps on the news, in
another chemistry class, in biology class or elsewhere.
Chapter 1 is composed of the fundamentals. It is not a fun or exciting chapter to read – nor
could you say that it is “chemistry in action”. It contains the building blocks that we will use to
talk and learn about chemistry for this year. This chapter is chock full of words in bold. You
are REQUIRED to know all of them! And future chapters will contains more along the way.
These are our vocabulary words – learn them – but most importantly understand them!
Chemistry: the study of matter, its properties, the changes it undergoes, the energy associated
with those changes, and the actions of the electrons in the matter!
Electrons are the key to chemistry; they are the portions of the atom doing all the
reacting. Chemistry deals with the exterior of the atom, the electrons, not the nucleus.
The nucleus, as far as chemistry goes, is unaffected by chemical reactions.
Matter: anything that has mass and volume (takes up space)
Composition: the types and amounts of simpler substances that make up a sample of matter
(e.g. chocolate chip cookies are composed of chocolate chips, butter, sugar, eggs, vanilla extract,
flour, baking soda, and salt. So these are the simpler substances that make up the matter of the
cookie).
Property: a characteristic that gives a substance its unique identity.
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Physical Property: a characteristic that a sample of matter displays without undergoing a
change in composition. Thus, the substance will not interact with other substances or change
into another substance.
Some examples of physical properties are: color, odor, solubility, melting and boiling
points of the substance, density, phase state (e.g. is the substance a solid, liquid, or gas)
1. when ethyl alcohol is identified by its odor, there is no change in its composition
2. when you observe the color of copper or its ability to conduct electricity we did not
change the composition of copper
3. when we observe the brilliance and hardness of a diamond we did not change the
composition
Chemical Property: a characteristic that a sample of matter displays as it undergoes a change in
composition. Thus the substance DOES interact with other substances and the substance DOES
change into another substance. Chemical properties can only be observed during chemical
reactions, when one substance changes into a new substance.
Some examples of chemical properties are: flammability, corrosiveness, reactivity with
acids.
1. when a log burns it forms hot vapor, smoke and ash
2. when a seed sprouts and grows into a plant
3. when NaCl (s) decomposes into Na (s) and Cl2 (g)
Physical Change: the substance retains its identity and NO NEW elements or compounds are
formed.
Some examples of physical changes include phase changes: solid → liquid → gas. H 2O
solid is still composed of the SAME thing as H2O liquid (2 hydrogens and 1 oxygen).
Some of the physical properties might have changed (e.g. hardness, density, and ability
to flow but the composition remained constant!). The crushing of stone is also a physical
change. It might look a little different but it is still the same material. Sometimes
physical changes are reversible (e.g. we can melt solid ice into liquid water and then
lower the temperature and turn liquid water back into solid ice!), while some are not
(good luck trying to put those crushed pieces of stone back together – you’ll need a LOT
of superglue!
Chemical Change: (or chemical reaction): the substance loses its identity and NEW elements or
compounds are formed. The substances that we started with (reactants) are different than the
substances we end up with (products)
In general, a chemical reaction looks as follows:
Some examples of chemical changes are substances burning, cooking food, and spoiling
food, silver tarnishing, iron rusting, copper oxidizing, the combination of oxygen gas
with hydrogen gas to make water.
Solids: matter that has a fixed shape and does not conform to its container,
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Liquid: matter that conforms to the shape of its container, it has no fixed shape but rather takes
the shape of its container and thus forms a surface.
Gas: no real shape. The gas will conform to the shape of its container if the container is closed.
It will take up all available space. If the container is open, the gas will freely go where it pleases
and diffuse away. Gases do not form surface layers.
Energy: the ability to do work. Energy enables us to get out of bed in the morning. Energy
enables objects to undergo change.
Energy is “intangible”. We cannot touch energy, we cannot buy energy, but we can see
and feel its effects. Light energy from the sun causes plants to grow, wind energy moves
ships and provides us with electricity to light our homes and use our appliances, the
energy of moving water also allows us to generate electricity, and even atoms, when
split, can release energy to produce motion, change, and atomic bombs!
The total energy an object possesses is the sum of its potential energy and kinetic energy.
Potential Energy: energy of position (height), or stored energy (e.g. chemical energy stored in
your muscles).
Kinetic Energy: energy of motion.
