MEASURING MASS

A mole is a quantity of things, just as…

1 dozen = 12 things1 gross = 144 things1 mole = 6.02 x 1023

things “Things” usually measured in moles

are atoms, molecules, ions, and formula units

2

You can measure mass, or volume, or you can count pieces

We measure mass in grams

We measure volume in liters

We count pieces in MOLES

3

A MOLE… is an amount, defined as the

number of carbon atoms in exactly 12 grams of carbon-12

1 mole = 6.02 x 1023 of the representative particles

Treat it like a very large dozen 6.02 x 1023 is called:

Avogadro’s number

4

Similar Words for an amount: Pair: 1 pair of shoelaces = 2 shoelaces

Dozen: 1 dozen oranges = 12 oranges

Gross: 1 gross of pencils= 144 pencils

Ream: 1 ream of paper= 500 sheets of paper

5

What are Representative Particles (“RP”)?

The smallest pieces of a substance:1. For a molecular compound: it is

the molecule.2. For an ionic compound: it is the

formula unit (made of ions)3. For an element: it is the atom

Remember the 7 diatomic elements? (made of molecules)

6

Practice Counting Particles How many oxygen atoms in the following?1. CaCO3 3 atoms of oxygen2. Al2(SO4)3 12 (4 x 3) atoms of oxygen

How many ions in the following?1. CaCl2

3 total ions (1 Ca2+ ion and 2 Cl1- ions)2. NaOH

2 total ions (1 Na1+ ion and 1 OH1- ion)3. Al2(SO4)3

5 total ions (2 Al3+ + 3 SO4 ions)

7

CONVERSION FACTOR

RPs x ____1 mole___ = MOLES

6.02 x 1023 RPs

8

EXAMPLES: ATOMS MOLES

How many moles of B are in 3.15 x 1023 atoms of B? Conversion: 1 mole B = 6.02

x 1023 atoms B(b/c the atom is the RP of

boron)

1 mole B

3.15 x 1023 atoms of B

6.02 x 1023 atoms B

= 0.523 mole

9

EXAMPLES: MOLES ATOMS

How many atoms of Al are in 1.5 mol of Al? Conversion: 1 mole = 6.02 x 1023

atoms

1.5 mol of Al6.02 x 1023 atoms Al

1 mole Al

= 9.03 x 1023 atoms of Al

10

CAUTION: Identify RPs Carefully!

See next slide!

11

EXAMPLES: MOLECULES MOLESHow many atoms of H are there in 3 moles of H2O? (HINT: Are atoms the RP for water?)Conversions:1 mole = 6.02 x 1023 molecules

(b/c molecules are the RP for H2O)

3 moles of H2O 6.02 x 1023 molec H2O

1 mole H2O

2 atoms H

1 H2O molecule

= 3.612 x 1024 atoms H

H2O molecule = 2 atoms of Hydrogen

12

MOLAR MASSDef: The mass of a mole of representative particles of a substance.

Each element & compound has a molar mass.

13

MOLAR MASS OF AN ELEMENTDetermined simply by looking at the periodic table

Molar mass (g) = Atomic Mass (amu)

Ca20

40.08

* Thus, 1 mol Ca = 40 g

1 atom of Ca weighs 40.08 amu1 mole of Ca atoms weighs 40.08 grams

14

MOLAR MASS FOR COMPOUNDS

To calculate the molar mass of a compound, find the number of grams of each element in one mole of the compound

Then add the masses within the compound

Example: H2O

H= 1.01 2 (1.01) + 1 (15.999)= 18.02 g/mol

O= 15.99915

SOME PRACTICE PROBLEMS How many atoms of O are in 3.7 mol of

O? 2.2 X 1024 atoms of oxygen

How many atoms of P are in 2.3 mol of P? 1.4 x 1024 atoms of phosphorus

How many atoms of Ca are there in 2.5 moles of CaCl2? 1.5 x 1024 atoms Ca

How many atoms of O are there in 1.7 moles of SO4? 4.1 x 1024 atoms of oxygen

16

Remember!!!! The molar mass of any substance (in

grams) equals 1 mole This applies to ALL substance: elements,

molecular compounds, ionic compounds Use molar mass to convert between mass

and moles Ex: Mass, in grams, of 6 mol of MgCl2 ?

mass of MgCl2 = 6 mol MgCl2 92.21 g MgCl2 1 mol

MgCl2

= 571.26 g MgCl2

17

VOLUME AND THE MOLE

Volume varies with changes in temperature & pressure

Gases are predictable, under the same physical conditions

Avogadro’s hypothesis helps explain:equal volume of gases, at the same temp and pressure contains equal number of particles

Ex: helium balloon

18

MOLAR VOLUME Gases vary at different

temperatures, makes it hard to measure

To make it easier to measure gases, we use something called “STP” “Standard Temperature and Pressure” Temperature = 0° C Pressure = 1 atm (atmosphere)

19

Molar Volume

At STP:1 mole, 6.02 x 1023 atoms, of any gas has a volume of 22.4 L

1 mole gas = 22.4 L gas

Use it to convert between # of moles and vol of a gas @ STP Ex: what is the volume of 1.25 mol of sulfur

gas?

