6.02 Atomic Vs. Macroscopic Scale
Counting By Weighing
Atoms, Molecules, Moles and Grams
Dr. Fred O. Garces
Chemistry 100
Miramar College
1
Atomic Vs. Macroscopic Scale
January 10
Atomic Mass Unit
What is the mass of an object that cannot be seen ?
What scale / units of mass is used for such small objects ?
Unit of mass that is comparable to object of that size.
atomic mass unit (amu) has been used as a standard for a mass of an atom.
1 amu = 1.66 • 10-27 Kg = 1/12 mass of 12C
Atoms: Atomic mass
one atom of potassium 19K weighs 19 amu.
one atom of zinc 30Zn weighs 30 amu.
Molecule: Molecular mass
one water (H2O) molecule 2-H, 1-O = 2amu + 16amu = 18 amu
one glucose (C6H12O6) molecule: 6C, 12H, 6O
= [6 C •12amu] + [12 H • 1 amu] + [6 O • 16amu]
= 144 amu
2
Atomic Vs. Macroscopic Scale
January 10
Isotopic Distribution
Isotopic Distribution:
Question comes to mind: Why is the mass of carbon 12.011 according
the periodic table ? Why is the mass of chlorine 35.453 ? That of
copper 63.546 ?
Is not the mass of an atom reflected on the number of protons and neutrons
an atom possesses? If so, is there such a thing as 0.011 amu of subatomic proton or
neutron for carbon. Or 0.453 in chlorine and 0.546 in copper?
Atomic mass, as shown in the periodic table, is the average of all
isotope found in nature. Atomic mass is the weighted average mass for
the isotropic distribution(found in nature) for that element.
Weighted atomic mass average for the copper atom:
Copper has two stable isotope:
63Cu
- 72.70 %, and
65Cu
- 27.30 %
63 amu • (0.7270) + 65 amu • (0.2730) = 63.546 amu
3
Atomic Vs. Macroscopic Scale
January 10
The Mole: A rice story
The mole (a story of numbers)
Moral of story: Rufus favorite food is rice. But he rarely eats it even though it is
economical and easily prepared. He knows it is healthy for him and he was told once
that it takes one serving is 12000 grains. So every time Rufus wants to eat rice he
has to prepare 3 hr ahead of time and count out 12000 grains. How can we help my
friend Rufus? 1 grain of rice weights an average of 19 mg.
Count rice by weighing
Mass = 12000 grains ∗
19 mg
1 grain
∗
1g
1000mg
∗
16 oz
454 g
Mass rice for 1 serving = 8.0 oz
Weighs out 8.0 oz.
rice = 1 cup
€
5
Atomic Vs. Macroscopic Scale
January 10
Counting by mass
Method of Counting by mass
In chemistry we deal with such small particles we need a way to count
these particles. Like in Rufus case, the most efficient way of counting
very small items is by counting by mass.
As it turns out if we take 6.02•1023 atoms of carbon-12,
12C
and weight this amount, it weights exactly 12 grams.
Similarly,
6.023•1023
35Cl
atoms weighs exactly 35 g.
6.023•1023
16O
atoms weighs exactly 16 g.
It follows that if we take
6.023•1023 O2 molecules made from oxygen-16, that weighs 32 g O2.
This 6.02•1023 is call 1 mole. It is a chemist dozen.
1 mole of substance is equal
to its formula weight in grams
6
Atomic Vs. Macroscopic Scale
January 10
Size of a mole
Size of one mole;
1 mole of sand fill city of SD 5 miles deep.
Take 1 moles of pennies, distribute these to all 5 billion humans, we'd all be trillionaire.
If placing these pennies end to end, it would stretch... (how far?)
1 penny = 2.0 cm
Length of 1 mole of penny =
= 2.0 cm ∗ 6.02• 1023 ∗
s
∗
1 hr
∗
day
∗
yr
3• 1010 cm 3600s 24 hr 365 day
= 1, 268, 391.7 light - years = 1.3 million light - years
€
7
Atomic Vs. Macroscopic Scale
January 10
Atomic Vs Macroscopic Scale
What path relates the atomic scale to our Macroscopic scale ?
