Section 3.4

1
Section 3.4Counting Molecules
So the number of molecules affects pressure of an
airbaghow do we count molecules?
2
What is a Mole? Ted Ed video

• http//ed.ted.com/lessons/daniel-dulek-how-big-is-
  a-mole-not-the-animal-the-other-one

3
What is a mole?
Mole metric unit for counting
We use it just like we use the terms dozen and
ream!
The only acceptable abbreviation for mole is
molnot m!!
4
What is a counting unit?
Youre already familiar with one counting unita
dozen
A dozen 12
Dozen
12
A dozen doughnuts
12 doughnuts
A dozen books
12 books
A dozen cars
12 cars
5
What cant we count atoms in dozens?
Atoms and molecules are extremely small
We use the MOLE to count particles
6
A mole 6.02 ? 1023 particles (called
Avogadros number)
6.02 ? 1023 602,000,000,000,000,000,000,000
mole
6.02 ? 1023
1 mole of doughnuts
6.02 ? 1023 doughnuts
1 mole of atoms
6.02 ? 1023 atoms
1 mole of molecules
6.02 ? 1023 molecules
This number was named after Amadeo Avogadro. He
did not calculate it!
7
FUNNY!
8
Representative Particles

• Remember, matter is broken down into either
  SUBSTANCES or mixtures
• Substances are broken down into either ELEMENTS
  or COMPOUNDS

Type of Matter Example Representative Particle
Element Fe Atom
Ionic Compound NaCl Formula Unit
Covalent Compound CO2 Molecule
9
Example Particles MolesUse the conversion
factor (1 mol 6.02 x 1023) particles to convert
Example 1 How many molecules of water are in
1.25 moles?
10
Example Molecules Moles
Example 1 How many molecules of water are in
1.25 moles?
1 mol 6.02?1023 molecules
1.25 mol H2O
Molecules H2O
6.02 ? 1023
_______ molecules H2O
7.53?1023
1
mol H2O
11
Lets Practice 2
Example How many moles are equal to 2.8 1022
formula units of KBr?
12
Lets Practice 2
1 mol 6.02?1023 formula units
Example How many moles are equal to 2.8 1022
formula units KBr?
1
2.8 1022 formula units
mole
_______ moles
0.047
6.02 ? 1023
Formula units
13
Lets Practice 3
Example How many atoms are equal to 3.56 moles
of Fe?
14
Lets Practice 3
Example How many atoms are equal to 3.56 moles
of Fe?
1 mol 6.02?1023 molecules
6.02 x 10 23
3.56 moles Fe
atoms
_______ atoms
2.14 x 1024
1
moles
15
Molar Mass
Molar Mass The mass for one mole of an atom or
molecule.
Other terms commonly used for the same
meaning Molecular Weight Molecular Mass Formula
Weight Formula Mass
16
Molar Mass for Elements
The average atomic mass grams for 1 mole
Average atomic mass is found on the periodic table
Element
Mass
1 mole of carbon atoms (C)
12.01 g
1 mole of oxygen atoms (O2)
16.00 g x 2 32.00 g O2
1 mole of hydrogen atoms (H2)
1.01 g x 2 2.02 g H2
Unit for molar mass g/mole or g/mol
17
Molar Mass for Compounds
The molar mass for a molecule the sum of the
molar masses of all the atoms
18
Calculating a Molecules Mass
To find the molar mass of a molecule
1
Count the number of each type of atom
Find the molar mass of each atom on the periodic
table
2
3
Multiply the of atoms by the molar mass for
each atom
4
Find the sum of all the masses
19
Example Molar Mass
Example Find the molar mass for CaBr2
20
Example Molar Mass
1
Count the number of each type of atom
Example Find the molar mass for CaBr2
Ca
1
Br
2
21
Example Molar Mass
2
Find the molar mass of each atom on the periodic
table
Example Find the molar mass for CaBr2
Ca
1
40.08 g/mole
Br
2
79.90 g/mole
22
Example Molar Mass
3
Multiple the of atoms ? molar mass for each atom
Example Find the molar mass for CaBr2
?
Ca
1
40.08 g/mole

