Mole Concept and Avogadro’s Constant
Describe the mole concept
and apply it to substances.
The mole concept applies to all kinds of particles:
atoms, molecules, ions, formula units etc.
The amount of substance is measured in units of moles. The approximate value of Avogadro’s constant
(L), 6.02 x 1023 mol-1, should be known.
A mole (often abbreviated mol) is the
number equal to the number of carbon atoms in exactly 12 grams of pure 12C. Techniques such as mass spectrometry, which
count atoms very precisely, have been used to determine this number as 6.02214
x 1023 (6.02 x 1023 is good enough for IB). This number is called Avogadro’s number to
honor his contributions to chemistry.
One mole of something consists of 6.02 x 1023 units of that
substance. Just as a dozen eggs is 12
eggs, a mole of eggs is 6.02 x 1023 eggs.
The magnitude of the number 6.02 x 1023
is difficult to imagine. To give you
some idea, 1 mole of seconds represents a span of time 4 million times as long
as the earth has already existed, and 1 mole of marbles is enough to cover the
earth to a depth of 50 miles! However,
since atoms are so tiny, a mole of atoms or molecules is a perfectly manageable
quantity to use in a reaction.
The mole is also defined as such that a
sample of a natural element with a mass equal to the element’s atomic mass
expressed in grams contains 1 mole of atoms.
This definition also fixes the relationship between the atomic mass unit
and the gram. Since 6.02 x 1023
atoms of carbon (each with a mass of 12 amu) have a mass of 12 g, then
(6.02
x 1023 atoms)(12 amu/atom)= 12 g
6.02
x 1023 amu=1 g
Calculate the number of
particles and the amount of substance (in moles).
Calculate between the amount of substance (in moles)
and the number of atoms, molecules or formula units.
In order to convert from x moles of
anything to how many actual atoms, multiply x by Avagadro’s constant to find
how many actual particles you have.
For example, say you are given 2.3 moles of
hydrogen. In order to find how many
actual particles of hydrogen you have, you do the following calculations…
2.3
mol H x (6.02 x 1023 particles H/1 mol H) = 1.38 x 1024
1.2 Formulas
Define the term molar mass (M) and calculate
the mass of one mole of a species.
The molar mass of a substance is the mass
in grams of one mole of the compound.
How can we calculate the mass of one mole
of a substance? Let’s take methane for
example. Methane is CH4,
which means in a molecule of methane there is one carbon atom and four hydrogen
atoms. So, the molar mass of CH4
would be, what is the mass in grams of one mole of methane, or what is the mass
of 6.02 x 1023 CH4 molecules? The mass of 1 mole of methane can be found by
summing the masses of carbon and hydrogen.
Mass
of 1 mol C: 12.01 g (This can be found on the periodic table)
Mass
of 4 mol H: 4 x 1.008 g (If you don’t understand where the four came from,
learn what subscripts mean)
Add them.
Mass
of 1 mol CH4: 16.04 g
Traditionally, the term molecular weight
has been used for this quantity. The
molar mass of a known substance is obtained by summing the masses of the
component atoms as we did for methane.
Distinguish between atomic mass, molecular mass
and formula mass.
The term molar mass (in g mol-1) can be
used for all of these.
Molecular
Mass: The mass in grams of one mole of molecules or
formula units of a substance; the same as molar mass.
Formula
Mass: The mass of a formula, including ionic
compounds. Technically, molecular mass
only applies to molecules (which are defined by covalent bonding). Formula mass can also include ionic
compounds, etc.
Atomic
Mass: Atomic mass is somewhat difficult to
define. According to Zumdahl, atomic
mass is technically the average atomic mass of an element, which is determined
by finding the different isotopes of an element present in nature, and how much
percent of the total amount of that element in the world they make up. For example, in nature there are two primary
isotopes of Carbon, 12C and 13C (there are other isotopes
but they are so rare they are insignificant at this level of precision. 98.89% of Carbon is 12C, but 1.11%
is 13C. So to find the atomic
mass of Carbon, we do the following…
(.9889)(12
amu (mass of 12C by definition)) + (.0111)(13.0034 amu (mass of 13C))
= 12.01 amu
This is the atomic mass of carbon.