Atomic
Magnifier
(amu)
Atoms
Molecules
formula unit
8
Macroscopic
(grams)
Nav
Nav
Nav
moles
moles
Atomic Wt
Molar mass
moles
Atomic Vs. Macroscopic Scale
Formula wt
grams
grams
grams
January 10
Questions Relating
Atomic to Macroscopic Scale
How many Carbon atoms (or molecules) in a certain mass of sample?
12 g C
D
1mole
D
6.02•1023 atoms
6 g C
D
0.5 mole
D
3.01•1023 atoms
200 g C
D
? mole
D
? atoms
1mole 6.02 • 1023
200g C •
•
= 1.0 • 1025 C atoms
12g C
1mole C
9
€
Atomic Vs. Macroscopic Scale
January 10
Atomic Scale Vs. Macroscopic Scale
Atomic Scale
D
Atoms
Magnifier
Molecules
Macroscopic Scale
Grams
pounds
12C
1-atoms
12amu
12C
1-mole
12 grams
H2O 1-molecule
18.0 amu
H2O 1-mole
18.0 grams
NaCl 1-Formula Unit
58.5 amu
10
Atomic Vs. Macroscopic Scale
NaCl 1-mole
58.5 grams
January 10
Defining the “MOLE”
What is a mole ?
… SI base unit for amount.
… 6.02•1023 anything.
… a magnifier between the atomic scale and macroscopic scale.
… a conversion factor.
… a chemist dozen.
… the sum of the atomic mass of all elements in a substance
when the mass is expressed in grams. (Molar Mass)
… the ratio of elements in a substance as indicated by its chemical
formula.
… the ratio of elements combining in a chemical reaction as
indicated by the balance equation.
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Atomic Vs. Macroscopic Scale
January 10
Questions RelatingNumber of Molecules to Mass
How much will 5.0•1026 molecules of H2O weight ?
Data: MW:
18.0 gH 2O =
Nav: 1mole H 2O =
1mole H 2O
6.02·1023 molecules H 2O
5.0·1026 molecule H 2O
5.0·1026 molecule H 2O ∗
1mole H 2O
∗
18.0 gH 2O
6.02·10 molecules H 2O 1 mole H 2O
23
= 14,950 g
What volume is this?
Data: Density :
14, 950 g H 2O ∗
12
1.0 g = 1L
1ml
∗
1000ml = 1ml
1L
1.0 g 1000ml
Atomic Vs. Macroscopic Scale
= 15L
January 10
Mole Relationship to Mass and Items (p261)
W
B
Y
D
X
C
14
Atomic Vs. Macroscopic Scale
January 10
Question Relating
Number of molecules to moles of Substance
i. What is the number of molecules in 2.9 moles of TNT ?
TNT = C7H5N3O6
Mol.Wt. = 227.0 g/mol g 227.0 g = 1 mol
ii How much will this amount of TNT weigh ?
iii How many N-atoms are in 1.0 g of TNT ?
Note that in TNT:
1 mole C7H5N3O6 ≅ 7 mol C ≅ 5 mol H ≅ 3 mol N ≅ 6 mol O
15
Atomic Vs. Macroscopic Scale
January 10
Mole Relationship to Mass and Items (p261)
W
Y
B
D
i What is the number of molecules in 2.9 moles of TNT ?
TNT = C7H5N3O6
Mol.Wt. = 227.0 g/mol
ii How much will this amount of TNT weigh ?
iii How many N-atoms are in 1.0 g of TNT ?
X
16
C
Note that in TNT:
1 mole C7H5N3O6 ≅ 7mol C ≅ 5mol H ≅ 3mol N ≅ 6mol O
Atomic Vs. Macroscopic Scale
January 10
Question Relating
Number of molecules to moles of Substance
i. What is the number of molecules in 2.9 moles of TNT ?
TNT = C7H5N3O6
2.9mol TNT •
€
6.02 • 1023 molc' TNT
1 mole TNT
€
227.0 gTNT
1 mole TNT
= 658.3 g TNT = 660 g TNT
iii How many N-atoms are in 1.0 g of TNT ?
Note that in TNT:
1 mole C7H5N3O6 ≅ 7 mol C ≅ 5 mol H ≅ 3 mol N ≅ 6 mol O
1.0g TNT •
17
= 1.75 • 1024 molc' = 1.8 • 1024 molc'
ii How much will this amount of TNT weigh ?