40.08 g/mole
?
Br
2
79.90 g/mole

159.80 g/mole
23
Example Molar Mass
4
Find the sum of all the masses
Example Find the molar mass for CaBr2
?
Ca
1
40.08 g/mole

40.08 g/mole

?
Br
2
79.91 g/mole

159.80 g/mole
199.88 g/mole
1 mole of CaBr2 199.90 g
24
Example 2 If you see a Parentheses in the
Formula
Be sure to distribute the subscript outside the
parenthesis to each element inside the
parenthesis.
Example Find the molar mass for Sr(NO3)2
25
Example 2 Molar Mass Parenthesis
Be sure to distribute the subscript outside the
parenthesis to each element inside the
parenthesis.
Example Find the molar mass for Sr(NO3)2
?
Sr
1
87.62 g/mole

87.62 g/mole
?
N
2
14.01 g/mole
28.02 g/mole

?

96.00 g/mole
6
16.00 g/mole

O
211.64 g/mole
1 mole of Sr(NO3)2 211.64 g
26
Lets Practice 3
Example Find the molar mass for Al(OH)3
27
Lets Practice 2
Be sure to distribute the subscript outside the
parenthesis to each element inside the
parenthesis.
Example Find the molar mass for Al(OH)3
?
Al
1
26.98 g/mole

26.98 g/mole
?
O
3
16.00 g/mole
48.00 g/mole

?

3.03 g/mole
3
1.01 g/mole

H
78.01 g/mole
1 mole of Al(OH)3 78.01 g
28
Using Molar Mass in Conversions
29
Example Moles to Grams
Example How many grams are in 1.25 moles of
water?
30
Example Moles to Grams
When converting between grams and moles, the
molar mass is needed
Example How many grams are in 1.25 moles of
water?
1 mole H2O molecules 18.02 g
1.25 mol H2O
g H2O
18.02
_______ g H2O
22.5
mol H2O
1
31
Example Grams to Moles
Example How many moles are in 25.5 g NaCl?
32
Example Grams to Moles
Example How many moles are in 25.5 g NaCl
1 moles NaCl molecules 58.44 g
25.5 g NaCl
mol NaCl
1
g NaCl
58.44
____ moles NaCl
.436
33
Example Grams to Molecules
Example How many formula units are in 25.5 g
NaCl?
34
Example Grams to Moles
Example How many formula units are in 25.5 g
NaCl
1 moles NaCl formula units 58.44 g
25.5 g NaCl
mol NaCl
1
6.02 x 1023 FUs
g NaCl
58.44
1 mol NaCl
____ FUs NaCl
2.63 x 1023
35
Percent Composition

• Defined as the percent by mass of each element in
  a compound
• Steps to Finding Percent Composition
• Add up the mass of each element within the
  compound to get the mass of the compound.
• Divide each elements mass by the mass of the
  compound.
• Multiply by 100

composition mass of element x 100
mass of compound
36
Percent Composition by Mass of Air
37
Example Calculate the composition of each
element in calcium carbonate.
CaCO3
Molar mass 100.09 g
C 12.01/100.09 x 100 12.00 Ca
40.08/100.09 x 100 40.04 O 48.00/100.09 x
100 47.96
38
Example What is the of each element in a
compound that contains 29.00g Ag and 4.30g S
only?
Total mass of compound 33.30 g
Ag 29.00/33.30 x 100 87.09 S
4.30/33.30 x 100 12.9
39
Hydrates

• A HYDRATE is an ionic compound with water trapped
  
• in its crystal.
• Examples are
• CuSO4 5H2O MgSO4 7 H2O CoCl2
  H2O
• Heating a hydrate removes the water and leaves
• behind just the salt which is called the
  anhydrate.