Comparing the two types of energy: Water sitting at the top of a dam is still, silent,
waiting. It is not really moving around all that much, it is a lake. It has the potential to
move, but it is being held back by the solid concrete dam. IF the water was
moving/flowing downhill in some way, we could get electricity from it. But- it is not. As
it sits behind the dam, held back from the forward motion, it only has potential energy.
As soon as we open the floodgates of the dam and that water starts moving through the
pipes to turn a turbine to generate electricity we turned that potential energy into kinetic
energy. The water is moving and we can turn our lights on in the house. When the
water reaches the bottom of the pipe it once again stops moving and becomes “lazy”, and
the water becomes still again. The water, which was once moving and had kinetic
energy now has only potential again. Thus a cycle exists between potential energy and
kinetic energy, it is converted from one form to another and back again, but it is not
destroyed.
In nature, the lower energy form is favored over a higher energy situation. Think of it
this way: water runs downhill. The water would have to work realllllly hard to stay on
higher ground, but it can just go with the flow down down down to reach the lower level
area. And thus it has a lower energy state. ALL matter wants to achieve as low an energy
state as possible.
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In chemistry, much of the matter is composed of positively and negatively charged
species. As you are probably already familiar, opposites attract.
When we do some work and separate the positive charge from the negative charge we
increase the potential energies of the particles. They are at a high energy state. Like a
couple that has been living apart, they are agitated, unhappy. Holding the particles apart
from one another they are still – but have a lot of potential energy as they are just waiting
to be able to come together. As the particles go into motion due to their attraction the
potential energy is converted into kinetic energy (energy of motion) and the particles
meet and come together at a lower energy state than when they were kept apart. Try this
at home with a pair of magnets – putting together the opposite poles – what happens??
They stick together!
Just the opposite is true if we examine like charges. Keeping the charges together is the
high energy state. Like charges (++ or --) repel one another. It takes a lot of work to
keep like charges next to one another (try it at home with magnets, try and force the
same poles of the magnets together – they push each other away!) This is the higher
energy state with a lot of potential energy. As soon as the ions get a chance, they push
themselves away from one another lowering their energy state as the potential energy is
converted to kinetic energy.
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The chemical potential energy of a substance results from the relative positions
(how close are the species?) and whether or not there is attraction or repulsion occurring
between the particles.
Through a physical or chemical change a less stable substance changes to a more
stable form as the potential energy is converted into kinetic energy, which can do work.
Energy is neither created nor destroyed – it is just converted from one form into
another.
1.
2.
3.
4.
Observations: the facts that the idea must explain. The most useful are quantitative
observations that can be compared and that allow trends to be seen.
For example: every time you bake a cake the mixture turns from a liquid
to a spongy solid and rises in the cake pan. Thus if you bake a cake and
you do not witness these happenings and the cake turns out to be horrible,
then you can compare your observations to what should have occurred
and see if you can find out why your cake didn’t bake correctly.
Hypothesis: a proposal made to explain the observation. It is often termed the
“educated guess”. It need not be correct, but it must be an idea that is testable. You
must be able to prove this idea either true or false.
For example: perhaps a reason that the cake turned out to be a flat pancake
is because I forgot to add the baking soda which causes the cake to rise.
Experiment: develop a procedure to test the hypothesis. If the experiment does not
prove the hypothesis perhaps it was a poor experiment, devise another, and if your
hypothesis cannot be proven experimentally then you must derive another hypothesis
which can be proven through experimentation. This step in the scientific method can
take years (e.g. cancer drugs, AIDS research, cures to disease etc . . .)
For example: I think that the reason that the cake did not rise was because I
forgot to add baking soda. So I will bake another set of cakes, one I will
add baking soda to (the control) and the other I will add all the same
ingredients EXCEPT the baking soda. I will bake the cakes in the same
oven for the same amount of time. If the cake with the baking soda turns
out fine but the cake without the baking soda resembles a flat pancake then
I have found an experiment that proves my hypothesis.
Theory: my hypothesis must be proven, and not just by one experiment. I must be able
to reproduce my results, others must be able to reproduce my results. The theory must
be universally accepted through extensive experimentation before we can develop the
theory behind the observation.
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For example: if another research group also had a cake disaster problem
and they found out that if they did not add salt the cake behaved
EXACTLY like a cake mixture that did not have baking soda added, then
we cannot say with 100% certainty that baking soda is needed for the cake
to rise. HOWEVER, if we tested all other possibilities and found that only
forgetting the baking soda causes the cake to not rise then we can develop
the “Theory of Cake Rising as Dependent upon the Presence of Baking
Soda”.