Define the terms relative molecular mass (Mr)
and relative atomic mass (Ar).
The terms have no units.
The relative atomic mass is the mass of one
atom of an element compared to the mass of Carbon 12. The relative atomic mass has no units because
it is a ratio of masses and the units cancel out. The relative molecular mass is the mass of
the relative atomic masses of all the atoms in a molecule added up. It’s basically the molecular mass without
units as far as I can tell.
State the relationship between the amount of
substance (in moles) and mass, and carry out calculations involving amount of
substances, mass and molar mass.
The relationship between moles and mass is
demonstrated in the mass formula.
Number
of Moles (N)= mass (m)/Molecular Mass (M)…
N=m/M
So, say you are given 40 grams of Carbon
Dioxide, how many moles do you have? The molecular mass of Carbon Dioxide (CO2)
is 44 g. So, the way to solve this would
be to divide 40 grams by 44 g.
Number
of Moles: 40g/44= .91 mol
Note: I am not sure how the units work out for
this. It would appear that the grams
cancel each other out leaving no value, but for some reason you are left with
moles. This may be something to ask your
teacher about.
Define the terms empirical formula and
molecular formula.
The molecular formula is a multiple of the empirical
formula.
The empirical formula is best understood by
knowing its usefulness. One way
scientists find the formulas for molecules is by determining the percent of the
mass each element in the molecule takes up.
For example, let us take CH5N. A scientist is attempting to find the formula
but doesn’t know what it is. He breaks
it up and finds that 38.67% Carbon, 16.22% Hydrogen, and 45.11% Nitrogen. By assuming the compound weighs 100 grams,
each of these percentages now becomes gram units. Then by changing them to moles and setting
them up in ratio to each other, the scientist finds that the ratio of Nitrogen
to Hydrogen to Carbon is 1:5:1. So, he
knows that the formula can be CH5N. However, the formula could also be C2H10N2,
or C3H15N3.
That is because all he has is a ratio.
The empirical formula is CH5N. This is the simplest form. The exact formula is called the molecular
formula, and that will be (CH5N)n where n is an integer. Sometimes the empirical and molecular formula
will be the same, other times they will not be.
If you did not understand the whole percent composition and ratios,
don’t worry, those will be explained later.
The important part is understanding the difference between empirical and
molecular formula and how they are related.
The empirical formula is the formula for the compound that has the
lowest values possible for it to still work.
The molecular formula is the formula with the actual values for the
compound, and it will always be the empirical formula multiplied by some
integer.
Determine the empirical formula and/or the
molecular formula of a given compound.
Determine the:
- Empirical formula from the percentage composition or from other suitable experimental data.
- Percentage composition from the formula of a compound.
- Molecular formula when given both the empirical formula and the molar mass.
The steps taken in the previous objective
will be examined in much more detail here.
In order to do these problems we will actually work the problems out,
and taking the same steps with any similar step should work out the same way.
1. Empirical formula from the percentage
composition or from other suitable experimental data.
When a new compound is prepared, one of the
first items of interest is the formula of the compound. This is most often determined by taking a
weighed sample of the compound and either decomposing it into its component
elements or reacting it with oxygen to produce substances such as CO2,
H2O, and N2, which are then collected and weighed. We will see how information of this type can
be used to compute the formula of a compound.
Suppose a substance has been prepared that is composed of carbon,
hydrogen, and nitrogen. When 0.1156 gram
of this compound is reacted with oxygen, 0.1638 gram of carbon dioxide (CO2)
and 0.1676 gram of water (H2O) are collected. Assuming that all the carbon in the compound
is converted to CO2, we can determine the mass of carbon originally
present in the 0.1156-gram sample. To do
this, we must use the fraction (by mass) of carbon in CO2. The molar mass of CO2 is
C: 1
mol x 12.01g/mol=12.01 g
O: 2
mol x 16.00 g/mol=32.00 g
Added
together, the molar mass of CO2 = 44.01 g/mol.
