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Chapter 10
Chemical Quantities
Measuring Matter
 Matter can be measured by 3 methods
 By count
 the number of CDs you have
 The number of atoms or molecules you have
 By mass or weight
 You buy vegetables by the pound
 The mass(g) of a compound or element you have
 By volume
 You buy soda in two liter bottles
 The number of milliliters of a substance you have
Measuring Matter
 Every measurement has a MAGNITUDE and
DIMENSION
 Magnitude is the numerical value
 Dimension is the unit of measurement
(gram, pound, etc)
Conversion factors
 Relationships between two numbers
 1 Dozen = 12 things
 1 Pair = 2 things
 1 Minute = 60 seconds
 1000 Meter= 1 kilometer
Conversion Factors continued
Can also be written as
fractions…
1 dozen
12 things
Dimensional Analysis
 Using conversion factors (T boxes )
to solve problems is called
dimensional analysis
Finding Mass from a Count
 What is the mass of 90 average-sized
apples if a dozen apples has a mass of
2.0kg?
Hint: use “T” box
90 apples
1 dozen
12 apples
2.0kg
1 dozen apples
= 15 kg or 15,000g
Practice Problems
 If 0.20 bushel is 1 dozen apples
and a dozen apples has a mass of
3.0 kg, what is the mass of 0.50
bushel of apples?
7.5 kg or 7500g
Assume 3.0 kg of apples is 1
dozen and that each apple has 8
seeds. How many apple seeds are
in 14kg of apples?
448 seeds
When determining quantities in
chemistry the method is the
same…..
You just use
different units !!!!!!!!
 dimensional analysis activity
Chemical Units
Comparing mass of molecules
-mass is measured in a.m.u.
(atomic mass units)
-Formula mass: the mass of the
atoms in the compound in amu
- round to the nearest hundredth.
Ex. Water
H
1.01
H
1.01
O
16.00
Formula Mass=
1.01
1.01
+16.00
18.02 a.m.u.
Finding formula mass:
1. Multiply # of atoms of each element
by its mass (amu)
2. Add them together
Ex. Fe2O3
Fe = 55.85 x 2 = 111.70
O = 16.00 x 3 = +48.00
= 159.70 amu
Calculate the formula mass for each of
the following:
AgNO3 =
KC2H3O2 =
Formula Mass of Hydrates
* Remember f.m. of hydrate includes
the mass of the water
1. Calculate the f.m. of compound
2. Calculate the f.m. of H2O x # of
molecules
3. Add together
Ex. BaCl2 2H2O
Step 1: Ba= 1 x 137.33
Cl = 2 x 35.45
=
137.33
= + 70.90
208.23
Step 2: H= 2 x 1.01 =
2.02
O= 1 x 16.00 = +16.00
Step 3:
18.02 x 2 =36.04
208.23 + 36.04 = 244.27a.m.u.
Ws. Chemical QuantitiesFormula Mass
But we have a problem…..
We can’t measure amu’s
in lab so scientists had
to come up with a
measurement we could
use.
The Mole
 Mole = 6.02 x 1023 particles of a substance –
could be atoms, molecules, or formula units
 Ex: A mole of hydrogen atoms is 6.02 x 1023
hydrogen atoms, a mole of paper is 6.02 x
1023 piece of paper
 6.02 x 1023 is known as Avogadro’s number-
Avogadro was an Italian scientist in the
1800’s helped clarify the difference between
atoms and molecules
A mole of any substance contains
6.02 x 1023 representative particles
How many atoms of carbon would
there be in a mole?
How many molecules of
water would there be in a
mole of water?
 mole is a unit
 TedEd
The Mass of a Mole (MOM)
of a substance =
formula mass in grams
Mass of a Mole
 The atomic mass of an element expressed in
grams is the mass of one mole of that
element.
 Example- 1 mole of carbon is 12.0 grams.
 The molar mass of any two elements contain
the same number of atoms
 Ex: a dozen apples – 12 apples

a dozen oranges – 12 oranges
Molar mass (MOM)
Formula Mass
1 atom
carbon
1 mole of carbon atoms
(6.02 x 1023atoms)
12.01 amu
12.01 grams
Would a mole of ping pong
balls have the same mass
as a mole of bowling balls?
Would a mole of carbon atoms have
the same mass as a mole of sodium
atoms?
 What would a mole of carbon
atoms weigh in grams?
 What about a mole of sodium
atoms?
Mass of a Mole of a Compound
 Find the number of grams of each element in the
compound, then add the masses together.
