1. The Mole Concept
12.00 g of Carbon-12 contains x 1023 atoms (1 mole)
Moles - How chemists count atoms

2. Chemist’s Definition of a Mole
particles (atoms, molecules, ions, formula units) of a substance
6.022 x 1023

3. The Mole is a Number The mole represents a # of particles.
A pair = 2 A dozen = 12
A mole = x 1023
This number is often referred
to as “Avogadro’s Number”

4. The Mole is a BIG number
6.022 x 1023 represents an incomprehensively large number!
If a mole of marbles were laid on the surface of the earth, how much of the earth would be covered?
Cover entire earth to a height of 50 miles!

5. 1 mole (6.022 x 1023 atoms) of different elements
63.55 g g
26.98 g g
32.07 g
55.85 g
Note 1 mole of elements takes up relatively little space – each individual atom is incredibly tiny. We need an a hugh number of atoms to be able to see them with our eyes.

6. How many particles are present?
In chemistry, it is important to know the # of atoms (or molecules) that you have.
Chemical formulas, like H2O, give us ratios of atoms: 2 H atoms bonded to 1 O atom.

7. How many particles are present?
Chemical equations: 2 H2 + O2  2 H2O give us ratios of reacting particles.
Both formulas and equations are needed to calculate recipes for reactions.

8. BIG Problem Atoms are too small to see with the naked eye!
STM image of Si
on 0.09 nm scale.
(0.09 x 10-9 m)
= 9 x 10-7 m
Counting would take a lifetime!

9. Chemist’s Solution to Problem Counting of Atoms or Molecules
The Mole Concept
The mole connects the # of particles present with a property we can measure in the lab: mass.
(Counting by grouping and counting by weighing)
Can’t see Can measure
Work HW 5-1 #1, p. 97

10. COUNTING BY WEIGHING How could you determine the number of marbles in the bag using a scale?
Bag of marbles
Scale
Problem: Marbles are similar, but not exactly the same mass
How can you account for small variations in the masses of individual marbles?

11. Determining the Average Mass of a Marble (or an atom)
Marbles (like atoms) will have similar but not necessarily identical masses.
Recall mass on periodic table represents average mass taking into account all of the isotopes of an atom.
Determination average mass of 10 marbles:
Average atomic mass
÷ 10 = 5.00 g

12. Counting by Weighing
Determine total mass of all marbles in the bag: g
Let N = number of marbles
N = total mass ÷ average mass
2000 / 5.00 = 400. marbles
A) amu B) 1.08 x 1010amu/ 10.8 amu/atom= 1 x 109
Work HW 5-1 #2, p. 97

13. Connecting Mass in Grams with Number of Atoms
How many carbon atoms (N) are present in g C?
Work HW 5-1 #3, p. 97
N = Total Mass (12.01 g) ÷ Average Mass of 1 Carbon
(Where N = # of Carbon Atoms)

14. How many C atoms are present in 12.01 g of C?
N = Total Mass (12 g) ÷ Average Mass of 1 Carbon
(Where N = # of Carbon Atoms)
N = g ÷ 1.99 x g =
6.02 x 1023

15. Developing the Definition of a Mole (back to p.84)
The definition of a mole (the # of atoms in 12 g of Carbon) was chosen to make it easy to determine the mass of a mole of atoms using the periodic table.

16. Connecting Atomic Mass with the Number of Atoms
Masses on periodic table represent the average mass on 1 atom measured in amu.
For example, the average mass of 1 carbon atom is amu.

17. Counting by weighing – Connecting Mass in Grams with the Number of Atoms
However, In the lab we can’t see single atoms so we have to work with very large numbers of atoms by measuring masses in grams.
We Need to work in grams (large #’s we can see, not amu (tiny numbers – can’t see)

18. What is the pattern in the following data?
Element
(atomic #)
# of atoms present
# of moles present
Mass in grams
He (#2)
6.022 x 1023
1.000
4.00 g
Li (#3)
6.93 g
B (#5)
10.81 g
C (#6)
12.01 g
Cu (#29)
63.55 g
Au (#79) g

19. Understanding the Mole Concept
Fill in the missing information
Mass of 1 mole ____________________
of an element = atomic _________ in _______
(6.022 x 1023 atoms)
mass
grams
Work HW 5-1 #4 - 6, p. 98

20. HW 5-1 #5 1 mole 12 g 0.25 moles 0.33 moles 3.0 g 4.0 g 0.50 moles

21. HW 5-1 #5
2.00 moles
2.50 moles
24 g
30 g
3.00 moles
36 g

22. HW 5-1, #6, p.98 Element Number of Atoms Mass in Grams Beryllium (#4)
6.022 x 1023
Magnesium (#12)
Aluminum (#13)
Copper (#29)
63.55
Carbon (#6)
12.01
3.011 x 1023
6.00
1.204 x 1024
9.01 g
24.31 g
26.98 g
6.022 x 1023
24.02 g

23. Examples of counting by grouping (Back to p. 85)

24. Could you go to the store and ask for 8,563 Rice Krispies please?
NO! THEY SELL RICE KRISPIES BY THE BOX BECAUSE BOXES ARE EASIER TO COUNT!

