The Mole: Avogadro’s number

How much is:n A dozen?n 12n A century?n 100n A mole?n 6.02 x 1023

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

Can you count a mole of pennies?n If you could count 5 per second, it

would take you n 6.02 x 10 23 ÷ 5 pennies/second ÷ 60

sec/min ÷ 60 min/hr ÷ 24hrs/day ÷365 days/yr =

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

Can you spend a mole of dollars?n If you could spend $1,000,000 every

second it would take youn 6.02 x 10 23 ÷ $1,000,000/sec ÷ 60

sec/min ÷ 60 min/hr ÷ 24hrs/day ÷365 days/yr =

n 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?n mole = number of particles equal to the

number of atoms in 12 g of C-12 n 1 atom of C-12 weighs exactly 12 amun 1 mole of C-12 weighs exactly 12 g

n The number of particles in 1 mole is called Avogadro’s Number = 6.0221421 x 1023

n 1 mole of C atoms weighs 12.01 g and has 6.022 x 1023 atoms

n the average mass of a C atom is 12.01 amu

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

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

n What is the mass of a mole of copper atoms?

n 63.55 gn 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

Substance 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

Find the mass of:n A mole of silicon atomsn 28.09 gn 6.02 x 1023 atoms of nitrogenn 14.01 gn 6.02 x 1023 atoms of sodiumn 22.99gn 2 moles of sodium atomsn 45.98 g

How many atoms are in:n A mole of siliconn 6.02 x 1023

n 14.01 g of nitrogenn 6.02 x 1023

n 2 moles of sodiumn 12.04 x 1023

n 45.98 g of sodium n 12.04 x 1023

How many things are in:n A mole of footballsn 6.02 x 1023 footballsn A mole of watern 6.02 x 1023 moleculesn 2 moles of pencilsn 12.04 x 1023

n ½ mole of leadn 3.01 x 1023 atoms

Molar mass is the mass of one mole of a substancen To find the molar mass of an element,

look on the periodic table.n To find the molar mass of a compound,

add all the masses of its elements

Chemical Formulas as Conversion Factors

n 1 spider º 8 legsn 1 chair º 4 legsn 1 H2O molecule º 2 H atoms º 1 O

atom

Molar Mass of Compounds• the relative weights of molecules can be

calculated from atomic weightsFormula 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 OMolar Mass = 1 mole H2O

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

Find the molar mass of:n Ammonium phosphaten NH4

+ PO43-

n (NH4)3PO4n =42.03 +12.12 +30.97 +64.00n =149.12g/moln Carbon dioxiden CO2n = 12.01 + 32.00 n = 44.01 g/mol

Find the molar mass of:n Hydrogen gas

n H2n = 2.02 g/mol

n Elemental hydrogenn Hn = 1.01 g/mol

Find the molar mass of:n Iron

n Fe n = 55.85 g/mol

n Iron (III) hydroxiden Fe3+ OH-

n Fe(OH)3n = 55.85 + 48.00 + 3.03 n =106.88 g/mol

Converting to and from moles.n Converting between moles and mass

requires the molar mass of the substance from the periodic table.

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

all values taken from the periodic table.

Converting to and from moles.n To convert from moles to grams, multiply by

molar mass:n 0.500 mol H2O x (18.02g/mol) = 9.01g H2O

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

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

Converting to and from moles.n To convert between moles and

particles, simply multiply or divide by Avogadro’s number.

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

particles

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

Remember unitfactors?

Converting to and from moles.n For gases, use the fact that at STP, 1 mol

of any gas has a volume of 22.4 Liters.n What is STP? Standard Temperature and

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

mm Hg (barometric) = 101.325 kPa.