 Ex: Find the molar mass of water.
 Step 1- write down the formula H2O
 Step 2- determine masses of each element
2 H atoms x 1.0 g = 2.0 g H
1 O atom x 16.0 g = 16.0 g O
Step 3- add masses together 16.0 g O + 2.0 g
H = 18.0 g H2O
The molar mass of water is 18.0 g/mol
H
O
H
Cl
Cl
C
Cl
Cl
Which would have a higher mass….
a mole of water or a mole of
carbon tetrachloride?
We can use the molar mass of a
compound to convert between
moles and masses of compounds
Avogadro’s Number (6.02 x 1023)
-is the # of atoms in the molar mass of
an element.
12.01g Carbon = 6.02 x 1023 atoms
OR
- is the # of molecules in the
molar mass of a compound.
18.02g H2O = 6.02 x 1023 molecules
Finding the Mass of a Mole of a
compound
 The decomposition of hydrogen
peroxide (H2O2) provides sufficient
energy to launch a rocket. What is the
molar mass of hydrogen peroxide?
34.02g
Practice problems
 Find the molar mass (MOM) of PCl3.
137.32g/mol
 What is the molar mass(MOM) of
1.00 mol sodium hydrogen carbonate?
(NaHCO3)
84.01g
What if there is more than one
mole of the compound?
Mole to Mass Conversion
 Use the molar mass of an element or compound
to convert between the mass of a substance and
the moles of a substance
 Conversion factor 12 inches = 1 foot
3 feet = 1 yard
molar mass = 1 mole
ex: 18.0 g H2O = 1 mol H2O
Mole – Mass Relationship
 Use the molar mass of an element
or compound to convert between
the mass and moles of a
substance.
 ****Remember:
molar mass = 1mol
Let’s try them with
“T” boxes/conversion
factors…
 What is the mass of 3.4 moles of Mg?
 What is the mass of 23.9 moles of Sn?
 How many grams are in 18.1 moles of F?
 How many grams are in 98.5 moles of Zn?
 How many grams are in 2.7 x102mol Pb?
 Find the mass in grams of 4.52x10-3mol of
C20H42.
1.27g C20H42
 Calculate the mass in grams of 2.50
mol of Iron(II)hydroxide.
225g Fe(OH)2
 What is the mass of 3.0 mol of
NaCl?
176g
 What is the mass of 9.45 mol of
Aluminum oxide?
964g Al2O3
 Find the number of moles in 3.70 x10-1g of boron.
3.43 x 10-2 mol B
Calculate the number of moles in 75.0 g dinitrogen
trioxide.
0.987 mol N2O3
Review: Practice problems
Moles ↔ Mass
Which would have more atoms
a mole of carbon or a mole of
sulfur?
… both would have 6.02 x 1023 atoms
Converting # of atoms to Moles
How many moles of magnesium is
1.25 x 10 23 atoms of magnesium?
(hint: use “T” box)
2.08 x 10-1 mol Mg or 0.208 mol Mg
Practice Problems
 How many moles is 2.80 x 1024 atoms
of silicon?
4.65mol Si
 How many moles is 2.17 x 1023
representative particles of bromine?
0.360 mol Br2
Use “T” Boxes to calculate
these…..
 How many moles is 15.38 x 1023 atoms of Ni?
 How many moles is 2 x 1032 atoms of Ti?
 How many moles is 17.93 x 1018 atoms of Be?
 How many moles is 8.7 x 10
23
atoms of Ag?
H
O
H
Cl
Cl
C
Cl
Cl
Which would have more atoms…. a
mole of water or a mole of carbon
tetrachloride?
…so a mole of different compounds can
have different numbers of atoms
Converting Moles of Compound
to Number Of Atoms
 Is C an element or compound?
 Element- 1 mole is 6.02 x 1023 atoms
 Is CO2 an element or compound?
 Compound – 1 mole is 6.02 x 1023 molecules (or
formula units)
 Remember a mole is 6.02 x 1023 things !!!
Be careful when counting
atoms.
 Determine if you have an element
or a compound
 If a compound, the moles is the
# of molecules
 You then have to multiply by the
# of atoms in that compound
Converting Moles of Compound
to Number Of Atoms
 Is C an element or compound?
 Element- 1 mole is 6.02 x 1023 atoms
 Is CO2 an element or compound?
 Compound – 1 mole is 6.02 x 1023
molecules (or formula units)
 Remember a mole is 6.02 x 1023
things !!!
Try these - use “T” boxes !!!!!
 How many atoms in 2.3 moles of C?