40
Example What is the water in the hydrate,
CuCl2 ? 2H2O
Molar mass of hydrate 170.48 g water
36.04/170.48 x 100 21.14
41
http//group.chem.iastate.edu/Greenbowe/sections/p
rojectfolder/flashfiles/stoichiometry/empirical.ht
ml
Heating of A Hydrate Animation Calculating the
experimental composition of water in a hydrate.
42
Empirical Formula

• A chemical formula showing the simplest whole
  number ratio of moles of elements (subscipts)
• Hydrogen Peroxide has an actual formula
  (molecular formula) of H2O2 but an
• empirical formula of HO

43
How to Calculate Empirical Formula

• RHYME Percent to Mass
• Mass to Mole
• Divide by Small
• Multiply til Whole
• Assume 100 grams of the sample of compound.
  Switch the percent sign to grams
• Convert each elements mass into moles.
• Divide each elements mole amount by the smallest
  mole amount in the entire problem. The answer is
  the subscript of the element within the compound.
• OPTIONAL If mole ratio is not within .1 of a
  whole number, multiply each amount by the
  smallest whole number that will produce either a
  whole number itself or a number within .1 of a
  whole number.

44
Example What is the empirical formula for 40.05
S and 59.95 O?

• Switch the percent sign to grams convert each
  elements mass into moles
• 40.05 g S / 32.01g 1.250 mol S
• 59.95 g O / 16.00 g 3.747 mol O

• Divide each elements mole amount by the smallest
  mole amount in the entire problem.
• 1.250 mol S 1 3.747 mol O 2.99 3
• 1.250 mole 1.250 mol

S1O3 ? SO3
45
Example What is the empirical formula for 43.64
P and 56.36 O?

• Switch the percent sign to grams convert each
  elements mass into moles
• 43.64 g P / 30.97g 1.409 mol S
• 56.36 g O / 16.00 g 3.522 mol O

• Divide each elements mole amount by the smallest
  mole amount in the entire problem.
• 1.409 mol S 1 3.522 mol O 2.49 ? 3
• 1.409 mole 1.409 mol

• If mole ratio is not within .1 of a whole number,
  multiply each amount by the smallest whole number
  that will produce either a whole number itself or
  a number within .1 of a whole number.
• 1 x 2 2 2.49 x 2
  4.998 5

P2O5
46
Molecular Formula

• Is the ACTUAL, true formula of the compound.
• They are usually multiples of their empirical
  formula
• N2O4 is the molecular formula the empirical
  formula is NO2
• Notice that the molecular formula is 2 times
  larger than the empirical formula

47
Molecular Formula
48
How to Calculate Molecular Formula
1. You need to find the empirical formula and
calculate its molar mass. Call this empirical
formula mass EFM. 2. Find the mass of the actual
formula which will most likely be given to you in
grams. Call this molecular formula mass MFM. 3.
Divide the MFM by the EFM to get a factor. 4.
Multiply the factor by the empirical formula to
get the MOLECULAR FORMULA
49
Example What is the molecular formula of a
compound whose empirical formula is CH4N and the
molecular mass is 60.12 g/mol?
1. Empirical Formula Mass (EFM) 12.01 4.04
14.01 30.06 g
2. Molecular Formula Mass (MFM) 60.12 g
3. 60.12 / 30.06 2
4. 2(CH4N) C2H8N2
50
Section 3.5Gas Behavior
How does the behavior of gases affect airbags?
What is PRESSURE?
Force of gas particles running into a surface.
51
Pressure is measured by a Barometer
52
Pressure and Moles ( of Molecules)
If pressure is molecular collisions with the
container

• As number of molecules increases, there will be
  more molecules to collide with the wall
• Collisions between molecules and the wall
  increase
• Pressure increases

As of moles increase, pressure increases
Think about blowing up a balloon!
53
of Gas Particles vs. Pressure
54
Pressure Volume
If pressure is molecular collisions with the
container

