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 atom3. 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 55.8 = 111.6

S: 3 x 32.1 = 96.3

O: 12 x 16.0 = 192.0

399.9 amu

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)

18.0 g/mol

mole

2. Mole = amount of substance that contains 6.02 x 1023 particles

abbreviated: molmol3. Avogadro’s Number = number of particles in a mole

= 6.02 x 1023 particlesParticles 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

Getting to know the terms…

MICROSCOPIMICROSCOPICC

Mass MACROSCOPICMACROSCOPICMolar Mass

Atom Atomic mass

amu Element g/mol

Molecule Molecular mass

amu Molecular

Compound g/mol

Formula UnitFormula mass

amu Ionic

Compound g/mol

Diatomic Molecules HOFBrINCl

H2 O2 F2 Br2 I2 N2 Cl2

MOLE RELATIONSHIPS1 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 ConversionsMUST use factor label!

A. Moles & Mass1. 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 & Particles1. How many atoms in 3.0 moles of copper?

know: 1 mole Cu =

2. How many atoms in 3.00 moles of water?know: 1 mole H2O =

know: 1 molecule H2O =

18.0 g H2O

63.5 g Cu

54 g H2O

0.945 g Cu

6.02 x 1023 atoms of copper

6.02 x 1023 molecules of H2O

1.8 x 1024 atoms Cu

3 atoms

5.42 x 1024 atoms

II. Mole ConversionsMUST use factor label!

C. Mass & Particles1. How many atoms in 100.0 g of copper?

know: 1 mole = _________ g copper1 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

63.5atoms

atoms

molecules

342.0

9.480 x 1023 atoms Cu

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.

molar mass

volume

4 He 222 Rn

constant

1 mole gas = 22.4 L = 6.02 x 1023 particles at STP (273 K & 1 atm)

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.

He RnO2

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 LawAlthough 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 molesR = 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.

PV = nRT

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 Formulas1. 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. Examplesa. 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.

b. Determine the empirical formula for an iron oxide that is 70.0% iron. Name the compound.

CaCl2

Fe2O3 iron(III) oxide

C. Molecular Formula1. 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:

D. 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

ExampleFind 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 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 solutionLarge amount of solute in 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

Transfer ________ grams of NaCl to a 500-mL volumetric flask, and add water to the line.

*Note: Always add acid to water.

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Problems – Molarity (mol/L)Molarity = mol solute/L solution1. Calculate the molarity if 37 g of NaCl are dissolved in 150

mL of solution.

2. How many moles of HCl are present in 145 mL of a 2.25 M HCl solution?

3. 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

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.

2. How many moles of HCl are present in a 2.25 m HCl solution that contains 750. g of water?

3. 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