 How many atoms in 2.3 moles of CO2?
 Propane is a gas used for heating and cooking. How
many atoms are in 2.12 mol of propane (C3H8)?
Hint: moles
molecules
1.40 x 1025 atoms
atoms
Practice Problems
 How many atoms are in 1.14 mol of
SO3?
2.75 x 1024 atoms
 How many moles are in 4.65 x 1024
molecules of NO2?
7.72 mol NO2
Ws. Converting Between Mass
mole and Number of Particles
HW.Ws. More Practice problems:
Chemical Quantities
Mole-Mass-Volume
Relationships
H
O
H
Cl
Cl
C
Cl
Cl
Which would have more molecules
in a mole….. water or carbon
tetrachloride?
… both would have 6.02 x 1023 molecules
H
O
H
Cl
Cl
C
Cl
Cl
Which would take up more room…..
a mole of water or a mole of
carbon tetrachloride?
….so a mole of different substances
can have different volumes.
Molar Volume
 The volumes of gases do not follow the pattern of
liquids and solids.
 Volume of gases change with change in
temperature and pressure
Cold O2
Hot O2
STP
 Standard Temperature and Pressure
 Temperature = 273K (0oC)
 Pressure =1 atm (101.3kPa)
 If no temperature or pressure are
given in a problem, assume the gas is
at STP
 A balanced equation, shows a gas at
STP
Molar Volume
 At STP 1 mol (6.02 x 10 23) any gas
occupies a volume of 22.4 Liters
Calculating Volume at STP
Calculating molar mass from density
1 mol of a gas at STP
 Occupies 22.4L
22.4L = molar volume of a gas
Calculating Volume at STP
Conversion factor is:
22.4L= 1 mol at STP
Ex: Determine the volume in
liters of 0.60 mol of SO2 gas
at STP
 13L SO2
 Ex: sulfur dioxide is a gas produced
by burning coal. It is an air pollutant
and one of the causes of acid rain.
Determine the volume, in liters, of
0.60 moles of sulfur dioxide gas at
STP.
13 L does this make sense?
Practice Problems
What is the volume of 3.20 x 10-3mol
of CO2(g) at STP?
 7.17 x10-2L CO2
 What is the volume of 3.70 mol of
N2(g) at STP?
 82.9LN2
More Practice
At STP, what volume does
1.25 mol He gas occupy?
28.0L He
At STP what volume does
0.335mol C2H6 gas occupy?
7.50L C2H6
Ws. Chemical Quantities (boxes)
Calculating Molar Mass from
Density
 Different gases have different densities.
 ***Remember density unit is g/L
 Ex. helium vs. nitrogen
 To calculate the molar mass of a gas you need:
Density of gas at STP and volume of gas at STP
 Conversion factor 22.4L
1 mol
Practice problems
 The density of a gaseous compound containing
carbon and oxygen is 1.964g/L at STP.
the molar mass of the compound?
 D= grams
liter
 44g/mol
1.964 g
22.4liter
1 liter 1 mole
What is
More Practice
 A gaseous compound of sulfur and
oxygen which is linked to the
formation of acid rain, has a
density of 3.58g/L. What is the
molar mass of this gas?
 80.2g/mol
Each stoppered flask below contains 2 liters of a gas at STP.
Does each gas sample have the same ……
(explain each- * hint set up “T” boxes)
(a) mass ?
(b) density ?
(c) number of molecules ?
(d) number of atoms ?
1.00 mol
22.4 L
22.4L
1.00mol
Volume of Gas (STP)
mole
Mass
Representative
Particles
Percent Composition
Percent Composition
 percent by mass
% composition = Mass of element x 100%
mass of compound
When you see %, think……
Part
X
100
=
%
Whole
Sample Problem
 Propane (C3H8) is one of the lighter compounds
obtained from petroleum. Calculate the percent
composition of propane. (when they ask for %
composition, they want the % of each thing in it)
Mass of C
X 100
%C=
mass of propane
= 81.8%
Mass of H
X 100
%H=
mass of propane
=18%
Try this…..
Calculate the % Nitrogen in
the following compound
Ammonium nitrate (NH4NO3)
Ammonium nitrate: N= 35%
Don’t forget about the
Law of Conservation of
Mass (matter)
Sample Problem
 When a 13.60g sample of a compound
containing only magnesium and oxygen
is decomposed, 5.40g of oxygen is
obtained. What is the percent
composition of this compound?