• As volume increases, molecules can travel farther
  
• before hitting the wall
• Collisions between molecules the wall decrease
• Pressure decreases

As volume increases, pressure decreases.
Think about how your lungs work!
http//www.youtube.com/watch?vq6-oyxnkZC0
55
What is Temperature?
Temperature measure of the average kinetic
energy of the molecules
Energy due to motion
(Related to how fast the molecules are moving)
As temperature increases, Average Kinetic Energy
Increases and Molecular motion increases
56
Pressure and Temperature
If temperature is related to molecular motion
and pressure is molecular collisions with the
container

• As temperature increases, molecular motion
  increases
• Collisions between molecules the wall increase
• Pressure increases

As temperature increases, pressure
increases
57
Volume and Temperature
If temperature is related to molecular motion
and volume is the amount of space the gas
occupies

• As temperature increases, molecular motion
  increases
• molecules will move farther away from each other
• Volume increases

As temperature increases, volume increases
Think of liquid nitrogen and the balloon.
http//www.youtube.com/watch?vQEpxr
GWep4E
58
Pressure In Versus Out
A container will expand or contract until the
pressure inside equals atmospheric pressure
outside
A bag of chips is bagged at sea level. What
happens if the bag is then brought up to the top
of a mountain.
Example
The internal pressure of the bag at low altitude
is high At high altitude there is lower pressure
Higher pressure
Lower pressure
Lower pressure
The internal pressure is higher than the external
pressure. The bag will expand in order to reduce
the internal pressure.
59
When Expansion Isnt Possible
Rigid containers cannot expand
An aerosol can is left in a car trunk in the
summer. What happens?
Example
The temperature inside the can begins to rise. As
temperature increases, pressure increases.
Can Explodes!
Higher pressure
Lower pressure
The internal pressure is higher than the external
pressure. The can is rigidit cannot expand, it
explodes!
60
Air Pressure Crushing Cans
http//www.csun.edu/scied/4-discrpeant-event/the_c
an_crush/index.htm
61
Air Pressure Crushing Cans
http//www.youtube.com/watch?vZz95_VvTxZM
Another cool video http//www.youtube.com/watch?v
JsoE4F2Pb20
62
Kinetic Molecular Theory(KMT)

• explains gas behavior based upon the motion of
  molecules
• based on an ideal gas
• IDEAL gases are IMAGINARY gases that follow the
  assumptions of the KMT

63
Assumptions of the KMT
All gases are made of atoms or molecules that are
in constant, rapid, random motion
1
The temperature of a gas is proportional to the
average kinetic energy of the particles
2
Gas particles are not attracted nor repelled from
one another
3
All gas particle collisions are perfectly elastic
(no kinetic energy is lost to other forms)
4
The volume of gas particles is so small compared
to the space between the particles, that the
volume of the particle itself is insignificant
5
64
So what is a REAL gas?
Real gases, (like nitrogen), will eventually
condense into a liquid when the temperature gets
too low or the pressure gets too high BECAUSE
Assumption 3
Gas particles do have attractions and repulsions
towards one another
Assumption 5
Gas particles do take up space
65
Real Gases Deviate from Ideal Gas Behavior when
at high pressure

• The gas molecules are compressed making the
  volume they take up more significant than if they
  were spread out

66
(No Transcript)
67
Real Gases Deviate from Ideal Gas Behavior when
at low temperature.

• The lower kinetic energy causes the molecules to
  move slower and ATTRACTIVE FORCES that really
  exist start to take effect
• ---------------------------
• Polar gases (HCl) deviate more than nonpolar
  gases (He or H2

68
At Lower Temperature
69
Gas Movement Effusion vs Diffusion
Effusion gas escapes from a tiny hole in the
container
Effusion is why balloons deflate over time!
70
Diffusion gas moves across a space from high to
low concentration
Diffusion is the reason we can smell perfume
across the room
71
Effusion, Diffusion Particle Mass
How are particle size (mass) and these concepts
related?