2.9mol TNT •
€
Mol.Wt. = 227.0 g/mol g 227.0 g = 1 mol
1mole TNT
227g TNT
•
3mol N
1mol TNT
•
6.02 • 1023 atoms
1mol N
Atomic Vs. Macroscopic Scale
=
January 10
Question Relating
Number of molecules to moles of Substance
i. What is the number of molecules in 2.9 moles of TNT ?
TNT = C7H5N3O6
Mol.Wt. = 227.0 g/mol
6.02 • 1023 molc' TNT
2.9mol TNT •
1 mole TNT
= 1.75 • 1024 molc' = 1.8 • 1024 molc'
ii How much will this amount of TNT weigh ?
€
2.9mol TNT •
227.0 gTNT
iii How many N-atoms are in 1.0 g of TNT ?
Note that in TNT:
1 mole C7H5N3O6 ≅ 7 mol C ≅ 5 mol H ≅ 3 mol N ≅ 6 mol O
€
1.0g TNT •
€
18
1 mole TNT
= 658.3 g TNT = 660 g TNT
1mole TNT
227g TNT
•
3mol N
1mol TNT
•
6.02 • 1023 atoms
1mol N
=
= 7.96 •1021 N atoms= 8.0 •1021 N atoms
Atomic Vs. Macroscopic Scale
January 10
Moles and Molar Mass: Example
#7.61-Ebbing
a) Calculate the moles of chloride ions in 1.11 g of magnesium
chloride. b) How many chloride ions are present?
1mole MgCl2 ≅ 1mol Mg+2 ≅ 2mol ClMg - 24.3 g/mol
= 24.3 g/mol
2 Cl - 35.45 g/mol•2
= 70.9 g/mol
Molar Mass (MgCl2)
a)
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$ "
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b)
19
Atomic Vs. Macroscopic Scale
#∗!
$ "
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95.2 g = 1mol
# = &Answer'
$ "
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= Answer'
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State the path
January 10
Moles and Molar Mass: Example
#7.61-Ebbing
a) Calculate the moles of chloride ions in 1.11 g of magnesium
chloride. b) How many chloride ions are present?
1mole MgCl2 ≅ 1mol Mg+2 ≅ 2mol ClMg - 24.3 g/mol
= 24.3 g/mol
2 Cl - 35.45 g/mol•2
= 70.9 g/mol
Molar Mass (MgCl2)
= 95.2 g/mol
a)
1.1 g MgCl2 ∗
1mole MgCl2
95.2g MgCl2
b)
0.0231 mol Cl ions •
-
€
20
€
∗
2mol Cl1mol MgCl2
= 0.0231 mol Cl - ions
6.02 •1023 Cl- ions
1mol Cl- ions
Atomic Vs. Macroscopic Scale
=
1.39 •1022 Cl- ions
January 10
Counting by Mass: A Review
One mole substance equivalent to:
Atomic Weight (in grams) - atoms
Molecular Weight (in grams) - molecules
Formula Weight (in grams) - ionic Compounds
Atoms
Compound
C6H12O6
mole
C6H12O6
mass
180 g
molecule
1 mole
(1 mol)
C
6-C atoms
6 mol C
6(12.0) = 72g C
H
12-H atoms
12 mol C
12(1.0) = 12g H
O
6-O atoms
6 mol O
6(16.0) = 96g O
180 g total
From Chemical Formula we obtain the conversion factors:
1 molecule C6H12O6 c 6C atoms ≅ 12H atoms ≅ 6 O atoms
or
1 mole C6H12O6 c 6 C moles ≅ 12 H moles ≅ 6 O atoms
21
Atomic Vs. Macroscopic Scale
January 10
Summary
Counting by Weighing at a Glance:
Counting and Weighing
Atoms and Molecules
Formula Mass
Mole
The sum of the atomic masses of
atoms in a formula. The formula
mass of glucose is: (6.0amu •12C) +
(1.0amu •12H) + (16.0amu • 6O) =
1.80•102 amu
Mole = Avogadro’s number of
particles
= 6.02•1023
1 Mole glucose = 6.02•1023 molc’
Molar Mass
The formula mass of a substance in
grams; containing = 6.02•1023 atoms or
molecules or formula unit
Molar mass of glucose = 180 g / mole.
C6H12O6
Glucose
24
Atomic Vs. Macroscopic Scale
Atomic Mass Unit
1 g = 6.02•1023 atomic mass unit
1 amu = 1/1 the mass of one 12C atom
January 10