% Mg = Mass of Mg
X 100 =60.3%
mass of compound
Mass
of
O
X 100
% O=
mass of compound
= 39.7%
** % of elements should add up to 100%
Practice Problems
 A compound is formed when 9.03g Mg
combines completely with 3.48g N. What
is the % composition of this compound?
 72.2%Mg and 27.8% N
 When a 14.2g sample of mercury(II) oxide
is decomposed into its elements by heating,
13.2g Hg is obtained. What is the %
composition of the compound?
 7.0%O and 93.0% Hg
Watch the Hydrates !!!
CuSO4 5H20
Practice :% composition from the
formula
 Ws. Percent Composition
Percent composition as a
conversion factor
 Multiply the mass of the compound
by a conversion factor based on the
percent composition in the
compound.
10.3
The Percent Composition of a
Compound
 Percent Composition from the Chemical Formula
 Ex: How many grams of hydrogen are
are contained in a 100 gram sample of of
propane? (the formula for propane is
C3H8?
10.3
The Percent Composition of a
Compound
 Propane (C3H8) is 81.8% carbon and 18% hydrogen. You can
calculate the mass of carbon and the mass of hydrogen in an
82.0 g sample of C3H8.
Empirical Formula vs. Molecular
Formula
Molecular formula – the actual # of
atoms in the compound
Ex.
C6H12O6 glucose
Empirical Formula – The simplest formula
in whole #’s
Ex.
CH2O
glucose
Empirical Formulas
 Empirical formula- lowest whole number
ratio of atoms of the elements in a
compound
 Ex. H2O2 hydrogen peroxide
 Empirical formula = HO
 Ex. H2O water
 Empirical formula and molecular formula are the
same
To Calculate Empirical
Formula
% to mass
(assume you have 100g)
Mass to moles
Divide by small
Multiply ‘til whole
10.3
Empirical Formulas
 Ethyne (C2H2) is a gas
used in welder’s torches.
Styrene (C8H8) is used in
making polystyrene.
 These two compounds
of carbon have the same
empirical formula (CH)
but different molecular
formulas.
If masses are given… just
start with “ Mass to mole”
step
Ws. Determining the Empirical
Formula for Compounds
What do these have in
common?
 CH2O
 C2H4O2
 C4H8O4
 C6H12O6
What is different about them ?
10.3
Molecular Formulas
Calculating empirical formula
from % composition
 Ex: Cisplatin is the common name for a
platinum compound used to treat
cancerous tumors has the composition (in
mass percent) of 65.02% Pt, 9.34% N, and
23.63% Cl. Calculate the empirical formula
for cisplatin.
 .
 1. determine how many grams of each
element are present in a 100 g sample of a
compound. (convert % to grams)
 Ex: there is 65.02 grams of platinum per 100 g of
compound, 9.34 g N, 2.02 g H.
 2. Convert mass to moles of each using the
molar mass of the elements
 Ex. 0.3333 mol Pt
0.667 mol N
2.00 mol H
0.6666 mol Cl
 Step 3 : Divide through by the element with
the lowest number of moles
 0.3333 mol Pt
0.6666 mol Cl
0.667 mol N
2.00 mol H
If formula (molecular) mass is
given….
 Calculate empirical formula
 Calculate the molar mass of the empirical formula
 Divide the formula (molecular) mass by the
empirical molar mass to see how many times you
need to multiply the subscripts.
A compound contains 40% carbon, 6.6%
hydrogen and 53.4% oxygen. It has a
molecular mass of 90 grams
 What is the empirical formula?
 What is the molecular formula?
Ws. Molecular and Empirical
Formulas #1-7
Ws. Molecular and Empirical
Formulas #7-13
Calculation of molecular formula
10.3
Molecular Formulas
 Molecular Formulas
 How does the molecular formula of a
compound compare with the
empirical formula?
 The molecular formula of a
compound is either the same as its
experimentally determined
empirical formula, or it is a simple
whole-number multiple of its
empirical formula.
10.12
10.12
Section Quiz.
 1. Calculate the
percent by mass of carbon
in cadaverine, C5H14N2, a compound
present in rotting meat
 67.4% C
 58.8% C
 51.7% C
 68.2% C
10.3 Section Quiz.
 2. Which of the following is NOT an empirical
formula?
 NO2
 H 2N
 CH
 C3H6
Section Quiz.
 3. Determine the molecular formula of a
compound that contains 40.0 percent C, 6.71
percent H, and 53.29 percent O and has a
molar mass of 60.05 g.
 C2H4O2
 CH2O
 C2H3O
 C2H4O
 B,d,a