The Mole

Chemistry 6.0

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 UnitFormula mass

amu Ionic

Compound g/mol

The following elements exist in nature as molecules:

H2 O2 F2 Br2 I2 N2 Cl2 S8 P4

MOLE RELATIONSHIPS

1 Mole = 6.02x1023 particles of substance

(atoms, formula units, molecules)

1 Mole = mass (g) of substance from PTAlso remember your formula information:

1 molecule = _________ atoms

1 formula unit = _________ ions or _________ atoms

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

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

Mole ConversionsMUST use factor label!

63.5atoms

atoms

molecules

342.0

9.480 x 1023 atoms Cu

1.45 x 1024 atoms

Molar Volume of Gases at STP

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

Avogadro’s Law

V1 = V2

n1 n2

n ____ P ____ (more gas, ____________)more collisions

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 L2. Calculate the pressure, in atm,

exerted by 54.0 g of xenon in a 1.00-L flask at 20.oC.9.9 atm

3. Calculate the density of nitrogen dioxide, in g/L, at 1.24 atm and 50.oC.

2.16 g/L

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 78% iron. Name the compound.

CaCl2

FeO iron(II) 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• Percent concentration by mass

– (solute/solution) x 100% = % Concentration

• Molarity (M)–Moles of solute/Liters of solution

= mol/L

• Molality (m)–Moles of solute/mass of solvent =

mol/kg

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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Problems1. 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

Example Problems1. Calculate the molarity of a solution

that contains 8.50 g of calcium nitrate in 2.0 L.

2. Calculate the molality of a solution that contains 8.50 g of calcium nitrate in 125 g H2O.