The Mole: Avogadro’s number

How much is:

A dozen? 12 A century? 100 A mole? 6.02 x 1023

(602,000,000,000,000,000,000,000)

Can you count a mole of pennies?

If you could count 5 per second, it would take you

6.02 x 10 23 ÷ 5 pennies/second ÷ 60 sec/min ÷ 60 min/hr ÷ 24hrs/day ÷ 365 days/yr =

3,800,000,000,000,000 years!

Can you spend a mole of dollars?

If you could spend $1,000,000 every second it would take you

6.02 x 10 23 ÷ $1,000,000/sec ÷ 60 sec/min ÷ 60 min/hr ÷ 24hrs/day ÷ 365 days/yr =

19,000,000,000 years!

When measuring amounts, you can count or you can mass them.

If I want 2 dozen baseballs, I can count 24 baseballsOr I can mass 16 kg of baseballs.

How many tennis balls are in 6 kg?

( 2 dozen)

How many tennis balls are in a mole?

Since we can’t count a mole of atoms, we MUST mass chemicals to measure moles

6.02 x 10 23 atoms of sulfur32.07 grams of sulfur

6.02 x 10 23 atoms of carbon12.01 grams of carbon

How do we measure moles?

mole = number of particles equal to the number of atoms in 12 g of C-12 1 atom of C-12 weighs exactly 12 amu 1 mole of C-12 weighs exactly 12 g

The number of particles in 1 mole is called Avogadro’s Number = 6.0221421 x 1023 1 mole of C atoms weighs 12.01 g and has

6.022 x 1023 atoms the average mass of a C atom is 12.01 amu

How do we measure moles? The atomic mass on your periodic

table is the mass of a mole of atoms of that element.

What is the mass of a mole of copper atoms?

63.55 g So, to count 6.02 x 1023 copper

atoms, we mass out 63.55 g on the scale.

Mole and Mass Relationships

1 moleSulfur32.06 g

1 moleCarbon12.01 g

Find the mass of: A mole of silicon atoms 28.09 g 6.02 x 1023 atoms of nitrogen 14.01 g 6.02 x 1023 atoms of sodium 22.99g 2 moles of sodium atoms 45.98 g

How many atoms are in: A mole of silicon 6.02 x 1023 14.01 g of nitrogen 6.02 x 1023

2 moles of sodium 12.04 x 1023

45.98 g of sodium 12.04 x 1023

How many things are in: A mole of footballs 6.02 x 1023 footballs A mole of water 6.02 x 1023 molecules 2 moles of pencils 12.04 x 1023

½ mole of lead 3.01 x 1023 atoms

Molar mass is the mass of one mole of a substance

To find the molar mass of an element, look on the periodic table.

To find the molar mass of a compound, add all the masses of its elements

Chemical Formulas as Conversion Factors

1 spider 8 legs 1 chair 4 legs 1 H2O molecule 2 H atoms 1 O atom

Molar Mass of Compounds

• the relative weights of molecules can be calculated from atomic weights

Formula Mass = 1 molecule of H2O

= 2(1.0 amu H) + 16.0 amu O = 18.0 amu

• since 1 mole of H2O contains 2 moles of H and 1 mole of O

Molar Mass = 1 mole H2O

= 2(1.01 g H) + 16.00 g O = 18.02 g

Find the molar mass of: Ammonium phosphate NH4

+ PO43-

(NH4)3PO4

= = Carbon dioxide CO2 = =

Find the molar mass of: Hydrogen gas

H2

= Elemental hydrogen H =

Find the molar mass of: Iron

Fe = Iron (III) hydroxide Fe3+ OH-

Fe(OH)3 = =

Converting to and from moles.

To convert between moles and particles, simply multiply or divide by Avogadro’s number.

2.0 mol x (6.02 x 1023 particles/mol) = 1.2 x 1024 particles

3.1 x 1024 particles x (1 mol/ 6.02 x 1023 particles) = 5.0 mol

Remember unitfactors?

Converting to and from moles.

Converting between moles and mass requires the molar mass of the substance from the periodic table.

Element: Ag = 107.97g/mol Ionic compound: CaCl2 = 110.98 g/mol Covalent compound: NO2 = 46.01 g/mol Always keep at least two decimal places on

all values taken from the periodic table.

Converting to and from moles.

To convert from moles to grams, multiply by molar mass:

0.500 mol H2O x (18.02g/mol) = 9.01g H2O

To convert from grams to moles, divide by molar mass:

54g H2O x (1mol/18.02g) = 3.0 mol H2O

Converting to and from moles.

For gases, use the fact that at STP, 1 mol of any gas has a volume of 22.4 Liters.

What is STP? Standard Temperature and Pressure

Standard Temperature = 273K or 0.0°C Standard Pressure = 1 atmosphere = 760

mm Hg (barometric) = 101.325 kPa.

Converting to and from moles.

To go from moles to volume, multiply by 22.4L.

3.00 mol x (22.4L/mol) = 67.2L of gas

To go from volume to moles, divide by 22.4L

44.8L x (1mol/22.4L) = 2.00 moles of gas

Converting to and from moles.

