In the metric system, every quantity has a unit that
can be modified by prefixes. The seven basic quantities and their
units are:
Quantity
Modifiable Unit
Unit Abbreviation
length
meter
m
mass
gram
g
time
second
s
temperature
kelvin
K
amount of substance mole
mol
electric current
ampere
A
luminous intensity candela
cd
In the metric system, there are specific prefixes that are used to modify units. These prefixes are:
Prefix Abbreviation Meaning (words) Meaning (mathematically) Or. . .
deci-
d
one-tenth
0.1
1 m = 10 dm
centi-
c
one-hundredth
0.01
1 m = 100 cm
milli-
m
one-thousandth
0.001
1 m = 1 000 mm
micro- m
one-millionth
0.000001
1 m = 1 000 000 m
nano-
n
one-billionth
0.000000001
1 m = 1 000 000 000 nm
pico
p
one-trillionth
0.000000000001
1 m = 1 000 000 000 000 pm
Any time a measurement is recorded, it includes all the digits that are certain plus one estimated digit. These certain digits plus one uncertain (estimated) digit are referred to as significant figures.
***VERY IMPORTANT CONCEPT!!!*** The further the estimated digit lies to the right in a measurement, the less relative uncertainty there is, so the more reliable the measurement.
Throughout this course, you will be given measurements with which you will need to perform calculations. You must be able to determine the correct number of significant figures in any measurement in order to calculate the correct answers to the given problems. You must know the following rules in order to continue your success in chemistry.
Rule
1. All digits other than zero are always significant. 12345 m contains 5 S.F.
2. Zeros between nonzero digits are significant. 101001 m contains 6 S.F.
3. Final zeros to the right of the decimal point are significant. 25.1000 m contains 6 S.F.
4. In numbers smaller than 1, zeros to the left of a decimal point or directly to the right of the decimal point are not significant. 0.0000000345 m contains 3 S.F.
5. All zeros between significant digits are significant. 34.005006 m contains 8 S.F.
6. All zeros to the left of a decimal and right of a significant figure are significant. 2000000.00 m has 9 S.F.
7. When there is no decimal point: Final zeros in a whole number may or may not be significant. In these instances, the uncertain zero is identified by placing a bar over it. The zero with the bar over it and all final zeros to its left are significant. Final zeros to the right of the zero with the bar over it are not significant.
Basics: Single
Mathematical Operations and Significant Figures
Adding and Subtracting Significant Figures
When adding or subtracting measurements with significant
figures, the sum or difference can only be as certain as the least certain
measurement used.
Remember that properly recorded measurements are recorded using significant figures, all certain digits plus only one uncertain digit.
The position of the uncertain with relation to the decimal point in the least certain measurement determines the position of the uncertain digit with relation to the decimal point in the answer. For our purposes, the uncertain digit should be rounded up or down, just as in math.
Example: 23.0042
m + 9.0 m = 32.0 m
9.1 m + 11.01 m + 10 m = 30 m
Multiplying and Dividing Significant Figures
When multiplying or dividing measurements, the answer
may contain only as many significant figures as does the measurement used
with the least amount of significant figures.
Example:
42.0 m x 4.0 m = 170 m2
1.78 cm2 ¸ 0.05 cm = 40 cm
Note that unlike addition and subtraction of significant
figures, the position of the uncertain digit with relation to the decimal
point in the answer does not have to be in the same position as the position
of the uncertain digit in any of the measurements.
Basics: Multiple
Mathematical Operations and Significant Figures
Rule 1: Multiplication,
division, and exponent operations only:
When multiplying, dividing, and using exponents only, perform all operations
first and then apply the rules for significant figures to the answer.
Example: [ (2.48 m)2 (2.58
m) ] ¸ 5.78 m = 2.75 m2
Rule 2: Addition and/or
subtraction in combination with other operations:
When addition or subtraction operations are used in combination with other
operations, follow the algebraic order of operations, applying the rules
for significant figures after addition or subtraction operations are complete.
Then perform the multiplication, division, and/or exponent operations as
necessary and apply the rules for significant figures again.
Example: [ (4.56 m + 5.679 m) (2.00 m + 9 m)
] ¸ 27.9 m = 4.0 m
Rule 3: Numbers with NO
uncertainty:
All conversion fractions, constants, and numbers that have no uncertainty
are treated as if they have an infinite number of significant figures.
Example: Convert 14.75 hours to seconds. 5.310
x 104
Rule 4: Averages and uncertainty:
When finding the average (mean) of measurements, the answer cannot be more
certain than the least certain measurement. Also keep in mind that you
are adding and dividing (two different significant figure rules).
Example: Calculate the mean of the following
measurements: 2.784 g and 9.863 g. 6.324 g = avg
Basics: Precision
and Accuracy
Two important factors to consider in measurement are precision and accuracy. They are not the same thing.
