Avogadro’s Number and … the Mole
When I buy eggs, how many come in a package?
What do we call that?
12 objects = 1 dozen
The MOLE (mol) is kind of like a dozen (in chemistry).
It’s based on the number of atoms of a particular element
equal to the number of atoms in exactly 12.0 grams of
Carbon-12.
Therefore the measure of a mole is always the
same...
1 mole = 6.02x1023 atoms, molecules, ions, whatever!
For Example:
There are always:
6.02x1023 hydrogen atoms in 1.0g of hydrogen
6.02x1023 lead atoms in 207.2 g of lead
Is 6.02x1023 a big number?
If I won a mole of dollars in the lottery that would be
equal to: $602,000,000,000,000,000,000,000.00
The concept of the mole was first proposed by Amadeo
Avogadro.
Atomic Masses
The atoms of different elements have different masses:
Since the mass of an atom is very small, we use a
special unit to describe it…
amu (atomic mass unit)
In addition, we describe the masses of atoms using a
relative scale:
We always compare them to the mass of carbon – 12
The mass of an atom, expressed with respect to the mass of
Carbon-12 is called the ATOMIC MASS of the atom.
What does this mean?
The experimentally determined mass of Carbon12 is 12.011 amu
o What is the mass of Mg? 24.035 amu
Therefore the atomic mass of Mg is roughly 2
times larger than Carbon-12.
Amadeo Avogadro developed a method to convert between
the mass of an element (in grams) and the number of atoms
present.
Recall that 1 mol = 6.02x1023 atoms, ions, or molecules.
The MOLAR MASS is the mass of one mole of a substance
and is equal to the atomic mass, or molecular mass,
expressed in grams.
Molar Mass = grams per mole of a substance
g/mol
For Example:
1 ATOM of Al = 27.0 amu
1 MOLE or 6.02x1023 atoms Al = 27.0g
Could be written as 27.0 g/mol
1 MOLECULE of H2 = 2.02 amu
1 MOLE or 6.02x1023 molecules H2 = 2.02g
H2 has a molar mass of 2.0 g/mol
When dealing with molar masses, only use ONE decimal
place.
Molar Mass
Find the molar mass of NaCl
Steps:
1. Determine what atoms and their amounts are
present.
NaCl = 1 Na + 1 Cl
2. Add up the individual masses of each atom present
to determine the molar mass.
1 x Na =
23.0 g
1 x Cl =
35.5 g
1 x NaCl = 58.5 g
Find the molar mass of:
NH3
KMnO4
Ca(CH3COO)2
USING THE MOLE
There are various types of problems you may run into:
DETERMINE THE MASS OF A SUBSTANCE GIVEN THE
# OF MOLES
You must determine the mass present, given the number of
MOLES of a substance or vice versa.
Use the following conversion factors:
1 mol
(molar mass of X)
or
(molar mass of X)
1 mol
For Example:
a. What is the mass in grams of 3.25 mol of CO2?
b. How many moles of N2 are there in 50.0 g of N2?
c. What is the Molar Mass of a 1.25 mol sample of Element
X if it has a mass of 22.34g?
Exercises p.80 # 6e,f,g,n & 7ab
p.82 # 8a-f, 9a-f,10a-c
CONVERSIONS BETWEEN NUMBERS OF PARTICLES &
MOLES OF PARTICLES
You must determine the number of moles that are present,
given the number of particles present.
Use the following conversion factors:
1 mol particles
6.02x1023 particles
or
6.02x1023 particles
1 mol particles
For Example:
a. How many moles of Carbon are there in 3.01x1024 C
atoms?
b. How many moles of Ag are present in 3.0x1016 atoms of
Silver?
c. A particular variety of carbon atom has a mass of
2.16 x 10-23 g/atom. What is the mass of a mole of this
variety of carbon atom?
CONVERSIONS BETWEEN NUMBER OF MOLES & THE
VOLUME OF A GAS
Calculations involving gas volumes are simplified
by Avogadro’s Hypothesis:
Equal volumes of different gasses, at the same
temperature and pressure, contain the same number of
particles.
The MOLAR VOLUME of a gas is the volume occupied by
one mole of gas at…
Standard Temperature and Pressure
Or
STP = 0ºC and 101.3 kPa
Another way to state Avogadro’s Hypothesis is…
All gas samples with the same pressure, temperature,
and number of particles occupy identical volumes.
