The Mole: Avogadro’s number

How much is:

• A dozen?

• A century?

• A mole?

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 =

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 =

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

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

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 1 mole of C-12 weighs exactly

The number of particles in 1 mole is called ____________ Number = 6.0221421 x 1023 1 mole of C atoms weighs and has

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?

• So, to count 6.02 x 1023 copper atoms, we mass out on the scale.

Mole and Mass RelationshipsSubstance Pieces in 1 mole Weight of 1 mole hydrogen 6.022 x 1023 atoms 1.008 g

carbon 6.022 x 1023 atoms 12.01 g

oxygen 6.022 x 1023 atoms 16.00 g

sulfur 6.022 x 1023 atoms 32.06 g

calcium 6.022 x 1023 atoms 40.08 g

chlorine 6.022 x 1023 atoms 35.45 g

copper 6.022 x 1023 atoms 63.55 g

1 moleSulfur32.06 g

1 moleCarbon12.01 g

Find the mass of:

• A mole of silicon atoms

• 6.02 x 1023 atoms of nitrogen

• 6.02 x 1023 atoms of sodium

• 2 moles of sodium atoms

How many atoms are in:

• A mole of silicon

• 14.01 g of nitrogen

• 2 moles of sodium

• 45.98 g of sodium

How many things are in:

• A mole of footballs

• A mole of water

• 2 moles of pencils

• ½ mole of lead

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 legs• 1 chair legs• 1 H2O molecule H atoms & O atom

Molar Mass of Compounds

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

Formula Mass = 1 molecule of H2O

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

Molar Mass = 1 mole H2O

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 mol x (6.02 x 1023 particles/mol) = 1.20 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 = g/mol• Ionic compound: CaCl2 = g/mol

• Covalent compound: NO2 = g/mol

• Always keep at least two decimal place 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 (18.0g/mol) = 9.00g H2O• To convert from grams to moles, divide by

molar mass:54g H2O x (1mol/18.0g) =

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 Liters.

• What is STP?

• Standard Temperature = K or °C• Standard Pressure = atmosphere =

– mm Hg (barometric) = kPa.

Converting to and from moles.

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

• 3.00 mol x (22.4L/mol) = of gas

• To go from volume to moles, divide by 22.4L• 44.8L x (1mol/22.4L) = 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

Percent Composition• Percentage of each element in a compound

– By mass• Can be determined from 1. the of the compound2. the experimental mass analysis of the compound3. the total mass of • The percentages may not always total to 100% due to

100%wholepart

Percentage

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 g of the compound– the fact that NaCl is 39% Na by mass means that

100 g of NaCl contains 39 g Na

• this can be used as a conversion factor– 100. g NaCl 39.0 g Na

Na g NaCl g 100

Na g 39 NaCl g NaCl g

Na g 39

NaCl g 100 Na g

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

molecule is called the

– 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 = Empirical Formula =

BenzeneMolecular Formula =Empirical Formula =

Finding an Empirical Formula1) convert the

a) skip if already grams2) convert

a) use molar mass of each element3) divide all by4) 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

Example:• A laboratory analysis of aspirin determined the following

mass percent composition. Find the empirical formula.C = 60.00%H = 4.48%

O = 35.53%

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

Name Molecular

Formula

EmpiricalFormula

glyceraldehyde

C3H6O3 CH2O

erythrose C4H8O4 CH2O

arabinose C5H10O5 CH2O

glucose C6H12O6 CH2O

Molecular Formulas

• The molecular formula is a multiple of

• To determine the molecular formula you need to know and the of the compound

What is the molecular formula for ethane if it has a molar mass of 30.0 g/mol?

ratio

CH3= g/mol

Molecular formula =

Determine the Molecular Formula of Cadinene if it has a molar mass of

204 g and an empirical formula of C5H8

Solutions

Ask a chemist, they always have

Solutes and Solvents

• Solution:

• Solute:

• Solvent: – (usually found in the largest amounts)– If the solvent is water, then it is called an

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

– Solvent

States and Solutions

• Solutions can be any state of matter– Solid-solid:

– Solid-liquid: – Liquid-liquid:

– Liquid-gas:

– Gas-gas:

How Things Dissolve

• Need to find/ create “__________” in water for the dissolving substance to move

• Get _______________ between water molecules and molecules of the solute

Why some coffee is so strong it can “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:

Molarity (M)• Most common way to express concentration • Molarity is the number of ____________ of solute

dissolved in each __________of solution• Formula

M = moles of solute

liters of solution

• Dependent on _______________• 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.

End of Chapter