All measured quantities consist of a number AND a unit. The unit is used to identify the
number – it quantifies and clarifies the number. If someone comes up to you and asks how tall
you are and you say 60. Well – what does that 60 mean? 60 feet?? I hope not! 60 cm?? Again, I
hope not!! How about 60 inches? That seems reasonable as 60 inches is 5 feet tall.
The mathematic operations that we use with numbers can also be applied to the units as well.
Thus:
1cm x 1cm = 1 cm2
1cm x 1cm x 1cm = 1 cm3
1cm x 1 cm x 1cm x 1cm = 1 cm4
and so on . . .
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The next big step is converting one unit (like inches) into another unit (like feet). We use a
series of conversion factors for doing so. Simply put, there are base units that have a direct
relationship to another different unit. For example: 1 foot = 12 inches; 1 inch = 2.54 cm; 1 lb =
453.6 grams
Knowing these direct relationships we can convert something more complicated than 1 foot
directly to inches.
Converting 987,654.321 inches is how many feet?
Setting up the problem is the MOST important thing. We want to make sure that our units
cancel out and the ONLY unit we are left with at the end it feet:
Correct:
987,654.321 in x
1 foot = 82304.527 feet
12 in
Incorrect:
987,654.321 in x 12 inches = 11,851,851.852 in2
1 foot
ft
NOTICE THAT THE UNITS DO NOT CANCEL OUT – YOU HAVE NOT GIVEN THE
ANSWER IN FEET! I will say this time and again with conversion problems “FOLLOW YOUR
UNITS”. Your numbers MUST have units, all numbers are therefore labeled, and this tells you
whether or not you need to multiply or divide to cancel or keep a unit in place. Without units
on numbers, we are likely to invert conversions or solve problems “upside down”.
What about multiple conversions? Say we wanted to know how many seconds there are in a
month. Below are all the conversions that you need in order to solve the problem. As in ANY
problem. START with WHAT YOU KNOW! Start with the number in the problem whose units
you are asked to change. Never begin with a conversion factor (a ratio relationship) unless you
are asked to convert that value. Conversion factors can be used “right side up” or “upside
down”.
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1 month = 30 days
1 day = 24 hours
1 hour = 60 min
1 minute = 60 seconds
Above are conversion factors. We can set them up as ratios – and as such, we can write them in
either direction. This is often called, “multiplying by one”.
30 days
1 month
or
and the same can be done with the rest of the relationships above.
1 month
30 days
And we will use this relationship to cancel units that we need to cancel, and keep units that we
need to keep. Since the factor can be used either way- we will choose the appropriate set up
based on the problem asked.
We were asked about seconds in 1 month. Therefore are we going to start with seconds? No,
we don’t know anything about them at this point – but we do know that we are examining 1
month. And we are asked to change the month unit into something else – so remember to
always start with the value and unit that you are asked to change!
1 month
30 days x 24 hours
1 month
1 day
x
x
60 minutes x 60 seconds =
1 hour
1 minute
2,592,000 seconds
notice that ALL the units cancel each other out except the seconds. We have found what we
were looking for. Be careful to follow correct mathematical rules when entering in numbers
into your calculator! This one turned out to be easy since all the denominators are 1 – but
sometimes you will have to multiply and divide – so pay attention!!
Known as fundamental units or base units. They are the units from which all others are
derived. For example, the derived unit for density (g/ml) comes from the SI unit for mass (grams
from kilograms) and volume (milliliters from liters).
Parameter
Length
Volume
Mass
Energy
Time
Pressure
Force
SI
meter
liters
grams
Joule or Cal
sec
Pascal
Newton
English
foot
gallons
slugs/stones
BTU
sec
psi
Pound
Because we deal with large and small quantities of substances we use decimal prefixes and
scientific notation. The prefixes are based on powers of 10. You should KNOW and be able to
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convert between these prefixes and the base parent unit (e.g. you should know how to convert
liters to milliliters, grams to kilograms and back again).
G
giga
109
billion
1000000000
M
mega
106
million
1000000
k
kilo
103
thousand
1000
c
centi
10-2
hundredth
.01
m
mill
10-3
thousandth
.001

micro
10-6
millionth
.000001
n
nano
10-9
billionth
.000000001
1000000000
1
1000000
1
1000000
1
1
100
1
1000
1
1000000
1
1000000000
There are two ways of doing the conversions. Either is acceptable. You should find ONE way
and stick to it.