Precision indicates the reproducibility of a measurement.
Example: Imagine you took three readings
on a thermometer to try to determine the boiling point of pure water at
sea level. The results of your trials were 96.8°C,
96.9°C, and 97.0°C.
Note how close the measurements are to one another. The measurements show
a high degree of reproducibility, they are precise.
Accuracy indicates how close a measurement is to its accepted value.
O = Observed or experimental value. A = Accepted or actual value.
Formula for Absolute Error: |O – A| (also called experimental error)
Formula for Percent Error: |O – A| / A x 100 (also called relative error)
From the example above, we have three different values: 96.8° C, 96.9° C, and 97.0° C.
We can now calculate the percent error for the individual measurements. We may also determine the mean (or average) of those measurements and then calculate the percent error for the average of the measurements. (You need to read carefully to see what you are being asked to calculate.)
The mean of the measurements: 96.9oC
Percent error for the mean of the measurements: 3.1%
Determining Precision (Calculating Deviation)
Calculating how precise measurements are is a six-step process. We will use the three temperature readings for the boiling water example at the beginning of these notes to complete the six steps that follow.
STEP 1: Determine the Mean (or average) of the measurements. Average = 96.9oC.
STEP 2: Calculate the Absolute Deviation for EACH measurement. In this step, we are determining how much each individual measurement deviates from the average.
Absolute Deviation for EACH measurement:
|96.8oC – 96.9oC| = 0.1oC
|96.9oC – 96.9oC| = 0.0oC
|97.0oC – 96.9oC| = 0.1oC
STEP 4: Express
the measurements in terms of Mean ±
Average Absolute Deviation.
Measurement = 96.9oC + 0.1oC
STEP 5: Calculate the Relative Deviation. (Also referred to as Percent Deviation.)
Formula for Relative Deviation: DR = DA (AV)
/ M x 100
Relative Deviation: 0.1%
STEP 6: Express
the measurements in terms of Mean ±
Relative Deviation.
Measurement = 96.9oC + 0.1%
It is useful to classify chemical reactions because the
classification enables us to organize information and ultimately predict
the results of similar without having to carry them out.
There are five basic types of reactions that we will
need to be able to classify.
A synthesis is a reaction is one in which
a product is being created (or synthesized) from two or more elements.
It is also a reaction where a more complex compound is created from the
reaction of two or more simpler complex. There are always two or more reactants
but only one product. Synthesis reactions are also known as composition
reactions or combination reactions.
Examples: calcium + sulfur ®
calcium sulfide
Ca + S ® CaS
carbon dioxide + sodium oxide ® sodium carbonate
CO2 + Na2O ® Na2CO3
In other words: element
+ element ® compound
or
compound + compound ® complex compound
A decomposition reaction is one in which
the single reactant is broken down into two or more elements or simpler
compounds. It is the reverse of the synthesis reaction. It has only one
reactant but two or more products. In such a reaction, the single reactant
is decomposed into its constituent parts.
Example: sodium hydrogen carbonate ®
sodium hydroxide + carbon dioxide
NaHCO3® NaOH + CO2
In other words: compound
®
element + element or
complex compound ® compound + compound
A single replacement reaction is one in
which one element of a reactant replaces an element in another reactant.
In other words, one partner is switched. Key point: the resulting
compound must have a + and a – ion. The switch cannot result in two positive
ions or two negative ions forming a compound.
Examples: calcium oxide + magnesium ®
magnesium oxide + calcium
CaO + Mg ® MgO + Ca
In other words:
element + compound ® element + compound
A double replacement reaction (also known
as a double displacement reaction) is a reaction where the positive ions
of the two reactants switch places. As products, each ion know has a new
and different partner than it originally had.
Example: sodium chloride + silver nitrate
®
sodium nitrate + silver chloride
NaCl + AgNO3 ®NaNO3
+ AgCl
In other words:
compound + compound ® compound + compound
A combustion reaction is a rapid reaction
that usually places a flame. For our purposes (but not always), oxygen
(from the air) is a reactant. Hydrocarbons are compounds
that contain hydrogen and carbon. (Hydrocarbons in our class may also
contain oxygen.) When hydrocarbons combust (react with oxygen), the products
are always carbon dioxide and water vapor (CO2 and H2O).
Examples: methane + oxygen ®
carbon dioxide + water vapor
CH4 + 2 O2 ® CO2
+ 2 H2O
methanol + oxygen ® carbon dioxide + water
vapor
2 CH3OH + 3 O2 ® 2
CO2 + 4 H2O
In other words: hydrocarbon +
oxygen ® carbon dioxide (CO2)
+ water vapor (H2O)
TYPES OF SYNTHESIS REACTIONS