Chapter 7

The Mole

Collection Terms

1 trio = 3 singers

1 six-pack Cola = 6 cans Cola drink

1 dozen donuts = 12 donuts

1 gross of pencils = 144 pencils

A Moles of Particles

Contains 6.02 x 1023 particles

1 mole C = 6.02 x 1023 C atoms

1 mole H2O = 6.02 x 1023 H2O molecules

1 mole NaCl = 6.02 x 1023 Na+ ions and

6.02 x 1023 Cl– ions

Examples of Moles

Moles of elements

1 mole Mg = 6.02 x 1023 Mg atoms

1 mole Au = 6.02 x 1023 Au atoms

Moles of compounds

1 mole NH3= 6.02 x 1023 NH3molecules

1 mole C9H8O4 = 6.02 x 1023 aspirin molecules

Avogadro’s Number is 6.02 x 1023 or, 1 mole

6.02 x 1023 particles 1 mole

or

1 mole

6.02 x 1023 particles

Using Isotopic Abundances to

determine the Average Atomic Mass of an

Element

Atomic Mass Determination What is this number 35.453 for Cl??

The atomic mass - is an average based on the percents and masses of each of the

isotopes of chlorine

Chlorine consists of 75.77% chlorine-35 (mm = 34.968853 amu) and 24.23%

chlorine-37 (36.965903 amu)

Atomic Mass Determination Chlorine consists of 75.77% chlorine-35

(mm = 34.968853 amu) and 24.23% chlorine-37 (36.965903 amu)

1: convert the percentage to a decimal:

0.7577 chlorine-35 0.2423 chlorine-37

2: 0.7577 x 34.968853 amu = 26.4958992 amu

0.2423 x 36.965903 amu = 8.9651 amu 35.4527 amu

Atomic Mass Determination Nitrogen consists of two naturally

occurring isotopes 99.63% nitrogen-14 with a mass of

14.003 amu 0.37% nitrogen-15 with a mass of

15.000 amu What is the atomic mass of

nitrogen?

Finding the Molar Masses of Elements

and Compounds

Molar Mass of Elements remember these are atoms

Number of grams in 1 mole of atoms Equal to the numerical value of the atomic mass

from the 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

Learning CheckGive the molar mass to 1.0 mole

A. 1 mole of Br atoms =________

B. 1 mole of Sn atoms =________

Solution

Give the molar mass to 0.1 g

A. 1 mole of Br atoms = 79.9 g/mole

B. 1 mole of Sn atoms = 118.7 g/mole

Molar Mass of Compounds Both molecules and Ionic Compounds

Mass in grams of 1 mole is equal to the sum of the atomic masses of all the atoms present

1 mole of CaCl2 = 111.1 g/mole

(1 mole Ca x 40.1 g/mole) + (2 moles Cl x 35.5 g/mole)

1 mole of N2O4 = 92.0 g/mole

(2 moles N x 14.0 g/mole) + (4 moles O x 16.0 g/mole)

Learning Check

A. 1 mole of K2O = ______g

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

Solution

A. 1 mole of K2O

(2 K x 39.1 g/mole) + (1 O x 16.0 g/mole) = 94.2 g

B. 1 mole of antacid Al(OH)3

(1 Al x 27.0 g/mol) +(3 O x 16.0 g/mol) + (3 H x 1.0) = 78.0 g

Learning Check

Prozac, C17H18F3NO, is a widely used

antidepressant that inhibits the uptake of serotonin by the brain. It has a molar mass of

1) 40.0 g/mole

2) 262 g/mole

3) 309 g/mole

Solution

Prozac, C17H18F3NO, is a widely used

antidepressant that inhibits the uptake of serotonin by the brain. It has a molar mass of

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

(16.0)

3) 309 g/mole

Determine the% composition of H2SO4

1 – Calc the # grams in a mole of the formula

2 – Divide each of the elements total masses by the molar mass

3 – Mult by 100 to make a percent

Determine the percent composition of H2SO4

H 2 x 1.0 g = 2.0 g 98.1

S 1 x 32.1 g = 32.1 g 98.1 O 4 x 16.0 g = 64.0 g

98.1 g/mol

x 100 =

x 100 =

x 100 =

What is the percent composition of

C5H8NO4 MSG, a compound used to

flavor foods and tenderize meats?

What is the percent composition of Ca(NO3)2

Molar MathConverting moles particle,

and Converting moles mass

Convert 0.187 mol Na+ to ions.

0.187 mol Na+ 6.02 x 1023 ions Na

1( ) = 1.13 x 1023 ions

Na

Convert 5.66 x 1023 atoms Xe to moles.

5.66 x 1023 atoms Xe

( )=0.940 mol Xe6.02 x 1023 atoms Xe

1 mole Xe

Moles = grams/molar mass

Determine the number of moles in 27.35 g of the element sulfur.

 Calculate the number of moles of SiO2 in a 18.95 g sample

 

Moles = grams/molar mass

Determine the number of grams in 0.0595 moles of H2O ( mm = 18.0 g/mol)?

    Determine the number of grams in 1.83 x 10-

3 moles of SiO2 (SiO2 mm = 60.1 g/mol)

Learning Check

The artificial sweetener aspartame

(Nutri-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?

Solution

Molar mass of Aspartame C14H18N2O5

(14 x 12.0) + (18 x 1.01) + (2 x 14.0) + (5 x 16.0) = 294 g/mole

Setup moles = 225 g aspartame = 0.765 mol

294 g aspartame/mol = 0.765 mole aspartame

Moles and Grams

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

Setup

grams = mol x molar mass

3.00 moles Al x 27.0 g Al = 81.0 g

Al

Mole Mass Conversions (grams = mol x molar mass)

Formulas

Chemical Formulas

Include the symbols of the elements and the subscripts, which indicate the number of

atoms, or ions, of each.

