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
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