1. There are either a lot of little things in 1 big thing
(100 cm = 1 m)
2. OR there is a small amount of the big thing in 1 small thing
(1 cm = 10-2 m )
Either way you should get the right answer. But DO NOT flip flop back and forth between
them! This is the first area where students generally get flustered – do not let it happen to you!
Just so you know, I use the first method and thus, all my calculations will be based off of the
idea that there are a lot of little things in 1 big thing. So I will never have (-) exponents in my
calculations.
100 = centi
1000 = milli
106 = micro
109 = nano
1012 = pico
Quantity
length
volume
mass
SI
km
m
m
cm
m3
dm3
SI Equivalents
1000 m
100 cm
1000 mm
10-2 m
106 cm3
1000 cm3
cm3
0.001 dm3
English
0.6214 mi
1.094 yd
39.37 in
0.3937 in
35.31 ft3
0.2646 gal
1.057 qt
0.03381 fl oz
kg
g
1000 g
1000 mg
2.205 lb
0.03527 oz
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English to SI Equivalent
1 mi = 1.609 km
1 yd =0.9144 m
1 ft = 0.3048 m
1 in = 2.54 cm
1 ft3 = 0.02832 m3
1 gal = 3.785 dm3
1 qt = 0.9464 dm3
1 qt = 946.4 cm3
1 fl oz. = 29.57 cm3
1 lb = 0.4536 kg
1 oz = 28.35 g
The SI unit for length is the meter (m).
The SI unit for volume is m3 (or cm3) . However, chemists typically measure volumes in liters
(L) and milliliters (mL) as well. Volume is the amount of space that an object takes up.
The SI unit for mass is the kilogram. The mass of an object refers to the amount of matter that
the object contains (e.g. the earth has more mass (is more massive) than the moon). DO NOT
confuse mass with weight!! The mass of an object remains constant no matter where the object
is. You have the same mass on Earth as you do on the moon – you have the same mass
wherever you go – unless your arm falls off or something like that. WEIGHT however, takes
into account the effect of gravity ON your mass. If there is less gravity then there will be a
difference in weight. So you if want to lose weight – climb to the top of a really tall mountain –
you will weight less up there as the effect of gravity is less! However, there is also less O2 way
up there so you might have problems breathing….
The SI unit for density is kg/m3. However, typically we use g/cm3 or g/ml as the units for density.
The density of a material is independent of the amount of material present. It does not matter if
you have a gallon of water or a glass, the density of the water remains the same. It is an
intensive property. However, density is composed of a mass divided by a volume. Both mass
and volume DO depend on the amount of substance present. 1 gallon ≠ 1 cup! And something
with a mass of 200 g ≠ something with a mass of 500 g! Thus, mass and volume are extensive
properties.
You are given a large cube of salt that has a mass of 5 grams. One side of the cube is measured
to be 1.323 cm. What is the density of the salt?
Remember: break these word problems down into what we KNOW!!
We know 1. mass which equals 5 g
2. we know one side of a cube is 1.323 cm
In order to get density we need the mass (5g) divided by the volume. How do we determine the
volume of a CUBE?
Volumecube= length x width x height which for a cube are all the same dimension!
So volume of the cube = 1.323 cm x 1.323 cm x 1.323 cm = 2.315 cm3 (REMEMBER to cube your
units too!!!!)
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Now we can calculate the density:
Density = d =
5 grams = 2.16 g/cm3
2.315 cm3
Now let’s try something a little more complicated – like you might see on an exam. Using both
our knowledge of calculating density AND practicing conversions!
You are given some unknown material and asked to determine the identity based off its density.
You weigh the material discover that it weighs 0.2025 pounds. You use your ruler – which only
has inches on it and discover that one side of the cube is 1.276 inches in length. Determine the
density and from the table in your book, the identity of the unknown.
Temperature: a physical property related to the kinetic energies (or motion) of the atoms or
molecules in a substance. Kinetic energy, as heat, is transferred from the substance with more
kinetic energy (higher temperature) to the substance with less kinetic energy (lower
temperature). Temperature should NOT be confused with heat!!!!! Temperature is a measure of
how hot or cold a substance is RELATIVE to another substance. Temperature is an intensive
property, as it does not rely on the amount of substance present. 4 gallons of boiling water will
have the same temperature as 20 gallons of boiling water.
heat: an energy that is transferred into or out of a system caused by a difference in temperature
between the system and the surroundings.
