1. The Mole
Chemistry

2. The Mole I. Formulas & Chemical Measurements
A. Atomic Mass
1. Definition: the mass of an atom, based on a C 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 atoms in a formula.
2. Example: formula mass of Fe2(SO4)3 =
Fe: 2 x =
S: x 32.1 =
399.9 amu
O: x =

3. units = grams/mole (g/mol)
C. MOLE 1. Atoms are too small to count or mass individually. It is easier to count many or mass many. amu gram (atomic scale) (macroscopic scale)
mole
2. Mole = amount of substance that contains 6.02 x 1023 particles
abbreviated: mol
3. Avogadro’s Number = number of particles in a mole
= 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)
18.0 g/mol
Example: the molar mass of H2O is

4. Getting to know the terms…
MICROSCOPIC
Mass
MACROSCOPIC
Molar Mass
Atom
Atomic mass
amu
Element
g/mol
Molecule
Molecular mass
Molecular Compound
Formula Unit
Formula mass
Ionic Compound
Diatomic Molecules
HOFBrINCl
H2 O2 F2 Br2 I2 N2 Cl2

5. 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

6. II. Mole Conversions MUST use factor label!
A. Moles & Mass 1. How many grams in 3.0 moles of water? know: 1 mole H2O = 2. How many moles in 60.0 g of copper? know: 1 mole Cu = B. Moles & Particles 1. How many atoms in 3.0 moles of copper? 2. How many atoms in 3.00 moles of water? know: 1 molecule H2O =
18.0 g H2O
54 g H2O
63.5 g Cu
0.945 g Cu
6.02 x 1023 atoms of copper
1.8 x 1024 atoms Cu
6.02 x 1023 molecules of H2O
3 atoms
5.42 x 1024 atoms

7. II. Mole Conversions MUST use factor label!
C. Mass & Particles 1. How many atoms in g of copper? know: 1 mole = _________ g copper 1 mole = 6.02 x 1023 __________ of copper 2. How many oxygen atoms are in 75.0 g of sucrose, C12H22O11? know: 1 mole = __________ g of C12H22O11 1 mole = 6.02 x 1023 _____________ of C12H22O11 1 molecule of C12H22O11 = 11 ________ of oxygen
63.5
atoms
9.480 x 1023 atoms Cu
342.0
molecules
atoms
1.45 x 1024 atoms

8. 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)

9. 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.

10. Molar Mass does not affect volume of a gas

11. 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 g Ar g Xe

12. 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)
n = number of moles
R = 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.
PV = nRT

13. Ideal Gas Law Problems
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 L
Calculate the pressure, in atm, exerted by 54.0 g of xenon in a 1.00-L flask at 20.oC atm
Calculate the density of nitrogen dioxide, in g/L, at 1.24 atm and 50.oC g/L

14. CaCl2 Fe2O3 iron(III) oxide
Empirical Formulas
Definition: always the smallest whole-number ratio of the atoms, or ions, in a formula
Use experimental data to find the empirical formula
Examples
Determine the empirical formula of a compound if a g sample contains g of calcium and g of chlorine.
Determine the empirical formula for an iron oxide that is 70.0% iron. Name the compound.
CaCl2
Fe2O3
iron(III) oxide

15. CH molecular formula = (empirical formula)n
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:
Molecular formula is always a whole-number multiple of the empirical formula. CH
molecular formula = (empirical formula)n
n = molar mass molecular formula
molar mass empirical formula

16. Empirical formula - PdH2 Molecular formula – Pd2H4
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 g/mol.
Empirical formula - PdH2
Molecular formula – Pd2H4

17. Small amount of solute in solution Large amount of solute in solution
Concentration
Definition: a measure of the amount of solute dissolved in a solution
1. Dilute 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
Small amount of solute in solution
Large amount of solute in solution

18. 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
Transfer ________ grams of NaCl to a 500-mL volumetric flask, and add water to the line.
*Note: Always add acid to water. 29

19. 4.2 M NaCl 0.326 mol HCl 220 g NaCl Problems – Molarity (mol/L)
Molarity = mol solute/L solution
Calculate the molarity if 37 g of NaCl are dissolved in 150 mL of solution.
How many moles of HCl are present in 145 mL of a 2.25 M HCl solution?
How many grams of NaCl are contained in 2.5 L of a 1.5 M solution?
4.2 M NaCl
0.326 mol HCl
220 g NaCl

20. Molality (m) = mol solute/mass of solvent(kg)
Problems – Molality (m)
Molality (m) = mol solute/mass of solvent(kg)
Calculate the molality if 37 g of NaCl are dissolved in 500 g of water.
How many moles of HCl are present in a 2.25 m HCl solution that contains 750. g of water?
How many grams of water are needed to make a 1.50 m NaCl solution with 78.0 grams of NaCl?
1.26 mol NaCl/kg water
1.69 mol HCl
889 g NaCl