1 mol of ANY GAS at STP has a volume of 22.4 L
In other words, the MOLAR VOLUME of any gas at STP is
22.4 L.
Use the following conversion factor:
1 mol
22.4 L
or
22.4 L
1 mol
For Example:
a. What is the volume occupied by 0.350 mol of SO2(g) at
STP?
b. How many moles of gas are contained in a balloon
with a volume of 10.0 L at STP?
Exercises p.83 # 11ab,12ab
p.84 # 15all, 16a,c, 17b,c, 18a,b,c
MULTI STEP CONVERSIONS MOLE CONVERSIONS
Before trying multi step conversions, there is one more type
of conversion to be aware of:
(atom count) atoms
1 molecule
or
1 molecule
(atom count) atoms
For Example:
a. How many atoms are there in 5 molecules of
CuSO4•5H2O?
b. How many Hydrogen atoms are there in 30
molecules of H3PO4?
The most difficult type of conversions involve changing
between various units requiring you to use several
conversions.
The following table summarizes all the conversion factors
you should be aware of:
It’s important for you to remember that the mole is “central”
to ALL conversions between mass, particles, and volume.
Each calculation goes from STARTING UNIT to MOLES to
FINAL UNIT.
For Example:
a. What is the volume occupied by 50.0 g of NH3(g) at
STP?
b. What is the mass of 1.00x1012 atoms of Cl?
c. How many Oxygen atoms are contained in 75.0 L
of SO3(g) at STP?
Exercises p.86 # 22a-f; 23a-f; 24a-d
Hand-in #4
Exercises p.86 # 22g-j; 23g-l; 24e-h
Problems involving density require you to recall:
d= m
v
Where:
m = mass (in g or kg)
v = volume (in L or mL)
Some tips:
PLAN AHEAD when doing problems involving
density.
Use the density as a CONVERSION FACTOR
to obtain the units that you want.
For Example:
a. What is the volume occupied by 3.00 mol of
ethanol, CH3CH2OH(l)? (d = 0.790 g/mL)
b. How many moles of Hg(l) are contained in 100 mL
of Hg(l) ? (d = 13.6 g/mL)
c. What is the density of O2(g) at STP?
d. A 2.50 L bulb contains 4.91 g of a gas at STP.
What is the molar mass of the gas?
e. Al2O3(s) has a density of 3.97 g/mL. How many
atoms of Al are in 100mL of Al2O3?
Exercises p.88 # 25, 27-29, 31, 34
Hand-in #5
p.88/89 # 35-40 a, c, (e)
41a, c, d, f, k
42 b, c, e, f, g, h, j, o, q, s
Exercises p.88/89 # 35-39; 40a-d; 41a,c,d,f,k
42b,c,e,f,g,h,j,l,n,o,q,s 43a,b,c,e,f,h,I,k,m,o,q,s
Percentage Composition
The PERCENTAGE COMPOSITION is the percentage (by
mass) of the species in a chemical formula.
For Example:
What is the percentage composition of CH4?
What is the percentage composition of H2SO4?
What is the percentage of water in CuSO4 • 5H2O?
Exercises p.91 # 44a,d,g,j; 45a,e,g,h
Hand-in #6 – Due Monday
Empirical and Molecular Formulae
The EMPIRICAL FORMULA is often called the SIMPLIST
FORMULA.
The smallest whole number ratio of atoms will represent
this.
Consider the following:
All of CH2, C2H4, C3H6, C4H8, and C5H10 contain twice
as many H’s as C’s and therefore the empirical formula
for all these molecules is CH2.
For Example:
a. What is the empirical formula of a compound consisting of
80.0% C and 20.0 % H?
b. A compound contains 58.5% C, 7.3% H, and 34.1% N.
What is the empirical formula of the compound?
c. What is the empirical formula of a compound
containing 81.8% C and 18.2% H?
You must be able to recognize the following fractions
and their decimal equivalents.
0.20 = 1/5
0.25 = 1/4
0.33 = 1/3
0.40 = 2/5
0.50 = 1/2
0.60 = 3/5
0.67 = 2/3
0.75 = 3/4
0.80 = 4/5
d. What is the empirical formula of a compound containing
43.2 g of C and 115.8 g of O?
Exercises p.93 # 46 a, b, c, f, g, k, l, m
FINDING THE MOLECULAR FORMULA
The molecular formula gives the actual number of atoms of
each element in a molecular compound.
The molecular formula can be found by dividing the molar
mass of the compound by the empirical formula mass.