The fraction of carbon present by mass is
Mass
of C/Total mass of CO2 = 12.01 g C/ 44.01 g CO2
This factor can now be used to determine
the mass of carbon in 0.1638 gram of CO2:
0.1638
g CO2 x 12.01 g C/44.01 g CO2 = 0.04470 g C
Remember that this carbon originally came
from the 0.1156-gram sample of unknown compound. Thus the mass percent of carbon in this
compound is
(0.04470
g C/0.1156 g compound) x 100= 38.67% C
The same procedure can be used to find the
mass percent of hydrogen in the unknown compound. We assume that all the hydrogen present in
the original 0.1156 gram of compound was converted to H2O. The molar mass of H2O is 18.02
grams, and the fraction of hydrogen by mass of H2O is
Mass
of H/Mass of H2O = 2.016 g H/18.02 g H2O
Therefore, the mass of hydrogen in 0.1676
gram of H2O is
0.1676
g H2O x (2.016 g H/18.02 g H2O)= 0.01875 g H
And the mass percent of hydrogen in the
compound is
(0.01875
g H/0.1156 g) compound x 100 = 16.22%
The unknown compound contains only carbon,
hydrogen, and nitrogen. So far we have
determined that is is 38.67% carbon and 16.22% hydrogen. The remainder must be nitrogen.
100.00%
- (38.67% + 16.22%) = 45.11% N
We have determined that the compound
contains 38.67% carbon, 16.22% hydrogen, and 45.11% nitrogen. Next we use these data to obtain the
formula. Since the formula of a compound
indicated the numbers of atoms in the compound, we must convert the masses of
the elements to numbers of atoms. The
easiest way to do this is to work with 100.00 grams of the compound in the
present case, 38.67% carbon by mass means 38.67 grams of carbon per 100.00
grams of compound, etc. To determine the
formula, we must calculate the number of carbon atoms in 38.67 grams of carbon,
the number of hydrogen atoms in 16.22 grams of hydrogen, etc. You can do that using the mass formula (found
in 1.2.4.). The answers are 3.220mol C,
16.09 mol H, 3.219 mol N. Thus 100.00
grams of this compound contains 3.220 moles of carbon atoms, 16.09 moles of
hydrogen atoms, and 3.219 moles of nitrogen atoms. We can find the smallest whole number ratio
(empirical formula) of atoms in this compound by dividing each of the mole
values above by the smallest of the three:
C:
3.220/3.219 = 1.000 = 1
H:
16.09/3.219 = 4.998 = 5
N:
3.219/3.219 = 1.000 = 1
So, the empirical formula for the unknown
compound is CH5N. Now, if you
want to know the molecular formula, you have to know the formula mass of the
unknown compound. If the formula mass of
the unknown is the same as the formula mass of the empirical formula, then the
empirical formula is the molecular formula, but if the formula mass of the
unknown is say n times more then the formula mass of the empirical formula,
then the molecular formula is n times the empirical formula.
2.
Percentage composition from the formula of a compound.
Say you are given the formula H2O,
and you want to find out the percentage composition of hydrogen. How you do this is you find the formula mass
of water, and then find the atomic mass of H2, and divide the latter
by the former. Then multiply by 100 to
get a percent value. So, formula mass of
H2O is 18, H2 is 2, so 2 g H2/ 18 g H2O=.11,
x 100=11.1%.
3. Molecular formula given both the empirical
formula and the molar mass.
Say you are given the empirical formula CH5N,
and are told that the molar mass is 62.12 g, and are told to find the molecular
formula. First you find the formula mass
of CH5N, which ends up being 31.06 g. You know that that multiplied by n equals the
molecular mass of the formula you want, and the n in this is case is 2 (you
could find this by dividing 62.12 g unknown/ 31.06 g empirical formula).
Chemical Equations
Balance chemical equations when all reactants
and products are given.
Distinguish between coefficients and subscripts.
