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Chemical QuantitiesThe Mole
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Collection Terms
A collection term statesa specific number of items.
• 1 dozen donuts
= 12 donuts• 1 ream of paper
= 500 sheets• 1 case = 24 cans
Copyright © 2005 by Pearson Education, Inc.Publishing as Benjamin Cummings
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A mole is a collection that contains
• the same number of particles as there are carbon atoms in 12.0 g of carbon.
• 6.02 x 1023 atoms of an element (Avogadro’s number).
1 mole element Number of Atoms1 mole C = 6.02 x 1023 C atoms1 mole Na = 6.02 x 1023 Na atoms1 mole Au = 6.02 x 1023 Au atoms
A Mole of Atoms
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A mole • of a covalent compound has Avogadro’s number of
molecules.1 mole CO2 = 6.02 x 1023 CO2 molecules
1 mole H2O = 6.02 x 1023 H2O molecules
• of an ionic compound contains Avogadro’s number of formula units.
1 mole NaCl = 6.02 x 1023 NaCl formula units1 mole K2SO4 = 6.02 x 1023 K2SO4 formula
units
A Mole of a Compound
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Samples of One Mole Quantities
1 mole C= 6.02 x 1023 C atoms
1 mole Al = 6.02 x 1023 Al atoms
1 mole S = 6.02 x 1023 S atoms
1 mole H2O = 6.02 x 1023 H2O molecules
1 mole CCl4 = 6.02 x 1023 CCl4 molecules
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Avogadro’s number 6.02 x 1023 can be written as anequality and two conversion factors.
Equality:1 mole = 6.02 x 1023 particles
Conversion Factors:6.02 x 1023 particles and 1 mole 1 mole 6.02 x 1023
particles
Avogadro’s Number
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Using Avogadro’s Number
Avogadro’s number is used to convertmoles of a substance to particles.
How many Cu atoms are in 0.50 mole Cu?
0.50 mole Cu x 6.02 x 1023 Cu atoms 1 mole Cu
= 3.0 x 1023 Cu atoms
Copyright © 2005 by Pearson Education, Inc.Publishing as Benjamin Cummings
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Using Avogadro’s Number
Avogadro’s number is used to convertparticles of a substance to moles.
How many moles of CO2 are in 2.50 x 1024 molecules CO2?
2.50 x 1024 molecules CO2 x 1 mole CO2
6.02 x 1023 molecules CO2
= 4.15 mole CO2
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1. The number of atoms in 2.0 mole Al is A. 2.0 Al atoms.
B. 3.0 x 1023 Al atoms. C. 1.2 x 1024 Al atoms.
2. The number of moles of S in 1.8 x 1024 atoms S is A. 1.0 mole S atoms. B. 3.0 mole S atoms. C. 1.1 x 1048 mole S atoms.
Learning Check
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Solution
C. 1.2 x 1024 Al atoms 2.0 mole Al x 6.02 x 1023 Al atoms
1 mole Al
B. 3.0 mole S atoms 1.8 x 1024 S atoms x 1 mole S
6.02 x 1023 S atoms
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Subscripts and Moles
The subscripts in a formula show• the relationship of atoms in the formula.• the moles of each element in 1 mole of compound.
GlucoseC6H12O6
In 1 molecule: 6 atoms C 12 atoms H 6 atoms OIn 1 mole: 6 mole C 12 mole H 6 mole O
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Subscripts State Atoms and Moles
9 mole C 8 mole H 4 mole O
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Factors from Subscripts
The subscripts are used to write conversion factors for
moles of each element in 1 mole compound. For aspirin
C9H8O4, the following factors can be written:
9 mole C 8 mole H 4 mole O 1 mole C9H8O4 1 mole C9H8O4 1 mole C9H8O4and 1 mole C9H8O4 1 mole C9H8O4 1 mole C9H8O4
9 mole C 8 mole H 4 mole O
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Learning Check
A. How many mole O are in 0.150 mole aspirin C9H8O4?
B. How many O atoms are in 0.150 mole aspirin C9H8O4?
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Solution
A. How many mole O are in 0.150 mole aspirin C9H8O4?
0.150 mole C9H8O4 x 4 mole O = 0.600 mole O 1 mole C9H8O4
subscript factorB. How many O atoms are in 0.150 mole aspirin
C9H8O4?
0.150 mole C9H8O4 x 4 mole O x 6.02 x 1023 O atoms 1 mole C9H8O4 1 mole O
subscript Avogadro’s factor Number
= 3.61 x 1023 O atoms
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•Chapter 10.2 Mole to Mass Relationships
Molar Mass
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Molar Mass
The molar mass
• is the mass of one mole of an element or compound.
• is the atomic mass expressed in grams.
Copyright © 2005 by Pearson Education, Inc.Publishing as Benjamin Cummings
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Molar Mass from Periodic Table
Molar mass is the atomic mass expressed in grams.
1 mole Ag 1 mole C 1 mole S = 107.9 g = 12.01 g = 32.07 g
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Give the molar mass for each (to the tenths decimal
place).
A. 1 mole K atoms = ________
B. 1 mol Sn atoms = ________
Learning Check
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Give the molar mass for each (to the tenths decimal
place).
A. 1 mole K atoms = 39.1 g
B. 1 mole Sn atoms =118.7 g
Solution
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Molar Mass of a Compound
The molar mass of a compound is the sum of the molar masses of the elements in the formula.
Example: Calculate the molar mass of CaCl2.
Element Number of Moles
Atomic Mass Total Mass
Ca 1 40.1 g/mole 40.1 g
Cl 2 35.5 g/mole 71.0 g
CaCl2 111.1 g
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Molar Mass of K3PO4
Calculate the molar mass of K3PO4.