When two objects of different temperature touch, the energy from the substance of a
higher temperature flows into the substance with the lower temperature. So when you
are holding a piece of ice, it feels cold and begins to melt because the heat is flowing
away from your hand and into the ice. Heat – as energy – is an extensive property. A
fire in a fireplace has more heat energy than a candle, even though the burning
temperature might be the same!
How does a thermometer work? Thermometers contain a liquid on the interior (alcohol
(red) or mercury) that expands when warmed and contracts when cooled – properties
typical of almost all liquids (but not water – remember if you fill a container with water
and put it in your freezer and cap it – it will burst the container – water actually expands
when frozen!). When the bulb is submerged in a liquid warmer than the thermometer,
the liquid transfers its heat to the thermometer causing the red liquid to rise. When the
bulb is submerged in a liquid colder than the thermometer, the heat is transferred from
the thermometer liquid to the substance and the red liquid contracts. We can take a
reading of the red liquid as it reaches equilibrium with the liquid it is submerged in.
Equilibrium for the thermometer is reached with the temperature of the red liquid =
temperature of sample solution.
Temperature scales: Three to be aware of!
oC
= Celsius
oF
= Fahrenheit
K = Kelvin
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NOTICE that Kelvin does not use the degree (o) sign!
The Kelvin scale is also known as the absolute scale and almost all calculations are done
with temperature converted into Kelvin, which is the SI unit for temperature. The three
scales differ in their scale (the size of the unit) and the temperature of the zero point.
0oC = 32oF = 273.15 K = freezing point of water
100oC = 212oF = 373.15 K = boiling point of water
4 Equations:
K = oC + 273.15
oF = 9/5(oC) + 32
oC = 5/9[oF – 32]
or
oC
= K – 273.15
time: the SI unit for time is the second.
Every measurement that we take includes some uncertainty. We can never measure something
exactly. The greater the number of digits in the measurement, the more certainty we know
about the number. For example, if we compare the mass of potatoes weighed on a big scale,
perhaps the mass would be 55.4 kg. But if we have a more accurate balance perhaps what we
would find is that the mass is 55.38721 kg. We are more certain about the exact mass when
looking at the second value. We assume that the uncertainty of one unit in the rightmost digit.
Thus 55.4 +/- 0.1 kg and 55.38721 +/- 0.00001 kg. When taking measurements, either at the
supermarket or in lab, we can go out one decimal place BEYOND what our measuring device
tells us. What that means, is that for the examples below we can attempt to more accurately
determine the temperatures.
The temperature for Figure A would NOT be 32.30C. We see the 32 marking and we see the
additional “tick” marks on the thermometer indicating temperatures in the tenths : 32.1-32.9oC.
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We can measure ONE additional decimal place to the right – making an assumption about
where we think the top of the fluid line lies, thus we can measure to the hundredths spot. Thus
the temperature could be measured by your eye to be somewhere around 32.33oC. Since the last
measurement is subjective, anything between 32.31 and 32.36 would be acceptable. Remember
that 32.39 would almost be touching the 32.40 mark – which in this case it does NOT.
We see that in Figure B we have temperature marking lines in even integers : 30, 31, 32, 33, 34,
etc. Thus we can only measure to the tenths place when determining our actual temperature.
Examining the thermometer we can attempt to determine the temperature. We see that it is
above 32oC but below 33oC. The next step would be to determine if it is greater than 32.50C. It
does not appear to be so. So our measurement would be something between 32.0oC and 32.4oC.
The last number is subjective, but again it should be as accurate as possible. A measurement of
32.2, 32.3 or 32.4oC would be acceptable.
Significant Figures: In a measured quantity the numbers of significant figures are all the digits
known with certainty plus the first uncertain digit. The greater the number of significant
figures in a measurement the more certainty there is in the measurement.
Many of you will look at sig figs as a “who cares” moment in general chemistry. Well, just
recently we had numerous examples of WHY we all should care!!
Take a look at some prime examples of significant figures and WHY they matter! What was the
difference between these numbers?? Well the minute differences meant who earned a gold
medal, who earned a silver medal, who earned a bronze medal and who got nothing at the
Olympic games in Athens this summer.