Example:C6H12O6 – Glucose

Contains 6 atoms of Carbon, 12 atoms of Hydrogen and 6 atoms of Oxygen.

Any change to the symbols or suscripts changes the formula.

Changing the formula changes the compound which is represented.

Example: C6H12O6 is Glucose!

C6H12O5 is Not Glucose!

Chemical Formulas

Other Types of Formulas

The formulas for compounds can also be expressed as: (1.) an empirical formula and

as (2.) a molecular (true) formula.

Empirical Molecular (true) Name

CH C2H2 acetylene

CH C6H6 benzene

CO2 CO2 carbon dioxide

CH2O C5H10O5 ribose

Defining Empirical and

Molecular Formula

Empirical formula: A formula that shows the simplest whole-number ratio of atoms in the formula.

Molecular formula: A formula that is a whole-number multiple of the

empirical formula.

Learning Check

A. What is the empirical formula for C4H8?

1) C2H4 2) CH2 3) CH

B. What is the empirical formula for C8H14?

1) C4H7 2) C6H12 3) C8H14

C. What is a molecular formula for CH2O?

1) CH2O 2) C2H4O2 3)

C3H6O3

Solution

A. What is the empirical formula of C4H8?

2) CH2

B. What is the empirical formula of C8H14?

1) C4H7

C. What is a molecular formula of CH2O?

1) CH2O 2) C2H4O2 3) C3H6O3

1. You need grams of each element to calculate the moles of each element.

Assume you have a 100 g sample! 2. Calculate the number of moles of

each element. 3. Find the smallest whole number ratio by dividing each mole value by the

smallest mole values: 4. Write the simplest or empirical

formula

Determining Empirical Formulas

Finding the Empirical Formula

A compound is 71.66% Cl, 24.28% C, and 4.06% H. The molar mass is known to be 99.0 g/mol. What

is the empirical formula?

1. Determine the number of grams of

each element. 71.66 % Cl becomes 71.66 g Cl

24.28 % C becomes 24.28 g C

4.06 % H becomes 4.06 g H

2. Calculate the number of moles of each element (divide by molar mass).

71.66 g Cl = 2.02 mol Cl

35.5 g/mol Cl

24.28 g C = 2.02 mol C 12.0 g/mol C

4.06 g H = 4.06 mol H 1.0 g/mol H

Why moles?Why do you need the number of

moles of each element in the compound?

The subscripts in the chemical formula will equal the mole to

mole ratio of the elements present.

3. Find the smallest whole number ratio by dividing each mole value by the smallest mole values:

Cl: 2.02 = 1 Cl 2.02

C: 2.02 = 1 C 2.02

H: 4.06 = 2.005 H 2.02

4. Write the simplest or empirical

formula = CH2Cl

Determining a Molecular Formula from

an Empirical Formula

In Order to Determine the Molecular Formula

from the Empirical Formula you must have

the mass of both the Molecular Formula and the Empirical Formula.

Empirical and Molecular Formulas

Molar Mass of the molecular formula Molar Mass of the empirical formula

or

Empirical formula x n = Molecular formula

= n

5. Determine the molecular formula

from the Empirical form of CH2Cl….remember,the formula

mass was 99.0 g/mol.

1(C) + 2(H) + 1(Cl) = 1(12.0) + 2(1.0) + 1(35.5) =

49.5g/mol

Determine multiplying factor = n

mm molec form = 99.0 g/mol

mm emp form 49.5 g/mol

Solution: CH2Cl x 2 = C2H4Cl2

n = = 2

Learning Check

A compound has a formula mass of 176.0 and an empirical formula of C3H4O3. What is the molecular

formula?

Solution

A compound has a formula mass of 176.0 and an empirical formula of

C3H4O3. What is the molecular

formula?

C3H4O3 = 88.0 g/mol

176.0 g

C6H8O6

88.0 g = 2

Learning Check

Aspirin is 60.0% C, 4.50 % H and 35.5% O. Calculate its

Empirical formula.

Solution

60.0 g C = ______ mol C

Molar mass C

4.50 g H = ______ mol H

Molar mass H

35.5 g O = ______ mol O

Molar mass O

Solution

60.0 g C = 5.00 mol C

12.0 g/mol C

4.50 g H = 4.50 mol H

1.01 g/mol H

35.5 g O = 2.22 mol O

16.0 g/mol O

5.00 mol C = 2.25 2.22 mol O

4.50 mol H = 2.002.22 mol O

2.22 mol O = 1.002.22 mol O Are the results whole numbers?_____

Divide by the smallest # of moles.

Finding Subscripts

A fraction between 0.1 and 0.9 must not be rounded if the given is in

percents. Multiply all results by an integer to give whole numbers for

subscripts.(1/2) 0.500 x 2 = 1

(1/3)0.333 x 3 = 1 (1/4)0.250 x 4 = 1(3/4)0.750 x 4 = 3

Multiply everything x 4C: 2.25 mol C x 4 = 9 mol C

H: 2.00 mol Hx 4 = 8 mol H

O: 1.00 mol O x 4 = 4 mol O

Use the whole numbers of moles as the subscripts in the simplest formula

C9H8O4

Practice

Finding the Molecular Formula

A compound is 71.65% Cl, 24.27% C, and 4.07% H. The molar mass is

known to be 99.0 g/mol. What are the empirical and molecular formulas?

Calculate the empirical formula for the following

compound 

15.8% carbon and 84.2% sulfur

 

 

Calculate the empirical formula for the following

compound

28.7% K, 1.5% H, 22.8% P and 47.0% O

Calculate the empirical formula for the following

compound

43.6% phosphorus and 56.4% oxygen