A convenient tool for making these conversions is called a “mole map.”

With the mole at the center, we can put all of the aforementioned calculations together into one simple picture.

The Mole Map

Mole

Mass

Gas Volume @ STP

# Particles

x

x

x

22.4L6.02 x 10

23

Mol

ar

Mas

s

Percent Composition

Percentage of each element in a compound By mass

Can be determined from 1. the formula of the compound2. the experimental mass analysis of the compound3. the total mass of each element The percentages may not always total to 100%

due to rounding

What percentage of water is Oxygen?

1. Formula of the compound

2. Mass of the compound

3. Mass of each element

Mass Percent as a Conversion Factor

the mass percent tells you the mass of a constituent element in 100.0 g of the compound the fact that NaCl is 39.0% Na by mass

means that 100.0g of NaCl contains 39.0g Na

this can be used as a conversion factor 100.0 g NaCl 39.0 g Na

Empirical Formulas• The simplest, whole-number ratio of atoms in

a molecule is called the Empirical Formula– can be determined from percent composition or

combining masses

• The Molecular Formula is a multiple of the Empirical Formula

% A mass A (g) moles A100g MMA

% B mass B (g) moles B100g MMB

moles Amoles B

Empirical Formulas

Hydrogen PeroxideMolecular Formula = H2O2

Empirical Formula = HO

GlucoseMolecular Formula = C6H12O6

Empirical Formula = CH2O

BenzeneMolecular Formula = C6H6

Empirical Formula = CH

Finding an Empirical Formula1) convert the percentages to grams

a) skip if already grams

2) convert grams to molesa) use molar mass of each element

3) divide all by smallest number of moles4) round or multiply all mole ratios by

number to make all whole numbersa) if ratio ?.5, multiply all by 2; if ratio ?.33

or ?.67, multiply all by 3, etc. b) skip if already whole numbers

Determine the empirical formula of a compound containing 80.0 grams of carbon and 20.0 grams hydrogen.

Grams to moles

Divide by smallest

Write Empirical Formula

All these molecules have the same Empirical Formula. How are the molecules different?

Name MolecularFormula

EmpiricalFormula

MolarMass, g

glyceraldehyde

C3H6O3 CH2O 90.09

erythrose C4H8O4 CH2O 120.12

arabinose C5H10O5 CH2O 150.15

glucose C6H12O6 CH2O 180.18

Molecular Formulas

The molecular formula is a multiple of the empirical formula

To determine the molecular formula you need to know the empirical formula and the molar mass of the compound

Molar Massreal formula

Molar Massempirical formula

= factor used to multiply subscripts

What is the molecular formula for ethane if it has a molar mass of 30.06 g/mol?

Determine the Molecular Formula of Cadinene if it has a molar mass of 204 g and an empirical formula of C5H8

Determine the Molecular Formula of Cadinene if it has a molar mass of 204 g and an empirical formula of C5H8

Solutes and Solvents

Solution: a homogenous mixture Solute: thing that dissolves Solvent: thing that does the

dissolving (found in the largest amounts) If the solvent is water, then it is called

an aqueous solution

Solubility

Why does sugar “disappear” in your iced tea?

How do fish breathe underwater? Why does soda go flat faster when

left out than when it is refrigerated?

It is all based on solubility!

Solubility Example: iced tea

Solute sugar tea Solvent water

States and Solutions

Solutions can be any state of matter Solid-solid: alloys (gold jewelry, brass,

etc.) Solid-liquid: salt water, sugar water Liquid-liquid: vinegar, peroxide,

rubbing alcohol Liquid-gas: soda, champagne, O2 in

H2O Gas-gas: air, air tanks (scuba)

How Things Dissolve

Need to find/ create “holes” in water for the dissolving substance to move into Need to over come hydrogen bonding

between water (or solvent) molecules Get interactions between water

molecules and molecules of the solute Ion-dipole interactions Dipole-dipole (and H bonding)

Why some coffees “Put hair on your chest.”

“Strong” coffee has more coffee dissolved in a given amount (say 1 pot) than “weak” coffee.

Strong coffee = concentrated

Weak coffee = dilute Concentration: the

amount of solute in a given amount of solvent (or solution).

Molarity (M)

Most common way to express concentration Molarity is the number of moles of solute

dissolved in each liter of solution Formula

M = moles of solute

liters of solution Dependent on temperature The higher the molarity the stronger the

concentration

Practice Problems1. What is the molarity when 6.0

moles of glucose is dissolved in water to make 3.0 L of solution.

2. How many moles of sodium chloride are there in 500 mL of 4.0 M solution?

3. What is the volume of 3.0 M solution that contains 15 moles of glucose?

How does something so strong become so weak?

The answer is dilution. The more dilute something is, the lower

the concentration (it’s weaker). To accomplish this, add more solvent How do we know how much to add?

M 1V1 = M 2V2 Typically start with a highly concentrated

solution and dilute down to what you need

Figure 15.8: Process of making 500 mL of a 1.00 M acetic acid solution.

Mole Day is October 23!