Section overview
Students are introduced to the idea of establishing an equivalent
relationship between two quantities by determining the number of
pennies in a bag. They will be able to determine this number by
knowing the mass of a single penny. Then, they play the game of
Equivalent Measures (with dominoes) to learn dimensional
analysis. Molar masses are but one kind of domino. Two others
come from ratios of stoichiometric coefficients in a balanced
equation, and the molar volume
of a gas at STP. Students revisit
the CO2 balloon from Section 1 and use stoichiometry to predict
the amount of baking soda needed to blow up the balloon. Finally,
they participate in a discussion of error analysis to question why
the prediction and reality are so different.
Background information the mole
If you want to quantify chemistry, you need a way to connect the
world that is visible (macroscopic) with the particles that make up
that world (nanoscopic). To do this, you have to be able to count
particles and keep track of what they do. Individual particles are
too small to count, so the counting unit, called the “mole” is used
to quantify. The key to understanding the mole is that one mole
always contains the same amount of particles, just as one dozen
always contains 12 items.
In 1896, Friedrich Wilhelm Ostwald introduced this word which is
derived from the Latin
word moles, meaning a heap or pile. The
mole (abbreviated as mol) is the standard SI unit for measuring a
quantity of material. (Be careful to point out to students that “mol”
is the correct abbreviation for the mole, not “m.” The letter “m” is
the abbreviation used for meters.)
The mole is defined as follows:
So, how many particles is that? Many scientists have carried out
experiments to determine exactly how many particles are in a
mole. The best data available now are:
This value is known as Avogadro’s number, to honor an Italian
lawyer and physicist who originally had the idea, although he
never determined the number.
Conversions and Dimensional analysis
Dimensional analysis is the process of converting quantities from
one unit of measurement to another, using ratios that are
equivalent. For example, a quantity of matter can be measured
either as mass (in grams, kilograms, etc.) or moles. In the
laboratory, you can only measure mass using a scale or balance.
Therefore, a conversion from mass to moles is necessary.
There are three kinds of dimensional analysis conversions
presented in this section:
1) Mass of a material moles of that material
2) Moles of one material moles of another material
3) Moles of a gas volume of that gas, under known conditions
of temperature and pressure
Often, conversions are done in a continuous series to arrive at the
desired answer.
Conversion 1:
mass of a material moles of that
material
If you know the identity of the material, you can convert between
the mass and the moles by using an equivalent measure called
molar mass (which is the mass of one mole of a material). The
molar mass is expressed in grams per mole (g/mol). For example,
one mole of sodium
(Na) atoms has a mass of 22.99 grams. The
molar mass of Na is 22.99 g/mol. This number can be obtained
from the atomic mass listed on the periodic table. This conversion
is used when changing between moles of sodium and mass
of
sodium. Two moles of sodium have a mass of 45.98 g. The
conversion can be shown using dimensional analysis as follows:
The fraction shown is the conversion factor, which in this case is
the molar mass, g/mol. The numerator and denominator of this
conversion factor are equivalent, except they are expressed
in
different units. In other words, one mole of
Na atoms always has
a mass of 22.99 grams.
The conversion factor is the “domino”
students are taught to use in this section to make this conversion
work. The trick to the “dominoes” game is that the denominator
unit must cancel
the numerator unit in the previous domino. So,
the moles of Na cancel each other out in this case, leaving grams of
Na as the units in the answer.
In the language of the dominoes
game, this conversion looks like:
To run the conversion backwards, the opposite domino would be
used. For example, if you want to know how many moles of Na are
in 45.98 grams of Na, the calculation would be:
The molar masses of materials that are not simple elements can be
calculated if you know how many of each type of particle are
inside a unit of the material. Examples of this are presented in Step
9 of the Investigate section in the Student Edition. For example,
one mole of water (H2O) has a mass of 18.02 grams, as shown in
the Student Edition. Therefore, the mass of 2.000 moles of water is
calculated this way.
Conversion 2:
moles of one material moles of
another material
When you have the quantity of a material expressed in terms of
particles, you can use balanced chemical equations to keep track of
what particles do. In this way, you can convert between particles of
one material and particles of another material. The conversion
factor used relates the quantity of particles of one type of material
to the quantity of particles of another type of material.
The balanced chemical equation
2H2O2 2H2O
shows the relations between how many units of each kind of
chemical are needed or produced. This is determined by the
coefficients in the balanced equation and in this equation it
takes
2 moles of H2 and 1 mole of O2 to make 2 moles of water
(H2O).
If you start with 4 moles of H2, then 2 moles
of O2 are needed to
react with all the H2. Or, it could be asked as a question: If you
begin with
4 moles of H2, how many moles of O2 are needed so
that all the H can react? The domino, using equivalent measures
derived from the coefficients in front of the chemicals in the
balanced reaction, is shown here:
While this calculation using whole numbers is easy for students to
do in their heads, more complicated numbers require the rigor of
calculations.
Conversion 3: moles of a gas volume of that gas
Most matter is measured in the laboratory in mass. However,
quantities of gases are often easier to measure by volume. So, it is
convenient to know how to convert between moles of a gas and the
volume of that gas. Since the volume of any gas under standard
laboratory conditions (standard pressure of 1 atmosphere,
temperature of 0oC) is the same (assuming ideal behavior), there is
one conversion factor that works for all gases under these
conditions. One mole of
a gas takes up 22.4 liters of space at
standard conditions (STP). As with any other conversion factor, it
can be used in either direction.
Using more than one conversion in a calculation
More than one conversion can be used to do a calculation. The idea
is that anything that appears in the denominator of one fraction can
cancel something that appears in the numerator of another fraction.
The trick to the calculation is
to get the conversions placed so that
everything cancels except the units you want in the end. This is the
only rule in the dominoes game, and one which students are asked
to figure out early in the section.
The goal of this section is not to teach students
to be able to do all
stoichiometry calculations (that would take more time than is
allotted for this section). The goal is to give students the tools they
need to predict how many grams of baking soda are needed to
inflate a balloon with enough CO2 gas to tip a lever by a specified
amount. Therefore, if beginning with liters of CO2 gas, and ending
with grams of baking soda (NaHCO3), the initial setup looks like
this:
(some amount) L CO2 gas (some conversion factors) = (some
amount) g NaHCO3
This means that in the first conversion factor or domino, L CO2 gas
must be in the denominator. And in the last domino, g NaHCO3
must be in the numerator. Since the only conversion you know that
involves liters of gas is the third kind, then the first conversion
factor must be:
The only conversion you know that involves grams of a material is
the first kind, so the last conversion factor must be:
The missing domino in the middle (?) must then convert between
moles of CO2 gas and moles of NaHCO3. For this, you must
consider the balanced equation:
NaHCO3 HC2H3O2 NaC2H3O2 H2O CO2
This shows that 1 mole of NaHCO3 yields 1 mole of CO2.
The final setup then is:
Stoichiometry
The word “stoichiometry” derives from two Greek words:
stoicheion, meaning “element” and metron, meaning “measure.”
Doing stoichiometry calculations in chemistry involves
mathematically relating the amount of one chemical to the amount
of another. The most common kind of stoichiometry calculation
asks what quantity
of one chemical can be produced if a specified
quantity of another chemical is used.
It is sometimes helpful to students to map stoichiometry
calculations. Examples 1A and 1C fit the same general map,
although the chemical (Na) and conversion factor (domino) shown
are specific to Example 1A only:
The map for the stoichiometric calculation to determine the mass
of baking soda required to inflate a balloon with CO2 gas to a
desired volume is: