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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

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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