N (whole number multiple of empirical mass) =
Molar Mass
Empirical Mass
Molecular formula = N x (empirical formula)
For Example:
a. 2-carotene, a compound found in carrots, can be broken
down to form vitamin A. The empirical formula for 2-carotene
is C5H7. The molar mass of 2-carotene is 536 g/mol. What is
the molecular formula for 2-carotene?
b. Ribose is an important sugar that is found in DNA and
RNA. Ribose has a molar mass of 150.0 g/mol and a
chemical composition of 40.0% carbon, 6.67% hydrogen,
and 53.3% oxygen. What is the molecular formula for
ribose?
c. A gas has the empirical formula POF3. If 0.350 L of the
gas at STP has a mass of 1.62 g, what is the molecular
formula of the compound?
Exercises p.95 # 47-55
Molar Concentration
Knowing the Concentration of a solution allows us to know
how much of a particular substance exists in a given volume.
CONCENTRATION:
The amount of a substance which exists in a given
volume of the solution
CONCENTRATED:
A solution with a relatively HIGH concentration (large
amount of substance dissolved in the solution).
DILUTE:
A solution with a relatively LOW concentration
(very little substance dissolved in the solution).
The MOLAR CONCENTRATION or MOLARITY of a
substance is the number of moles of substance contained in
1L of solution.
NOTE:
The above definition states 1 L of SOLUTION not 1L of
SOLVENT.
For Example:
If 2.0 L of solution contains 5.0 mol of NaCl, what is the
molarity of NaCl(aq)?
A couple of things to keep in mind...
The unit symbol for “mol/L” is “M”.
When expressed in words, the unit symbol “M” is
written as “molar”.
The short hand symbol for “molar concentration of...”
is a set of brackets: “[...]”.
Making up Solutions
Using a balance, obtain the required
mass of solute in a beaker.
Dissolve the solid in distilled water.
Transfer the solution and rinse all
equipment into a clean volumetric
flask.
Add distilled water up to the
calibration line on the flask.
An eye dropper may be used.
Stopper the volumetric flask and mix
the contents thoroughly.
The following equation defines molar concentration:
For Example:
a. What is the [NaCl] in a solution containing 5.12 g of NaCl
in 250.0 mL of solution?
b. What mass of NaOH is contained in 3.50 L of 0.200 M
NaOH?
c. What is the molarity of pure Sulfuric acid, H2SO4(aq), having
a density of 1.839 g/mL?
d. What is the molarity of the CaCl2 in a solution made by
dissolving and diluting 15.00 g of CaCl2-6H2O to 500 mL?
Exer p.98/99 # 59c,d,e; 60a,f; 61, 62, 64, 66, 68, 70
Dilution Calculations
There are several types of dilution calculations.
1. A simple dilution of a chemical in solution.
c1 •V1 = c2 •V2
Where:
c1= initial concentration of solution
V1= initial volume of solution
c2= final concentration
V2= final volume
The amount of chemical is not changed when the solution is
diluted, only the concentration.
Therefore:
Initial Moles
=
Final Moles
Example:
If 200.0 mL of 0.500 M NaCl is added to 300.0 mL of
water, what is the resulting [NaCl] in the mixture?
2. Mixing two solutions having different concentrations
of the same chemical.
Treat mixtures of two solutions as two separate “single
dilutions” then add the results of the individual single
dilutions.
For Example:
If 300.0 mL of 0.250 M NaCl is added to 500.0 mL of
0.100 M NaCl, what is the resulting [NaCl] of the
mixture?
Note:
The final concentration lies between the original
concentrations of the two NaCl solutions.
0.100 M < 0.156 M < 0.250 M
3. Making dilute solutions from concentrated solutions.
The procedure used is similar as scenario 1, but now
we are finding c1 or V1.
For Example:
A) What volume of 6.00 M HCl is used in making up 2.00 L
of 0.125 M HCl?
B) A student mixes 100.0 mL of water with 25.0 mL of a
NaCl solution having an unknown concentration. If the
student finds the molarity of the NaCl in the diluted solution
is 0.0876 M, what is the molarity of the original NaCl
solution?
Exercises p.102 # 78-82, 84-88, 92
Exercises p.103 # 95ab; 97abcd; 98ab; 99b; 100ab;
101ab; 102adf
Unit 5 Review Questions
What is on the test?
Introduction to the Mole
o Atomic Masses
o Molecular Masses
o Avogadro’s Number and the Mole
Using the Mole
o Single and Multi Step Mole Conversions
- Know conversion factors!
- Density Calculations
Percent Composition
Empirical and Molecular Formulae
o Finding the Empirical formula
o Finding the Molecular Formula
Molar Concentration
o Making Up Solutions
o Dilution Calculations