1 the mole 6.02 x 10 23 chemistry i mr. trotts summer 2008

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The MoleThe Mole

6.02 X 6.02 X 10102323

Chemistry I

Mr. Trotts

Summer 2008

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What we’re going to Learn

1. The concept of the mole

2. Given moles calculate number of particles

3. Be able to calculate molecular mass and gram formula mass and weight

4. Be able to convert moles to mass, particles, and volume and convert mass to moles, volume, and particles

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5. Calculate the percent composition of a compound by mass of each element.

and

6. Calculate both the empirical (simplest) formula and molecular formula of a compound.

NOTE: As we encounter Learning Checks write the answers down for a daily grade

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STOICHIOMETRYSTOICHIOMETRYSTOICHIOMETRYSTOICHIOMETRY

- the study of the the study of the quantitative aspects quantitative aspects of chemical of chemical reactions.reactions.

- Combines mole Combines mole problems with problems with balanced equationsbalanced equations

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The MoleThe Mole

• A counting unit• Similar to a dozen, except instead

of 12, it’s 602 billion trillion 602,000,000,000,000,000,000,000

• 6.02 X 1023 (in scientific notation)• This number is named in honor of

Amedeo Avagadro (1776 – 1856)Amedeo Avagadro (1776 – 1856), who studied quantities of gases and discovered that no matter what the gas was, there were the same number of molecules present

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Just How Big is a Mole?Just How Big is a Mole?

• Enough soft drink cans to cover the surface of the earth to a depth of over 200 miles.

• If you had Avogadro's number of unpopped popcorn kernels, and spread them across the United States of America, the country would be covered in popcorn to a depth of over 9 miles.

• If we were able to count atoms at the rate of 10 million per second, it would take about 2 billion years to count the atoms in one mole.

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Everybody Has Avogadro’s Everybody Has Avogadro’s Number!Number!

But Where Did it Come From?But Where Did it Come From?• It was NOT just picked!

It was MEASURED.• One of the better

methods of measuring this number was the Millikan Oil Drop Experiment

• Since then we have found even better ways of measuring using x-ray technology

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Suppose we invented a new collection unit called a rapp. One rapp contains 8 objects.

1. How many paper clips in 1 rapp?

a) 1 b) 4 c) 8

2. How many oranges in 2.0 rapp?

a) 4 b) 8 c) 16

3. How many rapps contain 40 gummy bears?

a) 5 b) 10 c) 20

Learning CheckLearning Check

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Suppose we invented a new collection unit called a mep. One mep contains 8 objects.

A. How many paper clips in 1 mep?

3) 8

B. How many oranges in 2.0 meps?

3) 16

C. How many meps contain 40 gummy bears?

1) 5

Solution

1010

The MoleThe Mole• 1 dozen cookies = 12 cookies• 1 mole of cookies = 6.02 X 1023 cookies

• 1 dozen cars = 12 cars• 1 mole of cars = 6.02 X 1023 cars

• 1 dozen Al atoms = 12 Al atoms• 1 mole of Al atoms = 6.02 X 1023 atoms

Note that the NUMBER is always the same, but the MASS is very different!

Mole is abbreviated mol (gee, that’s a lot quicker to write, huh?)

1111

= 6.02 x 1023 C atoms

= 6.02 x 1023 H2O molecules

= 6.02 x 1023 NaCl “molecules”(technically, ionics are compounds not

molecules so they are called formula units)

6.02 x 1023 Na+ ions and

6.02 x 1023 Cl– ions

A Mole of ParticlesA Mole of Particles Contains 6.02 x 1023 particles

1 mole C

1 mole H2O

1 mole NaCl

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6.02 x 1023 particles

1 mole

or

1 mole

6.02 x 1023 particles

Note that a particle could be an atom OR a molecule!

Avogadro’s Number as Avogadro’s Number as Conversion FactorConversion Factor

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Example: How many moles of Calcium are in 2.408 x 1024 calcium atoms?