Track & field - Women's 100-meter Hurdles (medals: Aug. 24th)
Medal
Gold
Silver
Bronze
Athlete
Joanna Hayes
Olena Krasovska
Melissa Morrison
Country
USA
Ukraine
USA
Result
12.37
12.45
12.56
The ability to measure time down to the hundredths of seconds accurately means that Joanna
Hayes not only earned the gold medal but also established a new Olympic record. It really
does not mean anything under these circumstances to simply say, well they all ran around 12
seconds – who would/should earn the medals and in what order?? The difference between
gold and silver was 0.08 seconds. The difference between silver and bronze was 0.09 seconds.
Take a look at another example.
Track & field - Men's 200 meters (medals: Aug. 26th)
Medal
Gold
Silver
Bronze
Athlete
Shawn Crawford
Bernard Williams
Justin Gatlin
Country
USA
USA
USA
Result
19.79
20.01
20.03
The difference between gold and silver was 0.22 seconds while the difference between silver
and bronze was a mere 0.02 seconds!
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What do you think a difference of 0.01 means?? HOW important could something like that
possible be?? I mean, if you only got back $1.05 from the cashier at the store instead of a $1.06
would anyone be mad or upset??? Well, that’s a difference of 1!!! This is a difference of 1/100
of that!! So really, in the grand scheme of things – how important is that?? That is like saying 1
in 100 times you get back the wrong change from the cashier. And he/she only shorts you a
penny. Whoppiteedo!!! Well, let’s see, 0.01 meant the difference between gold and silver in the
men’s 4x 100 relay. The USA team lost to Great Britain by one-one-hundreth of a second. Talk
about a bummer.
It gets even better when you look at gymnastics!! These scores go out to the thousandths place!
So you see, significant figures do matter, and they decide very important things. Who wins the
race, who wins the competition. In sports, significant figures can mean the difference of who
goes the Olympics and who does not even qualify.
Significant figures are important in your life as well. When prescription medication amounts of
determined, many drug dosages are based on your body weight. Do you want your physician
saying – ahhh, who cares, you weigh about 200 pounds when you actually weigh 165?? That
could mean giving you TOO much medication. Or if they think that you weigh more than you
really do – too little. Medication amounts are also based on how fast it takes the medicine to go
through your body (called metabolism). Some people’s bodies metabolize faster than others. If
the doctor’s simply say, well it takes 3 hours for a person to metabolize this and you metabolize
it in 2 hours 10 minutes, how much fun would it be lying around in pain for the next 50 minutes
before they give you your next shot??!!!?? Not fun at all!!
So they do matter, and they are important and you WILL be graded on your correct answer and
the correct number of sig figs from this point forward!!! 
1.
2.
3.
4.
All non-zero digits are significant (e.g. any number except zero is significant and we
count it as a significant digit)
The oreo-cookie rule: Zeroes sandwiched between two other significant digits ARE
significant (no matter how many you sandwich in the middle, they count). Examples:
1107 (4 sig figs); 50.002 (5 sig figs)
Numbers with decimal points: Find the first digit in the number that is NOT a zero.
That digit and ALLLLLLL digits to the right ARE significant. Examples: 0.99 (2 sig figs
(the 99)); 0.762 (3 sig figs); 0.00654010 (6 sig figs – the first non-zero digit is 6, count him
and everyone to his right!)
Numbers without decimal points (bad!!): Zeros at the end of the number may or may
not be significant if the number is written WITHOUT a decimal point. Example: 400. Is
there only 1 sig fig (the number 4), is the first zero significant too? (that would be 2 sf) or
are all three digits in the number significant? Scientific notation would clear the
significant figures up: 4 x 102 shows 1 sig fig. 4.0 x 102 shows 2 sig figs, and finally, 4.00
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5.
x 102 shows that all 3 are significant. Scientific notation must be used on these
“ambiguous numbers” or the value of sig figs cannot be assigned with confidence.
Exact Numbers: Significant figures do NOT apply to exact numbers. Examples: 12 in a
dozen, 4 sides to a square,1km =1000 m. Essentially these numbers have unlimited
significant figures: 12.000…; 4.00000…; and 1000.00000…
You are welcome to ask me at any time if a number given is exact. I will simply tell you yes or
no, I will not tell you what that means in terms of sig figs, nor how many sig figs are then in the
number.
Addition and Subtraction:
When we add and subtract numbers we do not need to be concerned with the number of
significant figures but rather, the location of the decimal point.
The result of addition and subtraction is that the number of sig figs to the RIGHT of the decimal
point MUST BE the SAME!!
The idea is, if you have a number of measurements taken to the nearest millimeter and ONE
measurement taken only to the nearest centimeter your final answer can only be to the nearest
centimeter.