Element Number of Moles
Atomic Mass Total Mass in K3PO4
K 3 39.1 g/mole 117.3 g
P 1 31.0 g/mole 31.0 g
O 4 16.0 g/mole 64.0 g
K3PO4 212.3 g
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Some One-mole Quantities
32.1 g 55.9 g 58.5 g 294.2 g 342.2 g
One-Mole Quantities
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What is the molar mass of each of the following?
A. K2O
B. Al(OH)3
Learning Check
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A. K2O 94.2 g/mole
2 mole K (39.1 g/mole) + 1 mole O (16.0 g/mole) 78.2 g + 16.0 g = 94.2 g
B. Al(OH)3 78.0 g/mole
1 mole Al (27.0 g/mole) + 3 mol O (16.0 g/mole) + 3 mol H (1.01 g/mole) 27.0 g + 48.0 g + 3.03 g = 78.0 g
Solution
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Prozac, C17H18F3NO, is an antidepressant that inhibits the uptake of serotonin by the brain. What is the molar mass of Prozac?
1) 40.1 g/mole2) 262 g/mole 3) 309 g/mole
Learning Check
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Prozac, C17H18F3NO, is an antidepressant that inhibits the uptake of serotonin by the brain. What is the molar mass of Prozac?
3) 309 g/mole
17 C (12.0) + 18 H (1.01) + 3 F (19.0)
+ 1 N (14.0) + 1 O (16.0) =
204 + 18.2 + 57.0 + 14.0 + 16.0 = 309 g/mole
Solution
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Molar mass conversion factors • are written from molar mass.• relate grams and moles of an element or compound.
Example: Write molar mass factors for methane, CH4,
used in gas stoves and gas heaters.Molar mass:
1 mol CH4 = 16.0 g
Conversion factors:
16.0 g CH4 and 1 mole CH4
1 mole CH4 16.0 g CH4
Molar Mass Factors
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Acetic acid C2H4O2 gives the sour taste to vinegar. Write two molar mass conversion factors for acetic acid.
Learning Check
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Acetic acid C2H4O2 gives the sour taste to vinegar.Write two molar mass factors for acetic acid.
Calculate molar mass:24.0 + 4.04 + 32.0 = 60.0 g/mole
1 mole of acetic acid = 60.0 g acetic acid
Molar mass factors1 mole acetic acid and 60.0 g acetic acid 60.0 g acetic acid 1 mole acetic acid
Solution
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Molar mass factors are used to convert between the grams of a substance and the number of moles.
Calculations Using Molar Mass
Grams Molar mass factor Moles
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Aluminum is often used to build lightweight bicycleframes. How many grams of Al are in 3.00 mole Al?
Molar mass equality: 1 mole Al = 27.0 g Al
Setup with molar mass as a factor:
3.00 mole Al x 27.0 g Al = 81.0 g Al1 mole Al
molar mass factor for Al
Moles to Grams
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Learning Check
Allyl sulfide C6H10S is a compound that has the odor of garlic. How many moles of C6H10S are in 225 g?
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Calculate the molar mass of C6H10S.
(6 x 12.0) + (10 x 1.01) + (1 x 32.1) = 114.2 g/mole
Set up the calculation using a mole factor.
225 g C6H10S x 1 mole C6H10S
114.2 g C6H10S
molar mass factor (inverted)
= 1.97 mole C6H10S
Solution
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Grams, Moles, and Particles
A molar mass factor and Avogadro’s number convert• grams to particles.
molar mass Avogadro’s number g mole particles
• particles to grams.
Avogadro’s molar mass number
particles mole g
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Learning Check
How many H2O molecules are in 24.0 g H2O?
1) 4.52 x 1023
2) 1.44 x 1025
3) 8.03 x 1023
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Solution
How many H2O molecules are in 24.0 g H2O?
3) 8.02 x 1023
24.0 g H2O x 1 mole H2O x 6.02 x 1023 H2O molecules 18.0 g H2O 1 mole H2O
= 8.03 x 1023 H2O molecules
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Learning Check
If the odor of C6H10S can be detected from 2 x 10-13 g in one liter of air, how many molecules of C6H10S are present?
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Solution
If the odor of C6H10S can be detected from 2 x 10-13 g in one liter of air, how many molecules of C6H10S are present?
2 x 10-13 g x 1 mole x 6.02 x 1023 molecules 114.2 g 1 mole
= 1 x 109 molecules C6H10S
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Chapter 10.2 Mole to Volume
Volume and Moles (Avogadro’s Law)
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Avogadro's Law: Volume and Moles
In Avogadro’s Law
• the volume of a gas is directly related to the number of moles (n) of gas.
• T and P are constant.
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The volumes of gases can be compared at STP, Standard Temperature and Pressure, when they have
• the same temperature.Standard temperature (T) 0°C or 273 K
• the same pressure. Standard pressure (P) 1 atm (760 mm Hg)
STP
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Molar Volume
At standard temperature and pressure (STP), 1 mole of a gas occupies a volume of 22.4 L, which is called its molar volume.
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Molar Volume as a Conversion Factor
The molar volume at STP can be used to form conversion factors.
22.4 L and 1 mole 1 mole 22.4 L
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Using Molar Volume
What is the volume occupied by 2.75 moles N2 gas
at STP?
The molar volume is used to convert moles to liters.
2.75 moles N2 x 22.4 L = 61.6 L 1 mole
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Guide to Using Molar Volume
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A. What is the volume at STP of 4.00 g of
CH4?
1) 5.60 L2) 11.2 L 3) 44.8 L
B. How many grams of He are present in
8.00 L of gas at STP?
1) 25.6 g 2) 0.357 g 3) 1.43 g
Learning Check
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