2.408 x 1024 Ca atoms x 1 mole Ca/6.02 x 1023 atoms Ca =

4.0 x 101 moles Ca

Example: How many atoms of Calcium are in 40 moles of Calcium

40 moles Ca x 6.02 x 1023 atoms Ca/1 mole Ca = 2.408 x 1024 atoms Ca

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4. Number of atoms in 0.500 mole of Ala) 500 Al atoms

b) 6.02 x 1023 Al atomsc) 3.01 x 1023 Al atoms

5.Number of moles of S in 1.8 x 1024 S atomsa) 1.0 mole S atomsb) 3.0 mole S atomsc) 1.1 x 1048 mole S atoms


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1. Number of atoms in 0.500 mol of Al3) 3.01 x 1023 Al atoms

0.500 mol Al x 6.02 x 1023 Al atoms1 mol Al

2. Number of moles of S if a sample of S contains 4.50 x 1024 S atoms2) 3.0 mole S atoms

4.50 x 1024 S atoms x 1 mol S 6.02 x 1023 S atoms

Solution

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• The Mass of 1 mole (in grams)

• Equal to the numerical value of the average

atomic mass (get from periodic table)

1 mole of C atoms = 12.0 g

1 mole of Mg atoms = 24.3 g

1 mole of Cu atoms = 63.5 g

Molar MassMolar Mass

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Other Names Related to Molar MassOther Names Related to Molar Mass

• Molecular Mass/Molecular Weight: If you have a single

molecule, mass is measured in amu’s instead of grams. But,

the molecular mass/weight is the same numerical value as 1

mole of molecules. Only the units are different. (This is the

beauty of Avogadro’s Number!)

• Formula Mass/Formula Weight: Same goes for

compounds. But again, the numerical value is the same.

Only the units are different.

• THE POINT: You may hear all of these terms which mean the SAME NUMBER… just different units

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Find the molar mass

(usually we round to the tenths place)

Learning Check!Learning Check!

6. 1 mole of Br atoms7. 1 mole of Sn atoms

= 79.9 g/mole

= 118.7 g/mole

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Mass in grams of 1 mole equal numerically to the sum of the atomic masses

1 mole of CaCl2 = 111.1 g/mol

1 mole Ca x 40.1 g/mol

+ 2 moles Cl x 35.5 g/mol = 111.1 g/mol CaCl2

1 mole of N2O4 = 92.0 g/mol

Molar Mass of Molecules and Molar Mass of Molecules and CompoundsCompounds

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8. Molar Mass of K2O = ? Grams/mole

9. Molar Mass of antacid Al(OH)3 = ? Grams/mole


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A. 1 mole of K2O = 94.2 g

2 K x 39.1 g/mole + 1 O x 16.0 g/mole

B. 1 mole of antacid Al(OH)3 = 78.0 g

1 Al x 27.0 g/mole + 3 O x 16.0 g/mole

+ 3 x 1.0

Solution

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10. Prozac, C17H18F3NO, is a widely used

antidepressant that inhibits the uptake

of serotonin by the brain. Find its molar

mass.

Complete the handout GRAM FORMULA MASS


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Prozac, C17H18F3NO, is a widely used

antidepressant that inhibits the uptake of serotonin

by the brain. It has a molar mass of

309 g/mole

17C (12.0) + 18H (1.0) + 3F (19.0) + 1N (14.0) + 1 O

(16.0)

Solution

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molar mass

Grams Moles

Calculations with Molar MassCalculations with Molar Mass

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Aluminum is often used for the structure of light-weight bicycle frames. How many grams of Al are in 3.00 moles of Al?