• As particle size (mass) increases, the particles
  move
• slower
• it takes them more time to find the hole or to go
  
• across the room

As mass of the particles increases, rate of
effusion and diffusion is lowered.
72
Rate of Diffusion Particle Mass
H2
Watch as larger particles take longer to get to
your nose
CO2
73
Section 3.6Gas Laws
How can we calculate Pressure, Volume and
Temperature of our airbag?
74
Pressure Units
Several units are used when describing pressure
Unit
Symbol
atmospheres
atm
Pascals, kiloPascals
Pa, kPa
millimeters of mercury
mm Hg
pounds per square inch
psi
1 atm 101300 Pa 101.3 kPa 760 mm Hg 14.7
psi
75
Conversions Between Different Pressure Units

• 1 atm 760 mmHg 101.3 kPa
• Examples
• Convert 654 mm Hg to atm
• Convert 879 mm Hg to kPa
• Convert 15.6 atm to kPa

.861 atm
654 mmHg x 1atm
760 mmHg
879 mmHg x 101.3 Kpa
760 mmHg
1.16 Kpa
15.6 atm x 101.3 Kpa
1atm
1580 Kpa
76
Temperature Unit used in Gas Laws
Kelvin (K) temperature scale with an absolute
zero
Temperatures cannot fall below an absolute zero

• Examples
• Convert 15.6 C into K
• 2. Convert 234 K into C

15.6 273 K
288.6 ? 289 K
C 273 234
-39 C
77
Standard Temperature Pressure (STP)

• the conditions of
• 1 atm (or the equivalent in another unit)
• 0C (273 K)

Problems often use STP to indicate
quantitiesdont forget this hidden information
when making your list!
78
GAS LAWS Before and After
This section has 5 gas laws which have before
and after conditions.
For example
P Pressure V Volume TTemperature n
moles(molecules)
1 initial amount 2 final amount
79
Boyles Law
Pressure Increases as Volume Decreases
80
Boyles Law
Volume Presssure are INVERSELY proportional
when temperature and moles are held constant
P pressure V volume
The two pressure units must match and the two
volume units must match!
Example
A gas sample is 1.05 atm when at 2.5 L. What
volume is it if the pressure is changed to 0.980
atm?
81
Boyles Law
The two pressure units must match the two
volume units must match!
A gas sample is 1.05 atm when 2.5 L. What volume
is it if the pressure is changed to 0.980 atm?
Example
P1 1.05 atm V1 2.5 L P2 0.980 atm V2 ? L
V2 2.7 L
82
Boyles Law Graph
83
Charles Law
Volume Increases as Temperature Increases
84
Charles Law
Volume Temperature are DIRECTLY proportional
when pressure and moles are held constant.
V Volume T Temperature
The two volume units must match temperature
must be in Kelvin!
Example
What is the final volume if a 10.5 L sample of
gas is changed from 25?C to 50?C?
Temperature needs to be in Kelvin!
V1 10.5 L T1 25?C V2 ? L T2 50?C
25?C 273 298 K
50?C 273 323 K
85
Charles Law
The two volume units must match temperature
must be in Kelvin!
What is the final volume if a 10.5 L sample of
gas is changed from 25?C to 50?C?
Example
V1 10.5 L T1 25?C V2 ? L T2 50?C
298 K
323 K
V2 11.4 L
86
Charles Law Graph
87
Gay-Lussacs Law
Temperature decreases as Pressure decreases
88
Gay-Lussacs Law
Pressure temperature are DIRECTLY proportional
when moles and volume are held constant
P Pressure T Temperature
The two pressure units must match and temperature
must be in Kelvin!
A sample of hydrogen gas at 47?C exerts a
pressure of .329 atm. The gas is heated to 77?C
at constant volume and moles. What will the new
pressure be?
Example
Temperature needs to be in Kelvin!
P1 .329 atm T1 47?C P2 ? atm T2 77?C
47?C 273 320 K
77?C 273 350 K
89
Gay-Lussac Law
Example
A sample of hydrogen gas at 47?C exerts a
pressure of .329 atm. The gas is heated to 77?C
at constant volume and moles. What will the new
pressure be?
P1 .329 atm T1 47?C P2 ? atm T2 77?C
320 K
350 K
P2 .360 atm
90
Gay Lussac Law Graph
91
Avogadros Law
Moles and Volume are directly proportional when
temp. pressure are held constant
V Volume n of moles of gas
The two volume units must match!
Example
A sample with 0.15 moles of gas has a volume of
2.5 L. What is the volume if the sample is
increased to 0.55 moles?
92
Avogadros Law
The two volume units must match!
A sample with 0.15 moles of gas has a volume of
2.5 L. What is the volume if the sample is
increased to 0.55 moles?
Example
n1 0.15 moles V1 2.5 L n2 0.55 moles V2 ?
L
V2 9.2 L
93
Combined Gas Law
P Pressure V Volume n of moles T
Temperature
Each pair of units must match and temperature
must be in Kelvin!
Example
What is the final volume if a 15.5 L sample of
gas at 755 mmHg and 298 K is changed to STP?
94
Combined Gas Law
P Pressure V Volume T Temperature
Moles is not mentioned so remove it from equation!
What is the final volume if a 15.5 L sample of
gas at 755 mmHg and 298K is changed to STP?
Example
P1 755 mmHg V1 15.5 L T1 298 K P2
760mmHg V2 ? L T2 273 K
STP is standard temperature (273 K) and pressure
(1 atm)
V2 14.1 L
95
Why you really only need 1 of these
The combined gas law can be used for all before
and after gas law problems!
For example, if volume is held constant, then
and the combined gas law becomes
96
Transforming the Combined Law
Watch as variables are held constant and the
combined gas law becomes the other 3 laws
Hold pressure and temperature constant
Avogadros Law
Hold moles and temperature constant
Boyles Law
Hold pressure and moles constant
Charles Law
97
Daltons Law
98
Daltons Law

