The Mole
Chemistry 6.0
The Mole
I. Formulas & Chemical Measurements
A. Atomic Mass
1. Definition: the mass of an atom, based on a C-12
atom, in atomic mass units, amu.
2. 1 amu = 1.66 x 10-24g = 1/12 the mass of a C-12 atom
3. Example: atomic mass of sodium =
23.0 amu
B. Formula Mass
1. Definition: the sum of the atomic masses of all the
in a formula.
2. Example: formula mass of Fe2(SO4)3 =
Fe:
S:
2 x 55.8
3 x 32.1
=
=
111.6
96.3
O:
12 x 16.0 =
192.0
399.9 amu
atoms
C. MOLE
1. Atoms are too small to count or mass individually.
It is easier to count many or mass many.
amu
gram
mole
(atomic scale)
(macroscopic scale)
2. Mole = amount of substance that contains 6.02 x 1023 particles
abbreviated: mol
3. Avogadro’s Number = number of particles in a mole
= 6.02 x 1023 particles
Particles can be atoms, ions, molecules, or formula units
4. Molar Mass = mass, in grams, per 1 mole of a substance
units = grams/mole (g/mol)
Example: the molar mass of H2O is
18.0 g/mol
Getting to know the terms…
MICROSCOPIC
Mass
MACROSCOPIC
Molar
Mass
Atom
Atomic mass
amu
Element
g/mol
Molecule
Molecular mass
amu
Molecular
Compound
g/mol
Formula Unit
Formula mass
amu
Ionic Compound
g/mol
Diatomic Molecules
HOFBrINCl
H2 O2 F2 Br2 I2 N2 Cl2
MOLE RELATIONSHIPS
1 Mole = 6.02x1023 particles of substance
(atoms, formula units, molecules)
1 Mole = mass (g) of substance from PT
Also remember your formula information:
1 molecule = _________ atoms
1 formula unit = _________ ions or
_________ atoms
II. Mole Conversions
MUST use factor label!
A. Moles & Mass
1. How many grams in 3.0 moles of water?
know: 1 mole H2O = 18.0 g H2O
54 g H2O
2. How many moles in 60.0 g of copper?
know: 1 mole Cu = 63.5 g Cu
0.945 g Cu
B. Moles & Particles
1. How many atoms in 3.0 moles of copper?
know: 1 mole Cu = 6.02 x 1023 atoms of copper
1.8 x 1024 atoms Cu
2. How many atoms in 3.00 moles of water?
know: 1 mole H2O = 6.02 x 1023 molecules of H2O
know: 1 molecule H2O = 3 atoms
5.42 x 1024 atoms
II. Mole Conversions
MUST use factor label!
C. Mass & Particles
1. How many atoms in 100.0 g of copper?
63.5 g copper
know: 1 mole = _________
atoms of copper
1 mole = 6.02 x 1023 __________
9.480 x 1023 atoms Cu
2. How many oxygen atoms are in 75.0 g of sucrose,
C12H22O11?
342.0
know: 1 mole = __________
g of C12H22O11
molecules of C12H22O11
1 mole = 6.02 x 1023 _____________
atoms of oxygen
1 molecule of C12H22O11 = 11 ________
1.45 x 1024 atoms
Avogadro’s Law
Amount - Volume Relationship.
Equal volumes of gases at the same temperature and
pressure contain an equal number of particles.
volume
constant
4 He
222 Rn
molar mass
1 mole gas = 22.4 L = 6.02 x 1023 particles
at STP (273 K & 1 atm)
He
O2
Rn
Therefore because of Avogadro’s Law if these
three gases have the same number of particles
and are at the same temperature and pressure,
they must take up the same volume.
Molar Mass does not affect
volume of a gas
Avogadro’s Law
• At STP, the amount of gas is directly
proportional to the volume.
Problem #1: Which of the following samples
of gases occupies the largest volume,
assuming that each sample is the same
temp and pressure?