Say you are given the reaction C6H14
+ O2à CO2 + H2O and
are told to balance it. The main idea
behind balancing an equation is you have to have the same amount of each
element on both sides of the equation, and the only thing you can edit are the
coefficients, not the subscripts. So,
for example, in this equation, in the hexane (reactant), you have 6 carbons,
but in the products you only have one carbon.
So, to balance the carbons you have to place a 6 in front of the
CO2. You now have 6 carbons on both sides. Next look at the hydrogen (a good rule of
thumb is whenever you have an element that is by itself, such as the oxygen in
the reactants, leave it for last). You
have 14 hydrogen on one side and only 2 on the other, so you have to multiply
the water on the right by 7 (because the hydrogen has a subscript of 2, which
means there are two hydrogen in the water compound.) You now have fourteen hydrogen on both
sides. You now move onto the
oxygen. There is 2 oxygen in the reactants
and 19 in the products. There is a rule
when balancing equations that you are not really supposed to use anything but
integers (although when you get into more advanced stuff you will occasionally
use fractions to make it easier on yourself, but you’re not supposed too). So, there is no way to balance it as is. So, you’ll have to go back and change your
original coefficients. If you put a 2 in
front of the hexane and a 12 in front of the carbon dioxide you’ll have
balanced the carbons. Then to balance
the hydrogen put a 14 in front of the water.
Now, you have 28 hydrogen on both sides.
You now have two oxygen in the reactants and 26 in the products. So, by multiplying the oxygen in the
reactants by 13, you have 26 oxygen on both sides and you have balanced the
equation.
2C6H14
+ 13O2à 12CO2
+ 14H2O
In reality, practice makes perfect when it
comes to balancing equations. The only
way to learn is to keep trying, and after a few you’ll get pretty good and fast
at it. Some other rules are that if all
of the coefficients have a common denominator, you can divide everything by
that common denominator (so if the reactants had coefficients of 2 and 4 and
the products had coefficients of 6 and 10, you could divide all of them by
2). And remember that you cannot change
a subscript, and when you multiply a compound by a coefficient the whole
compound is multiplied, not just the front element.
Identify the mole ratios of any two species in
a balanced chemical equation.
Use balanced chemical equations to obtain information
about the amounts of reactants and products.
Using the reaction from above, 2C6H14
+ 13O2à 12CO2
+ 14H2O.
The mole ration from hexane to Oxygen is 2
mol hexane/13 mol O2.
Assuming stoichiometric equilibrium (there are no limiting or excess
reagents) it takes 2 moles of hexane to react with every 13 moles of
oxygen. This can also be done from
reactants to products. Another mole
ratio is 13 mol O2/12 mol CO2. Once again assuming stoichiometric
equilibrium, for every 13 mol O2 you get 12 mol CO2. This can also be done for products and
products (it can be done for any two species in a reaction.)
Apply the state symbols of (s), (l), (g), and
(aq).
Encourage the use of state symbols in chemical
equations.
The state symbols are placed after each
species to specify what state each each species in a reaction is in. The symbol (s) stands for the solid state,
(l) stands for liquid, (g) stands for gaseous, and (aq) stands for in aqueous
solution (dissolved in water). Often
times you don’t have to write the state symbols and they won’t have much
importance, but when they are needed it is really bad to miss them. For that reason I HIGHLY recommend you get
used to using them every time you know what they are, it’ll save you later on
from making the stupid mistake of forgetting them when they are needed.
Mass and Gaseous Volume Relationships in Chemical
Reactions
Calculate stoichiometric quantities and use
these to determine experimental and theoretical yields.
Mass is conserved in all chemical reactions. Given a chemical equation and the mass or
amount (in moles) of one species, calculate the mass or amount of another
species.
The first rule to remember is mass is
always conserved (at least at this point in the syllabus). So the total mass of one side should always
add up on another side. Now, once again
we will use the chemical equation from above.
2C6H14
(g) + 13O2 (g)à 12CO2
(g) + 14H2O (l)
Say you are told that you have 40 grams of
hexane, how many grams of oxygen do you need to completely react with all the
hexane? Well, in order to solve this you
use mole rations.