3.00 moles Al ? g Al

Converting Moles and GramsConverting Moles and Grams

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1. Molar mass of Al 1 mole Al = 27.0 g Al

2. Conversion factors for Al

27.0g Al or 1 mol Al

1 mol Al 27.0 g Al

3. Setup 3.00 moles Al x 27.0 g Al

1 mole Al

Answer = 81.0 g Al

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11. The artificial sweetener aspartame

(Nutra-Sweet) formula C14H18N2O5 is

used to sweeten diet foods, coffee and

soft drinks. How many moles of

aspartame are present in 225 g of

aspartame?


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Atoms/Molecules and GramsAtoms/Molecules and Grams

• Since 6.02 X 1023 particles = 1 mole AND

1 mole = molar mass (grams)• You can convert atoms/molecules to

moles and then moles to grams! (Two step process)

• You can’t go directly from atoms to grams!!!! You MUST go thru MOLES.

• That’s like asking 2 dozen cookies weigh how many ounces if 1 cookie weighs 4 oz? You have to convert to dozen first!

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molar mass Avogadro’s number Grams Moles particles

Everything must go through Moles!!!

CalculationsCalculations

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Atoms/Molecules and GramsAtoms/Molecules and Grams

How many atoms of Cu are present in 35.4 g of Cu?

35.4 g Cu 1 mol Cu 6.02 X 1023 atoms Cu 63.5 g Cu 1 mol Cu

= 3.4 X 1023 atoms Cu

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Methane CH4 known as natural gas is used in gas cook tops and gas heaters. Express the molar mass of methane in the form of conversion factors.

Molar mass of CH4 = 16.0 g

16.0 g CH4 and 1 mole CH4

1 mole CH4 16.0 g CH4

Molar Mass Factors

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Methane CH4 known as natural gas is used in gas cook tops and gas heaters. Express the molar mass of methane in the form of conversion factors.

Molar mass of CH4 = 16.0 g

16.0 g CH4 and 1 mole CH4

1 mole CH4 16.0 g CH4

Molar Mass Factors

3333

12. Acetic acid CH3COOH is the acid in vinegar . It

has a molar mass of 60.0 g/mole.

1 mole of acetic acid = ____________

1 mole acetic acid or g acetic acid

g acetic acid 1 mole acetic acid

Learning Check

3434

Acetic acid CH3COOH is the acid in vinegar . It has

a molar mass of 60.0 g/mole.

1 mole of acetic acid = 60.0 g acetic acid

1 mole acetic acid or 60.0 g acetic acid

60.0 g acetic acid 1 mole acetic acid

Solution

3535


13. How many atoms of K are present in 78.4 g of K?

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14. What is the mass (in grams) of 1.20 X 1024 molecules of glucose (C6H12O6)?

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More mole equivalents

1 mole of a gas at standard temperature (0 Celsius) and pressure (1 atmosphere) occupies 22.4 liters by volume

Example: 2 moles of oxygen at STP would occupy 2 moles x 22.4L/1 mole or 44.8L

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15. How many atoms of O are present in 78.1 g of oxygen?

78.1 g O2 1 mol O2 6.02 X 1023 molecules O2 2 atoms O 32.0 g O2 1 mol O2 1 molecule O2

Complete the handout Mixed Mole Problems

Given 1 mole = 6.02 x 1023 particles = gfm = 22.4L @ STP

Complete Atoms Worksheet #2 (The Mole)

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16. What is the percent carbon in C5H8NO4

(the glutamic acid used to make MSG

monosodium glutamate), a compound used

to flavor foods and tenderize meats?

a) 8.22 %C

b) 24.3 %C

c) 41.1 %C

Percent CompositionPercent Composition

Complete Percentage Composition Worksheet

4040Chemical Formulas of Chemical Formulas of

CompoundsCompounds

• Formulas give the relative numbers of atoms or Formulas give the relative numbers of atoms or moles of each element in a formula unit - always moles of each element in a formula unit - always a whole number ratio (the law of definite a whole number ratio (the law of definite proportions).proportions).