50.0 g Ne
50.0 g Ar
50.0 g Xe
Ideal Gas Law
Although no “ideal gas” exists, this law can be used to
explain the behavior of real gases under ordinary
conditions.
P = pressure (atm)
V = volume (L or dm3)
PV = nRT
n = number of moles
R = 0.08206 L•atm/mol•K
universal gas constant
T = Kelvin temperature
• Individual gas laws describe the relationships between
these variables.
• Ideal gas law relates all 4 variables that describe a gas
at one set of conditions.
Ideal Gas Law Problems
1. Calculate the volume of a gas balloon filled
with 1.00 mole of helium when the pressure
is 760. torr and the temperature is 0.oC.
22.4 L
2. Calculate the pressure, in atm, exerted by
54.0 g of xenon in a 1.00-L flask at 20.oC.
9.89 atm
3. Calculate the density of nitrogen dioxide, in
g/L, at 1.24 atm and 50.oC.
2.15 g/L
B. Empirical Formulas
1. Definition: always the smallest whole-number
ratio of the atoms, or ions, in a formula
2. Use experimental data to find the empirical
formula
3. Examples
a. Determine the empirical formula of a compound if a
2.500-g sample contains 0.900 g of calcium and 1.600
g of chlorine.
CaCl2
b. Determine the empirical formula for an iron oxide that
is 70.0% iron. Name the compound.
Fe2O3
iron(III) oxide
C. Molecular Formula
1. Definition: the formula of a molecular
compound. The molecular formula shows the
actual number of atoms of each element
present in 1 molecule of a compound.
Molecular formula for benzene: C6H6
Empirical formula for benzene: CH
D. Molecular formula is always a wholenumber multiple of the empirical formula.
molecular formula = (empirical formula)n
n = molar mass molecular formula
molar mass empirical formula
Example
Find the molecular formula of a compound that
contains 42.5 g of palladium and 0.80 g of hydrogen.
The molar mass of the compound is 216.8 g/mol.
Empirical formula - PdH2
Molecular formula – Pd2H4
Concentration
Definition: a measure of the amount of solute dissolved in a
solution
Small amount of solute in solution
1. Dilute solution: _________________________________
Large amount of solute in solution
2. Concentrated solution: _________________________________
• Molarity (M)
• Moles of solute/Liters of solution = mol/L
• Molality (m)
• Moles of solute/mass of solvent = mol/kg
• ppm and ppb
• Used for very dilute solutions
• Drinking water additives or pollutants
• Atmospheric pollutants
• % Concentration by mass or volume
a. Definition:
1% NaCl: 1 g NaCl per 100 g solution
Molarity or Concentration
a. Definition: number of moles of
solute per liter of solution
1 L = 1 dm3 = 103mL = 103cm3 = 103cc
b. Abbreviation: M
Units: mol/L
c. Preparation of solutions
Need to know the desired volume & calculate the
mass of needed solute.
Prepare 500. mL of 1.0 M NaCl
29 grams of NaCl to a 500Transfer ________
mL volumetric flask, and add water to the
line.
*Note: Always add acid to water.
Problems – Molarity (mol/L)
Molarity = mol solute/L solution
1.
Calculate the molarity if 37 g of NaCl are dissolved in 150 mL
of solution.
4.2 M NaCl
2.
How many moles of HCl are present in 145 mL of a 2.25 M
HCl solution?
0.326 mol HCl
3.
How many grams of NaCl are contained in 2.5 L of a 1.5 M
solution?
220 g NaCl
Problems – Molality (m)
Molality (m) = mol solute/mass of solvent(kg)
1.
Calculate the molality if 37 g of NaCl are dissolved in 500 g of
water.
1.26 mol NaCl/kg water
2.
How many moles of HCl are present in a 2.25 m HCl solution
that contains 750. g of water?
1.69 mol HCl
3.
How many grams of water are needed to make a 1.50 m NaCl
solution with 78.0 grams of NaCl?
889 g NaCl