2
moles hexane/13 moles O2 = 40 g hexane/x moles O2. You then solve this like a normal ratio
problem (multiply diagonally then solve for x).
You answer is 260 grams of oxygen is needed to react with 40 g of
hexane. Note: This is not the best
example because you normally don’t use the measurement grams for gases, but it
would be the same way for liters.
Determine the limiting reactant and the
reactant in excess when quantities of reacting substances are given.
Given a chemical equation and the initial amounts of
two or more reactants:
- Identify the limiting reactant
- Calculate the theoretical yield of a product
- Calculate the amount(s) of the reactant(s) in excess remaining after the reaction is complete.
1. Identify the limiting reactant.
There are many ways to solve for the
limiting reactant, and everyone tends to like their own way. I will show mine below but if you don’t like
it feel free to ask your teacher or someone else for another way to do it. Say you have the equation
4FeCr2O4(s)
+ 8K2CO3(s) + 7O2(g) à 8K2CrO4(s) + 2Fe2O3(s) +
8CO2(g)
The
masses are 169 kg, 298 kg, and 75 kg respectively for the reactants, and you
want to find out which one is the limiting reagent. In order to do this, you first have to find
out how many moles of each of the reactants you have (using the mass formula),
we find their to be 7.55 x 102 mol chromite ore, 2.16 x 103
mol potassium hydroxide, and 2.34 x 103 mol O2.
You then set up the mole ratios you need to
react correctly and the mole ratios you have.
So,
to react correctly you should 4 moles of chromite ore for every 8 moles of
potassium carbonate. That is, 4 mol FeCr2O4/8
mol K2CO3(s), which equals .5. You then take the values that you actually
have, which are 7.55 x 102 mol chromite ore/2.16 x 103
mol potassium hydroxide, which equals .35.
This is smaller then .5, and that means that the numerator is too small
(if the answer was bigger then .5, the denominator would be too small). Whichever value is too small, that number is
the limiting reagent FOR THAT PAIR. You
then have to take that reagent and compare it with the other reactant, or the
rest of the reactants if there are more then three. So, taking chromite ore we do the same thing
comparing it with oxygen. We have 7.55 x
102 mol chromite ore/ 2.34 x 103 mol O2 which
then equals .32. The ratio we want is
4/7, or .57, which is bigger then the actual value we got, which means O2
is the limiting reagent of the entire reaction (you don’t have to then compare
it to the first reactant tested). So,
oxygen is the limiting reagent of the formula.
2 and
3. Calculate the theoretical yield of a
product and amount of excess reagent remaining after reaction is complete.
Theoretical yield of a product is the
amount of a product formed when the limiting reactant is completely
consumed. In order to obtain it, you go
through several steps, that we will go through with the reaction 2C2H6
+ 7O2 à 4CO2
+ 6H20 starting with 20 g of ethane and 40 grams of oxygen. So, the first step is to identify the
limiting reagent.
2
mol ethane/7 mol oxygen=.29 .66 mol
ethane/1.25 mol oxygen=.528. Since the
number is too big, that means the denominator is the limiting reagent, or
oxygen is the limiting reagent. We then
have to find how much ethane is used up before the oxygen is consumed. We do this by multiplying the actual amount
of oxygen by the mole ratio of the two reactants.
1.25
mol oxygen x (2 mol ethane/ 7 mol oxygen)= .36 mol ethane.
This is how much ethane is used up in the
reaction, so now we know how much ethane was used and we know how much ethane
we started with, so to find how much ethane is left over we do a simple
subtraction.
.66
mol ethane started with - .36 mol ethane used = .3 mol ethane left over.
So, we have .3 mol ethane left over after
the reaction. Then, to find theoretical
yield, you have two options. You can
use how much oxygen use, or you can use how much ethane you use in the
reaction, either should gain you the right answer. I would recommend using the value given to
you by the problem, so that way if you made a mistake in finding the excess
reagent left over you won’t mess up your second answer. You know you used 1.25 mol oxygen, so you do
another mole ratio.