NONO22 2 atoms of O for every 1 atom of N 2 atoms of O for every 1 atom of N

1 mole of NO1 mole of NO22 : 2 moles of O atoms to : 2 moles of O atoms to

every 1 mole of N atomsevery 1 mole of N atoms

• If we know or can determine the relative number If we know or can determine the relative number of moles of each element in a compound, we can of moles of each element in a compound, we can determine a formula for the compound.determine a formula for the compound.

4141Types of FormulasTypes of Formulas

• Empirical FormulaEmpirical FormulaThe formula of a compound that The formula of a compound that

expresses the expresses the smallest whole number ratiosmallest whole number ratio of the atoms present.of the atoms present.

The The Ionic formula is always the empirical Ionic formula is always the empirical formulaformula

• Molecular FormulaMolecular FormulaThe formula that states the The formula that states the actualactual

number of each kind of atom found in number of each kind of atom found in one one moleculemolecule of the compound. of the compound.

4242To obtain an To obtain an Empirical Empirical Formula Formula

1.1. Determine the mass in grams of each Determine the mass in grams of each element present, if necessary.element present, if necessary.

2.2. Calculate the number of Calculate the number of molesmoles of of each each element.element.

3.3. Divide each by the smallest number of moles Divide each by the smallest number of moles to obtain the to obtain the simplest whole number ratio.simplest whole number ratio.

4.4. If whole numbers are not obtainedIf whole numbers are not obtained** in step in step 3), multiply through by the smallest number 3), multiply through by the smallest number that will give all whole numbersthat will give all whole numbers

** Be careful! Do not round off numbers prematurelyBe careful! Do not round off numbers prematurely

4343A sample of a brown gas, a major air pollutant, is A sample of a brown gas, a major air pollutant, is found to contain 2.34 g N and 5.34g O. Determine a found to contain 2.34 g N and 5.34g O. Determine a formula for this substance.formula for this substance.

require require molemole ratios so convert grams to moles ratios so convert grams to moles

moles of N = moles of N = 2.34g of N 2.34g of N = 0.167 moles of N= 0.167 moles of N

14.01 g/mole14.01 g/mole

moles of O = moles of O = 5.34 g5.34 g = 0.334 moles of O = 0.334 moles of O

16.00 g/mole16.00 g/mole

Formula:Formula:

0.334 0.167ON 0.167 0.334 2

0.167 0.167

N O NO

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Empirical Formula from % Empirical Formula from % CompositionComposition

A substance has the following composition by mass: 60.80 % Na ; 28.60 % B ; 10.60 % H What is the empirical formula of the substance?

Consider a sample size of 100 gramsThis will contain 28.60 grams of B and 10.60

grams HDetermine the number of moles of eachDetermine the simplest whole number ratio

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Empirical Formulas from Percent Composition

• Given a compound that is 32.4% Na, 22.5% S, and 45.1% O

• 32.4gNa x 1 mole/23.0g = 1.41 mole Na• 22.5gS x 1 mole/32g = .70 mole S• 45.1gO x 1 mole/16g = 2.82 mole O• Na = 1.41/.70 = 2• S = .70/.70 = 1• O = 2.82/.70 = 4 therefore = Na2SO4

• Complete the Determining Empirical Formula worksheet

4646Calculation of the Molecular FormulaCalculation of the Molecular Formula

17. A compound has an empirical 17. A compound has an empirical formula of NOformula of NO22. The colourless liquid, . The colourless liquid, used in rocket engines has a molar used in rocket engines has a molar mass of 92.0 g/mole. What is the mass of 92.0 g/mole. What is the molecular formula molecular formula of this substance?of this substance?N = 14.0g/mole

O2 = 2 x 16 g/mole = 32g

NO2 = 46g 92.0g/46g = 2

2 x (NO2) = N2O4

Complete Determining Molecular Formulas Worksheet

1 the mole 6.02 x 10 23 chemistry i mr. trotts summer 2008

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