25. Notes p. 85
To avoid working with extremely large numbers, we count by grouping in units of x 1023 – called 1 mole.
Write 1 mole instead of x 1023
Write mole instead of
0.500 (6.022 x 1023) or x 1023
2 mole = 2 (6.022 x 1023) = x 1024
3 mole = 3 (6.022 x 1023) = 1.81 x 1024

26. HW 5-1, #7, p. 99
Count the atoms by drawing a box around each set of 12 atoms. How total sets are present? How many total atoms?
Ans: 3 boxes; 36 atoms

27. HW 5-1, #8 Group Number of objects 1 Pair of Aces 2 2 Pairs of Aces
1 Dozen Doughnuts 12
3 Dozen Doughnuts
Dozen Doughnuts 60
1.5 Doughnuts
1 Mole of B atoms
6.022 x atoms
2(6.022 x 1023) atoms
3(6.022 x 1023) atoms
4(6.022 x 1023) atoms
½ ( x 1023) atoms 4 36 5 18
2 Moles of B atoms
3 Moles of B atoms
4 Moles of B atoms
1/2 Moles of B atoms

28. HW 5-1, # 9, p. 99
Formula to calculate # of moles present in a given number of atoms (N)?
Moles = N atoms ÷ x 1023 atoms/mole

29. HW 5-1, #10 1.204 x 1024 atoms B ÷ 6.022 x1023 atom/mole
= moles B

30. HW 5-1, #11 Element Number of Atoms Number of Moles He 6.022 x 1023
1.00 Li Ne Ar Cu
3.01 x 1023
0.50
1.20 x 1024
1.81 x 1024 Zn
3.00
1.00
6.022 x1023
2.00
3.00
0.50
1.81 x1024
2.00

31. HW 5-1, #11 Element Number of Atoms Number of Moles Ag 0.500 2.00
1.81 x 1024
3.01 x1023
1.20 x1024
3.00

32. Relationship between # of particles,“packing boxes” and mass
If each
Has a mass of 10 mass units, (Ignore mass of “packing box”)
HW 5-1 #12A p. 100
? MASS UNITS
WEIGHES ? MASS UNITS
1 “PACKING BOX”
12 particles
Ignoring the container mass, how much would 1 box weigh?
ANS: 120 mass units (12 particles per box x 10 mass units per particles)

33. HW 5-1, #12, p. 100 11B) 600 mass units ÷ 120 mass units/box = 5 boxes
5 boxes x 12 atom/box = 60 atoms
11C) 1260 mass units ÷ 120 mass units/box = 10.5 boxes
10.5 boxes x 12 atom/box = 126 atoms

34. HW 5-1, #13
moles
Number of atoms
Element
Mass in grams
3.011 x 1023 He
6.022 x 1023
1.204 x 1024
1.806 x 1024
0.5000 Ne
1.000
2.000
3.000
0.5000
2.00 g
1.000
4.00 g
2.000
8.00 g
3.000
12.00 g
3.011 x 1023
10.09 g
6.022 x 1023
20.18 g
1.204 x 1024
40.36 g
1.806 x 1024
60.54 g

35. HW 5-1, #13
moles
Number of atoms
Element
Mass in grams
6.022 x 1023
26.98 1
39.95 1 Al
6.022 x 1023 Ar

36. HW 5-1 #14
Which of the following contains the same # of atoms as g of C?
Equal masses does NOT mean equal # of atoms because each type of atom has a different mass.
Need to compare # of particles – chemists unit for # of particles = mole
How many moles are present in g?
Ans: 1 mole
C = 12 amu
He = 4 amu

37. HW 5-1 #14
Question now becomes which of the following also represents 1 mole?
A) (1 mole = 6.94 g); g Li ≈ 2 moles
B) (1 mole = 4.00 g); 12.0 g He ≈ 3 moles
C) (1 mole = 10.8 g); 5.4 g of B ≈ 1/2 moles
D) g Ne = mass on periodic table = 1 mole

38. Link to mole review