Rounding off only occurs in the final step! You may ASSUME, for rounding off only, that
missing sig figs are zeroes.
Examples:
49.1467 + 23.456 = ???
Arrange the numbers VERTICALLY instead of horizontally and you will better see the answer.
49.1467
+23.456(0)
72.6027
There is NO number to add to the seven
but we can use the number for rounding:
our final answer would thus be 72.603
Notice our first number extends out to the ten-thousandths place but our second only goes out
to the thousandths place. Our answer can therefore only go out to the thousandths place as
well.
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49.146 + 72.13 – 9.1434 = ?????
Again, set it up vertically and do the order of operations:
49.146
+ 72.13X
9.1434
112.1326 = 112.13
Why 112.13?? Because our least certain measurement was 72.13 – to the hundredths place –
THEREFORE our final answer can only be to the hundredths place as well!
Multiplication and Division:
The number of sig figs in the final answer will have the SAME number of sig figs as the number
used in the calculation that had the least amount of sig figs. Do not worry about decimal place
location, only about the number of sig figs in the numbers used in the problem!
Examples:
1.827
x
0.762 = 1.392174 =
1.39
(4 sig figs)
(3 sig figs) (calculator)
(3 sig figs)
453.6
 21
=
21.60
(4 sig figs)
(You are told 21 happens to be an exact number) (4 sig figs – exact numbers do
not count in the sig fig roundup)
Putting it all together:
Technically you are not supposed to round your answers until the very end – but I will also
perform the same problem rounding in-between mixed operations and let’s see what we get as a
final answer.
(51.5 + 2.67) x (33.42 – 0.124) = ???????
51.5 (0)
+ 2.6 7
54.1 7
(really only 3 sig figs)
33.42 (0)
- 0.12 4
33.30 (4)
(really only 4 sig figs)
54.17 x 33.304 = 1804.0777
54.2 x 33.30 = 1804.86
BUT!!! Our final answer can only have 3 sig figs!!
Scientific notation will help!
1804.0777 = 1.80 x 103 AND 1804.86 = 1.80 x 103 ALSO!
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Our answer has 3 sig figs (from the number with the lowest number of sig figs used in the
multiplication step and we have rounded our answer correctly by not prematurely
rounding/deleting sig figs until the very end. However – unless your numbers are very large,
or very small, rounding between mixed operations will get you a reasonably close to the correct
answer. Therefore, while not mathematically “correct” it is and will be “close enough” and I
encourage you to round between mixed operations so that you can better “see” the significant
figures you are supposed to have.
Do not be concerned if your answer differs in the last sig fig – it was probably a rounding
“thing”. The important thing is that you have a very similar answer and have the correct
NUMBER of sig figs.
Precision: or reproducibility refers to how close the measurements are to each other. Think of it
as consistency. Example: you might score a 21, 23, 24, and 22 on each exam – you were very
precise.
Accuracy: how close a measurement is to the actual value/quantity. In our test example we are
looking to get a 100! So the above test scores, while precise, were not very accurate 
Low accuracy
Low precision
Low accuracy
High precision
High accuracy
Low precision
High accuracy
High precision
The concepts of precision and accuracy are linked with two types of error:
Systematic error: a repeatable error, whether it is mechanical, due to the equipment, or on the
part of the user. The error can be either all higher or all lower than the actual value. This is a
consistent error from one measurement to the next caused by an imperfection in the instrument
or the experimental method. For example, a thermometer that always reads one degree too
high would introduce error, but it is always the same. This is why it is important for laboratory
technique to always use the same equipment throughout an experiment (same thermometer,
same balance, same beaker, same graduated cylinder, etc!!!!) Systematic errors reduce your
accuracy.
Random error: non-repeatable (thus random) values can be either higher or lower and results
from some things that are beyond the experimenter’s control. It is a small variation in
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measurement that appears to be caused by chance alone. For example, if you were to measure
my height several times, you might get different numbers each time. This would be due to a
different posture stance that I might have in-between each measurement or be due to the
crudity of the measuring device used. Random errors reduce the precision of a result, and if the
deviations between each measurement are large, we lose faith in the measurements as a whole.
Truly random errors are equally likely to be positive and negative and will tend to cancel out
when the measurements are averaged over several trials. Common sense tells us to average as
many trials as possible in order to get the best result!
Random errors are often hard to correct, but can be compensated for by taking an average.
Systematic errors tend to remain hidden unless the experimenter is very alert.