• Each gas in a mixture exerts its own pressure
  called a partial pressure P1, P2.
• Total Pressure PT

• Example A gas mixture is made up of oxygen(2.3
  atm) and nitrogen(1.7 atm) gases. What is the
  total pressure?

PT 2.3 atm 1.7 atm
4.0 atm
99
Modified Daltons Law
When a gas is Collected over water, the total
pressure of the mixture collected is a
combination of water vapor and the gas you are
collecting!
100
Modified Daltons Law

• Example What is the pressure of the water vapor
  if the total pressure of the flask is 17.5 atm
  and the pressure of the oxygen gas is 16.1 atm?

17.5 16.1 atm PH2O
1.4 atm
101
The Ideal Gas Law (anAT NOWequation)
The volume of a gas varies directly with the
number of moles and its Kelvin temperature
P Pressure V Volume n moles R Gas Law
Constant T Temperature
There are three possibilities for R!
Choose the one with units that match your
pressure units!
Volume must be in Liters when using R to allow
the unit to cancel!
102
The Ideal Gas Law
Example
A sample with 0.55 moles of gas is at 105.7 kPa
and 27C. What volume does it occupy?
103
The Ideal Gas Law
The Ideal Gas Law does not compare situationsit
describes a gas in one situation.
Example
A sample with 0.55 moles of gas is at 105.7 kPa
and 27C. What volume does it occupy?
n 0.55 moles P 105.7 kPa T 27C 273 300
K V ? R 8.31 L kPa / mole K
Chosen to match the kPa in the P above
V2 13 L
104
The Ideal Gas Law
Example 2
What mass of hydrogen gas in grams is contained
in a 10.0 L tank at 27C and 3.50 atm of pressure?
n ? P 3.50 atm T 27C 273 300 K V
10.0 L R .0821 L atm /mole K
Chosen to match the atm in the P above
n 1.42 mol ?
1.42 mol x 2.02 g 2.87 g 1
mol