Converting to and from moles.n To go from moles to volume, multiply

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

n To go from volume to moles, divide by 22.4L

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

Converting to and from moles.n A convenient tool for making these

conversions is called a “mole map.”

n 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÷

÷

÷

Mol

ar

Mas

s

Percent Compositionn Percentage of each element in a compound

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

rounding

€

Percentage=partwhole

×100%

What percentage of water is Oxygen?1. Formula of the compound

* H2O2. Mass of the compound

* 2 (1.01 g/mol) + 16.00 g/mol = 18.02 g/mol

3. Mass of each element* H is 1.01 g/mol, O is 16.00 g/mol

O 88.79% 100% H2O g 18.02

O g 16.00=×

Mass Percent as a Conversion Factor

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

means that 100.0g of NaCl contains 39.0g Nan this can be used as a conversion factor

n 100.0 g NaCl º 39.0 g Na

Na g NaCl g 100.0Na g 39.0 NaCl g =× NaCl g

Na g 39.0NaCl g 100.0 Na g =×

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 A

100g MMA

% B mass B (g) moles B100g MMB

moles Amoles B

Empirical Formulas

Hydrogen PeroxideMolecular Formula = H2O2Empirical Formula = HO

GlucoseMolecular Formula = C6H12O6Empirical Formula = CH2O

BenzeneMolecular Formula = C6H6Empirical Formula = CH

Finding an Empirical Formula1) convert the percentages to grams

a) skip if already grams2) convert grams to moles

a) use molar mass of each element3) 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

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

Grams to molesC mol 6.67

C g 12.01C mol 1

C 80.0g =×

H mol 19.8 H g 1.01H mol 1 H 20.0g =×

Divide by smallest

1.00 mol 6.67

mol 6.67 C ==

3.00 2.96 mol 6.67

mol 19.8 H ≈==

Write Empirical Formula

CH3

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

Name MolecularFormula

EmpiricalFormula

glyceraldehyde C3H6O3 CH2O

erythrose C4H8O4 CH2O

arabinose C5H10O5 CH2O

glucose C6H12O6 CH2O

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

FormulaEmpiricalFormula

MolarMass, g

glyceraldehyde C3H6O3 CH2O 90.09

erythrose C4H8O4 CH2O 120.12

arabinose C5H10O5 CH2O 150.15

glucose C6H12O6 CH2O 180.18

Molecular Formulasn The molecular formula is a multiple of

the empirical formulan To determine the molecular formula you

need to know the empirical formula and the molar mass of the compound

Molar Massreal formulaMolar 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?

CH3= 15.04 g/mol

Molecular formula = 2 x the empirical formulaC2H6

2.0001.99867 g/mol 15.04

g/mol 30.06 ratio ===

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

Solutes and Solventsn Solution: a homogenous mixturen Solute: thing that dissolvesn Solvent: thing that does the dissolving

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

aqueous solution

Solubilityn Why does sugar “disappear” in your

iced tea?n How do fish breathe underwater?n Why does soda go flat faster when left

out than when it is refrigerated?

n It is all based on solubility!

Solubilityn Example: iced tea

n Solutesugar tea

n Solventwater

States and Solutionsn Solutions can be any state of matter

n Solid-solid: alloys (gold jewelry, brass, etc.)n Solid-liquid: salt water, sugar watern Liquid-liquid: vinegar, peroxide, rubbing

alcoholn Liquid-gas: soda, champagne, O2 in H2On Gas-gas: air, air tanks (scuba)

How Things Dissolven Need to find/ create “holes” in water

for the dissolving substance to move inton Need to over come hydrogen bonding

between water (or solvent) molecules n Get interactions between water

molecules and molecules of the soluten Ion-dipole interactionsn Dipole-dipole (and H bonding)

Why some coffees “Put hair on your chest.”

n “Strong” coffee has more coffee dissolved in a given amount (say 1 pot) than “weak” coffee.n Strong coffee = concentratedn Weak coffee = dilute

n Concentration: the amount of solute in a given amount of solvent (or solution).

Molarity (M)n Most common way to express concentration n Molarity is the number of moles of solute

dissolved in each liter of solutionn Formula

n M = moles of soluteliters of solution

n Dependent on temperaturen 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.

0.5 L NaCl( )

4.0 moles1 L

! " # $

% & = 2 moles NaCl

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

M =

6.0 moles3.0 L

= 2.0 M

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

15 moles( )

1 L3.0 moles! " # $

% & = 5.0 L

How does something so strong become so weak?

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

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

nM 1V1 = M 2V2 n 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!