Suppose a measuring device measures 2.20 ml too low when determining the amount of
base needed to neutralize an acid solution. Using those volumes in the calculations
would result in an acid concentration being lower than it really is. Thus, even though the
volumes are precise, they are not accurate and do not reflect the correct value for the
concentration of the acid solution. The systematic error is thus propagated through all
calculations associated with that experiment.
Systematic errors can be corrected for by calibration, that is, by comparing the volumes with a
known standard. In our example above, if we measure the volume in a buret and we titrate the
solution into a graduated cylinder we would see that 10 ml measured by the buret is only 7.8 ml
(10 ml – 2.2 ml) indicating that the buret is reading low. Thus we would need to either get a
new buret or know that each volume reading is off by 2.2 ml!
element: the simplest type of matter with unique physical and chemical properties. An element
consists of only one type of atom and it cannot be broken down into a simpler type of matter by
any physical or chemical method.
pure substance: matter whose composition is fixed. A pure substance is either an element or a
compound.
molecule: a structural unit consisting of two or more atoms that are chemically bonded
together. Several elements exist as molecules in their natural state. You should know them: H 2,
N2, O2 and the halogens (Group VIIA) all exists as diatomic molecules: X2
compound: a type of matter that consists of two or more different elements that are chemically
bonded together. The elements are present in a compound in a fixed ratio for each unique
compound – thus water is always H2O, never HO or HO2. Because of this fixed ratio a
compound is also considered to be substance. It is also important to note that the properties of
the compound are different from the properties of the atoms that make up the compound.
Thus, water has different physical and chemical properties than either pure H2 or pure O2.
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mixture: a group of two or more substances (elements AND/or compounds). The components
of the mixture can vary in their parts by mass (the ratios of one substance with respect to the
other).
For example, italian salad dressing is a mixture of an oil base and water. We shake our
italian dressing and put it on our salads, but if we let the dressing sit still, the two layers,
vinegar and oil separate from one another based on their densities. We could then, very
carefully pour off the top layer and separate the oil from the vinegar. Mixtures do not
have to be liquids. Raisin bran is a mixture. We have the bran flakes and the raisins and
we could easily – though it would take time – separate the two from one another. Since
the mixture is merely a group of individual units (e.g. raisins and bran flakes) it retains
many of the properties of the individual components. Raisins do not taste any different
in the cereal or out of the box. Just because they got mixed with some bran flakes does
not mean that they lost their unique property of flavor.
Matter usually always occurs as a mixture: air is a mixture of oxygen, nitrogen, carbon dioxide,
water vapor, and argon. Sea water is also a mixture of many different salts. Milk, orange juice,
soup, wine, beer, blood, etc are all mixtures.
Heterogeneous mixtures are not uniform throughout. What this means is that individual
samples taken of the mixture will contain different ratios of the substances that make up our
mixture. Our raisin bran is a heterogeneous mixture. With heterogeneous mixtures it is often
apparent that there are many substances involved and sometimes it is not very clear how to
separate the substances from one another.
Examples: raisin bran, vegetable soup, macaroni and cheese, pizza
Examples of heterogeneous mixtures that might not be so apparent: blood, milk,
wheat beer, red wine
Homogenous mixtures are uniform throughout. Each random sampling of the mixture results
in uniform ratios of the substances within the mixture. Vinegar is a homogenous mixture,
alcoholic beverages are also homogenous mixtures. It is often difficult to realize that we are
looking at a mixture of two components when examining homogenous mixtures so we must be
careful not to classify them as pure substances!
Examples: spirits (hard alcohol), soda, sugar water, salt water, nail polish, nail
polish remover (acetone and water), rubbing alcohol (70% isopropyl alcohol and
water)
Homogenous mixtures are termed solutions, however, they do not have to be in the liquid
state. Air is an example of a homogenous solution in the gaseous state – good thing too – we
would not want the composition of air to change from place to place or we might not be able to
breathe! Plastics used throughout industry as well as steel are both examples of solid mixtures.
Even 14 karat gold is a homogenous mixture.
Homogenous solutions in water are given a special name, aqueous solutions. They are given a
special notation in chemical reactions as well:
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NaCl(s)
Na+(aq) + Cl-(aq)
Where (s) indicates solid salt and (aq) indicates the aqueous solution containing sodium and
chloride ions.
Mixtures differ from compounds in three ways:
1.) the proportions of the components can vary
2.) the individual properties of the components can still be observed.
3.) the components can be separated by physical means
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