Download The Mole

Unit 10 – The Mole
The mole
Measuring Matter
What do you ask for when you buy:
2 shoes
1 pair
12 eggs
1 dozen
48 doughnuts
4 dozen
500 sheets of paper
1 ream
Pair, Dozen, Ream
These are all ways to batch a
group of objects to make them
easier to count!
The object may change
Eggs to Doughnuts
But the number they represent
is always constant!
What do eggs have to do with
Chemistry?
How many carbon atoms are in a teaspoon
of carbon?
200,666,666,666,666,666,666,667 atoms!!!
Can you even pronounce this?
200,666,666,666,666,666,666,667
atoms!!!
It would be nice if chemists
had a batch like a dozen (but
muuuucchh bigger) to
handle this kind of number!
Meet the Mole!
S/He is the Chemist’s “dozen”!
What is a mole?
The chemist’s “dozen” is called the:
MOLE (or the unit mol)
1 dozen atoms = 12 atoms
1 mole atoms = 602213670000000000000000 atoms
Or
1 mole = 6.02  1023
How many moles are in 1 teaspoon of carbon atoms?
.33 moles
Measuring Matter – Moles and
Avogadro’s number
• Mole (mol) – the amount of a substance that
contains the same number of particles as the
number of atoms in 12 g of carbon-12. Like
doughnuts are counted in dozens, the mole is a
SI unit for counting the amount of a substance.
– 1 dozen pencils have the same number of particles as
1 dozen doughnuts
– 1 mole of carbon atoms have the same number of
particles as 1 mole of water molecules
This does not mean they both weigh the same,
only that they have the same number of units
or particles.
Measuring Matter – Moles and
Avogadro’s number
• Avogadro’s Number – the number of
particles (6.02  1023) in exactly one mole
of a pure substance.
– 1 mole pencils = 6.02  1023 pencils
– 1 mole water molecules = 6.02  1023
molecules of water
1 mole of
Guaca-”mole”
Measuring Matter – Moles and
Avogadro’s number
If Avogadro’s number is the number of particles in 1 mole,
how do you know what kind of particle you have?
Remember…
Particles can be an atom, molecule, or formula
unit?
What kind of particle?
Particles can be an atom, molecule, or
formula unit?
• Atom – one atom
• Molecule – more than one nonmetal atom
• Formula unit - compound with a metal or
NH4+
Measuring Matter – Moles and
Avogadro’s number
How do you know what kind of particle you
have?
Examples
1. NaCl formula unit (form.unit)
molecule
2. H2O
molecule
3. H2
atom
4. Na
Measuring Matter – Moles and
Avogadro’s number
Avogadro’s number is really an equality!
1 mole C = 6.021023 atoms C
What can you use equalities to do?
Equalities are conversion factors in
Dimensional Analysis problems!
Measuring Matter – Moles and
Avogadro’s number
How many atoms are in 3.2 mol of C?
3.2 mol C
6.021023 atoms C
1 mol C
=
1.91024
atoms C
Measuring Matter – Moles and
Avogadro’s number
How many moles of water molecules are in
3.7  1021 molecules of H2O?
3.7  1021 molecules H2O
1
mol H2O
6.021023 Molecules H2O
= .0061 mol H2O
Mass and the Mole
•
Molar mass – the mass, in grams, of one
mole of a substance.
How do you find this mass?
The atomic mass printed on the periodic
table has two meanings!
1. It is the average mass of one atom in
atomic mass units (u).
2. It is also the mass of one mole of atoms
of a given element in grams.
Mass and the Mole
• Finding molar mass
– Atoms – the mass of 1 mole of any atom is
the same as the atomic mass in grams.
(Round your masses to the tenths)
1mole H atoms = 1.008 g  1.0 g
1mole C = 12.011 g 12.0 g
1mol Cu = 63.546 g  63.5 g
Mass and the Mole
• Molar mass continued
– Compounds – the mass of 1 mole of a
compound is the sum of the masses of the
atoms.
1mole H2O = 18.0g
2 H = 2(1.0g) = 2.0g
1 O = 16.0g
2.0g + 16.0g = 18.0g
As a molar mass, it would be expressed as 18.0 g/mol
Mass and the Mole
Molar mass is really an equality!
For water:
1mole H2O = 18.0 g
What can you use equalities to do?
Equalities are conversion factors in
Dimensional Analysis problems!
Mass and the Mole
How many moles are in 242 g of water?
242 g H2O
1 mol H2O
18.0 g H2O
= 13.4
mol H2O
Mass and the Mole
What is the mass of 3.77 mol of gold?
3.77 mol Au
197.0 g Au
1 mol Au
= 743
g Au
The Last Conversion Factor!
What do you do if you are
asked to find atoms (or
ions) and your
representative particle is
NOT an atom (or ion)?
The Formula Conversion Factor
Think about what a formula really tells you!
1 molecule of H2O
Doesn’t this mean:
1 molecule H2O = 2 hydrogen atoms
The formula is a conversion factor between
atoms (or ions) and compounds!
The Formula Conversion Factor
How many hydrogen atoms are in
6.51014 molecules of water?
6.51014 molecules H2O
2
atoms H
= 1.31015 atoms H
1 molecules H2O
Typically, this type of conversion factor
is usually a final step in a multi-step
problem!
The Formula Conversion Factor
How many ammonium ions are in
6.51014 formula units of (NH4)2CO3?
6.51014 form. unit (NH4)2CO3
2 ions NH4
1
form. unit (NH4)2CO3
= 1.31015 ions NH4
Conversion Review
Mass
Formula
Particles
Atoms
or ions
Moles
Multi-step Problems
How many water molecules are in 242 g of water?
242 g H2O
1
mol H2O
18.0 g H2O
6.021023 molecule H2O
= 8.09  1024 molecules H2O
1 mol H2O
Remember, if the question asked for hydrogen
atoms, you would have to do a 3rd step!
Percent Composition
How would you calculate the percent
females in this room?
# females
 100
# people
All percents are calculated in the same way!
part
 100
whole
Percent Composition
• Percent Composition – the percent by
mass of each element in a compound.
mass element
 100
mass compound
molar mass
Percent Composition
What is the percent composition of
each element in water?
Mass H = 2(1.0 g) = 2.0 g
+
16.0 g
Mass O =
mass H
%H
 100
mass H 2O
2.0 g