1.25
mol oxygen x (4 mol carbon dioxide/7 mol oxygen)=.714 mol carbon dioxide.
So, .714 mol carbon dioxide is your
theoretical yield for that product.
Note:
Rarely do you ever calculate the theoretical yield, because side reactions
normally occur that decrease from the theoretical yield. The actual yield is sometimes compared to the
actual yield by doing the following calculations: actual yield/theoretical
yield x 100= Percent Yield.
Apply Avagadro’s law to calculate reacting
volumes of gases.
Avagadro’s law is V=an, where V stands for
volume, a stands for proportionality constant, and n is the number of moles of
gas particles. Basically, what this
equation states is that for constant temperature and pressure, the volume is
directly proportional to the number of moles of gas. This relationship is obeyed closely by gases
at low pressures. An example of this can
be exemplified by the following reaction 3O2(g) à 2O3(g) . The
temperature and pressure of this reaction are constant (25 degrees C and 1
atm). Say we start with a 12.2-L sample
containing 0.50 mol oxygen gas. What
would be the volume of the ozone?
0.50
mol oxygen x 2 mol ozone/3 mol oxygen= 0.33 mol ozone.
Avagadro’s law can be rearranged to show
V/n=a. Since as is a constant, an
alternative representation is V1/n1= a =V2/n2
So, for this reaction n1 equals
0.50 mol, V1 equals 12.2 L, n2=0.33 mol, and V2=? By setting up the above rearrangement of
avagadro’s law, 12.2/0.5=?/0.33, so the volume is 8.052 L.
Solutions
Define the terms solute, solvent, solution and
concentration (g dm-3 and mol dm-3).
Concentration in mol dm-3 is often
represented by square brackets around the substance under consideration, eg.
[CH3COOH].
Solute:
A substance dissolved in a liquid to form a solution.
Solvent:
The dissolving medium in a solution.
Molarity:
moles of solute per volume of solution in
liters. This often times written by IB
with units mol dm-3, which means moles/dm3, and a dm3
equals a liter. Same meaning, just
different ways of writing it. I recommend
writing it mol dm-3 whenever your in IB class because it gets you
well practiced, but if you are working with people outside of the IB program
write it per liters, because I have found they have a hard time understanding
IB notation. This is also often times
written short hand in square brackets such as [CH3COOH]. That means the molarity of that
compound. This could also be written as
g dm-3,(molality) however I have never seen it written that way,
even by IB. If it is ever written that
way, I would recommend converting it to moles (by just using Avagadro’s
number), however I could see how having it in grams may help calculate it at
some point. So, if you dissolve 5 moles
of HCl in 3 Liters of water, your molarity [HCl] is 5 mol/3 L, or 1.66 mol L-1,
or 1.66 mol dm-3.
Carry out calculations involving concentration, amount of solute and volume of
solution.
These are fairly easy. Just remember that concentration equals
amount of solute/volume of solution. So
say you know the concentration of a solution is 4 mol dm-3, and you know the
volume is 5 L. That means x mol/ 5 L=5
mol/L. That means x must equal 20 mol.
Note: A good rule to remember is the equation m1L1=m2L2. m stands for the molarity, and L stands for
volume. So, if you had a 2 L
concentration of 5 M HCl solution (M is often used to stand for molarity) and
you wanted to dilute it to a 2 M HCl, how much water would you need to
add? Well, m1=5, L1=2, m2=2, and L2=?. So, (5 mol/L)(2 L)=(2 mol/L)(? L). By solving for the unknown, you find your
final solution will be a volume of 5 liters, and since you started with 2
liters, you need to add 3 liters to get to 5 liters.
Solve solution stoichiometry problems.
Given the quantity of one species in a chemical
reaction in solution (in grams, moles or in terms of concentration), determine
the quantity of another species.
When it is given to you in grams or moles,
it’s just like a regular stoichiometric problem. However, if it is given to you in terms of
concentration, work your way around it to find moles or grams (so, if you have
a concentration of 5 M, then you have 5 moles per liter, and if you have 3
liters, that means you have 15 moles.)
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