1.25 mol S 22.4 L S = 28.0 L

1 mol S 20

MOLAR MASS FROM DENSITY Different gases have different densities Density of a gas measured in g/L @ a specific

temperature Can use the following formula to solve :

grams = grams X 22.4 Lmole L 1 mole Ex: Density of gaseous compound containing

oxygen and carbon is 1.964 g/ L, what is the molar mass?

grams = 1.964 g X 22.4 L then you solve

mole 1 L 1 mole = 44.o g/mol

21

Atoms, molecules, etc. 22

Molarity

Def: the concentration of a solution. How many moles/liter

Can be used to calculate # of moles of a solute

Ex: Household laundry bleach is a dilute aqueous solution of sodium hypochlorite (NaClO). How many moles of solute are present in 1.5 L of 0.70 M NaClO?

23

Calculating Percent Composition of a Compound Like all percent problems: a part ÷ the

whole1. Find the mass of each of the components

(the elements)2. Next, divide by the total mass of the

compound3. Then X 100 % = percent

Formula:% Composition = Mass of element X 100%

Mass of compound

24

Method #1: % Comp When Actual Masses are Given

A compound is formed when 9.03 g of Mg combines completely with 3.48 g of N.

What is the percent composition of the compound?1. First add the 2 mass of the 2 compounds to

reach the total mass 9.03 g Mg + 3.48 g N = 12.51 g Mg3N2

2. Find the % of each compound

% Mg= 9.03 g Mg X 100 = 72.2 % 12.51 g Mg3N2

% N= 3.48 g N X 100 = 27.8 % 12.51 g Mg3N2

25

Method 2: % Comp When Only The Formula is Known Can find the percent composition of a

compound using just the molar mass of the compound and the element

% mass=mass of the element 1 mol cmpd X100%

molar mass of the compound Example:

Find the percent of C in CO2

12.01 g C X 100 = 27.30% C

44.01 g CO2 26

Using % Composition Can use % composition as a conversion factor

just like the mole After finding the % comp. of each element in

a cmpd. can assume the total compound = 100g

Example: C= 27.3% 27.3 g C O= 72.7 % 72.7 g O

In 100 g sample of compound there is 27.3 g of C & 72.7 g of O

How much C would be contained in 73 g of CO2?

73 g CO2 27.3 g C = 19.93 g C

100 g CO2

27

EMPIRICAL FORMULAS Empirical formulas are the

lowest WHOLE number ratios of elements contained in a compound

28

REMEMBER… Molecular formulas tells the actual

number of of each kind of atom present in a molecule of the compound

Ex:H2O2 HOMolecular Empirical Formula Formula

CO2 CO2

Molecular Empirical For CO2 they are the same

Formula Formula

29

Formulas for ionic compounds are ALWAYS empirical (the lowest whole number ratio = can not be reduced)

Examples: NaCl MgCl2 Al2(SO4)3 K2CO3

Simplest whole number ratio for NaCl

30

A formula is not just the ratio of atoms, it is also the ratio of moles

In 1 mole of CO2 there is 1 mole of carbon and 2 moles of oxygen

In one molecule of CO2 there is 1 atom of C and 2 atoms of O

Formulas for molecular compounds MIGHT be empirical (lowest whole number ratio)

Molecular: H2O C6H12O6 C12H22O11

(Correct formula)

Empirical:

(Lowest whole H2O CH2O C12H22O11

number ratio)

31

STOP HERE!!!

32

CALCULATING EMPIRICAL We can get a ratio from the percent

composition 1.Assume you have a 100 g sample the

percentage become grams (75.1% = 75.1 grams)

2.Convert grams to moles3.Find lowest whole number ratio by

dividing each number of moles by the smallest value

33

Example calculations Calculate the empirical formula of a

compound composed of 38.67 % C, 16.22 % H, and 45.11 %N

Assume 100 g sample, so 38.67 g C x 1 mol C =

12.0 g C 16.22 g H x 1 mol H =

1.0 g H 45.11 g N x 1 mol N =

14.0 g N *Now divide each value by the smallest value

3.22 mole C

3.22 mole N

16.22 mole H

34

…Example 1

The ratio is 3.22 mol C = 1 mol C 3.22 mol N 1

mol N The ratio is 16.22 mol H = 5 mol H

3.22 mol N 1 mol N

C1H5N1 which is = CH5N

35

MORE PRACTICE

A compound is 43.64 % P and 56.36 % O

What is the empirical formula? PO3

Caffeine is 49.48% C, 5.15% H, 28.87% N and 16.49% O

What is its empirical formula?

C4H5N2O

36

EMPIRICAL TO MOLECULAR

Since the empirical formula is the lowest ratio, the actual molecule would weigh more

Divide the actual molar mass by the empirical formula mass – you get a whole number to increase each coefficient in the empirical formula

37

EXAMPLE Caffeine has a molar mass of 194 g, what

is its molecular formula?1.Find the mass of the empirical formula,

C4H5N2O

2.Divide the molar mass by the empirical mass:194.0 g/mol =97.1 g/mol

3.Now multiply the entire empirical formula by 2

2(C4H5N2O) =

final molecular formula

2

C8H10N4O2

38