 100
18.0 g
% H = 11%
18.0 g
mass O
%O
 100
mass H 2O
16.0 g

 100
18.0 g
% O = 88.9%
Using Percent Composition
If a glass of water contains 648 g of
water, how many grams of hydrogen
would it hold?
Remember, water is 11% hydrogen
What is 11% of 648 g?
(648 g)  (.11)  71.28 g
71 g
C H N O
8 10 4
2
Empirical Formula
What does H2O mean?
Does it mean 2 atoms of H for every atom of O?
YES
Does it mean 2 g of H for every 1 g of O?
NEVER
Empirical Formula
What does H2O mean?
Does it mean 2 moles of H for every mole of O?
Always!
Formulas are not only ratios of atoms, they are
also ratios of MOLES
Formulas are ratios of moles!
Formulas are ratios of moles!
Formulas are ratios of moles!
Empirical Formula
• Empirical Formula – simplest whole
number ratio of moles of the atoms in a
substance. Experimental method that is
the first step in finding the formula of a
compound.
Circle the empirical formulas!
H2O
H2SO4
NaCl
C2H6
C6H12O6
NO2
N 2O 4
Empirical Formula
Finding the empirical formula
1. Find the mass of each element in the
compound.
–
–
Usually given
If given as %, then change % to g.
36% H and 64% C  36 g H and 64 g C
2. Convert masses to moles.
–
Use molar masses. (Don’t worry about significant digits in this step!)
36 g H 1 mol H =
1.0 g H
36 mol H
Empirical Formula
3. Find the smallest whole number ratio of
moles.
a. Write the results of step 2 like a formula.
If C = 1.2 mol and H = 4.8 mol
C1.2H4.8
b. Divide by the smallest mole amount.
C1.2H4.8
1.2
CH4
1.2
c. If not all whole numbers, multiply by 2,3, or 4 …
Empirical Formula
Examples for step 3
X = .029 mol
Y = .039 mol
X = .009 mol
Y = .006 mol
X.029Y.039
.029
.029
X.009Y.006
.006
.006
X1Y1.34
X1.5Y1
Multiply by 3
Multiply by 2
X3Y4
X3Y2
Empirical Formula
More Examples for step 3
X = 2.4  10-4 mol
Y = 7.3  10-4 mol
X = 1.47 mol
Y = 3.68 mol
X1.47Y3.68
1.47
1.47
X1Y2.5
Multiply by 2
X2Y5
X
2.410
-4
2.410-4
Y
7.310  4
2.410-4
X1Y3.04
X1Y3
Empirical Formula - Example
1.
2.
A sample of an unknown gas contains 43.2 g of
carbon and 115.8 g of oxygen. What is the empirical
formula?
Find Masses
43.2 g C
115.8 g O
Change to moles
43.2 g C
1 mol C
= 3.60 mol C
12.0 g C
115.8 g O
1 mol O
16.0 g O
= 7.24 mol O
Empirical Formula - Example
3.
Get whole numbers
C3.60O7.24
3.60
3.60
C1O2.01
CO2
Molecular Formula
• Molecular formula - is some whole number
multiple of the empirical formula.
–
–
–
–
HO is an empirical formula
H2O2 is twice HO
(HO)X and X = 2
For C6H12O6, the empirical formula is CH2O and X=6
• To convert an empirical formula to a molecular
formula you must find X.
molar mass
X
empirical mass
Molecular Formula - Example
An unknown gas is found to have an
empirical formula of NO2 and a molar mass of
92.0 g/mol. What is the molecular formula?
molar mass
X
empirical mass
92.0 g
X
46.0 g
2
Molecular formula = (NO2)X = (NO2)2 = N2O4