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1
Lecture 9 Professor Hicks
Inorganic Chemistry (CHE151)
Properties of gases
Three factors affect the properties of gases
1) P = pressure
2) T = Kelvin temperature
3) V = volume
4) n = number of moles of gas
2
Pressure
• Force divided by area
• Force visualized as all matter piled up on
top of a surface
Calculate the pressure due to a 150 pound man
if his feet have a total area of 40 square inches
pressure = 150 pounds
40 square inches = 3.75 lbs/in2
force
area
Pressure on earth
pressure
1.0 atm
Column of air above
every square inch
weighs 14.7 pounds
1.0 atm = 14.7 psi
Earth
Earth’s atmosphere
Space
3
Scuba diving space
Earth’s atmosphere
Water
pressure
1.0 atm
the 10 m column
of water above
every square inch
weighs 14.6 pounds 10
meters
Column of air above
every square inch
weighs 14.7 pounds
pressure
1.0 atm
+
= 2 atm!
Units of pressure
1) Pounds per square inch (psi)
2) Atmospheres (atm) average P on earth = 1 atm
3) Millimeters of mercury (mm Hg) aka torr
pressure on earth
pressure
1.0 atm
Earth
Earth’s atmosphere
space
column
of air
Column of
mercury
metal
760 mm
A 760 mm column Hg
creates same force as
an air column of same
area that goes from
earth up to space
Mercury metal (Hg) is
very dense (13.6 g/ml)
Column
of air
from earth
to space
1.0 atm = 760 mm Hg
4
Barometer
vacuum P = 0
liquid
mercury (Hg)
or water
atmospheric = Patm
pressure
P mercury column 2
= PHg2
P mercury column 1
= PHg1
h=PHg2 – PHg1
Patm + PHg1 = PHg2
Patm = PHg2 – PHg1
PHg2
Patm
+ PHg1
Patm = h
Average day on earth
h = 760 mm mercury
1.0 atm = 760 mm Hg
Water has a density 1/13th that of mercury
barometer using water will have h = 13 x 760 mm
h = height difference
between columns
measured with a ruler
Used to measure the
atmospheric pressure
Manometer
Liquid
mercury (Hg)
or water
Atmospheric = Patm
pressure
+ PHg1
Ps Patm
+ PHg2
Pgas + PHg1 = Patm + PHg2
P mercury 1
= PHg1
Unknown P
of sample
= Psam
P mercury 2
= PHg2
Pgas = Patm + PHg2 - PHg1
h Pgas = Patm + h
Used to measure
unknown pressures
Patm is found with
a barometer
5
Empirical gas laws (discovered by experimentation)
• Charles’ Law
• Boyles Law
= constant V
T
Applies to a sample of gas
kept at constant temperature
Applies to a sample of gas
kept at constant pressure
(T must be in Kelvins)
PV = constant
Boyles Law PV = constant Applies to a sample of gas
kept at constant temperature
The deepest part of the ocean is known as the Mariana’s Trench.
The depth is 11,000 meters! This produces a pressure of 1101 atm!
Estimate the volume of a 2.0 liter soda bottle filled with air on the earth’s
surface if it was brought to the bottom of the Mariana’s Trench without
changing its temperature.
PV = constant (Boyles Law) On earths surface, for this sample of air
the Boyles law constant is
PV = 2.0 liters x 1.0 = 2.0 lit*atm 1101 atm x V = 2.0 lit*atm
V= 2/1100 lit = 0.0018 liter
6
Empirical gas laws Charles’ Law
= constant V
T
applies to a sample of gas
kept at constant pressure
(T must be in Kelvins)
Liquid nitrogen boils at -196 C. It is commonly used to
achieve low temperatures in the laboratory. If a balloon
is filled with 1.55 liters of air at 25 C, what volume will
the balloon shrink to if it is placed in a liquid nitrogen bath?
V/T = constant (Charles law)
the Charles law constant under the lab conditions is
V/T = 1.55 liters / 298 K
= 5.20 x 10-3 lit / K
V/T = 5.20 x 10 -3
Always express temperature in
Kelvin's when using gas laws
V/77 = 5.20 x 10 -3
K= 273 + C K= 273 + 25 = 298
K= 273 + -196 = 77 K
V = 77 x 5.20 x 10 -3
V = 0.400 liters
at 77 K
Charles’ Law and Kelvin
Temperature scale V = constant*T
Volume cannot become negative
T = -273 C
Absolute zero!
gas sample 1
gas sample 2
gas sample 3
extrapolate to
V=0
Find T = -273 C
equation for a line
y = mx + b
m = Charles’ law
constant
b = 0
Basis of the Kelvin temperature scale
samples of gas taken and cooled.
Volume measured at each
temperature
0
8
5.19 A gas occupying a volume of 725 mL at a pressure
of 0.970 atm is allowed to expand at constant
temperature until its pressure reaches 0.541 atm.
What is its final volume?
5.23 A 36.4-L volume of methane gas is heated from
25°C to 88°C at constant pressure. What is the final
volume of the gas?
9
5.30 Why is the density of a gas much lower than that of
a liquid or solid under atmospheric conditions? What
units are normally used to express the density of
gases?
Ideal Gas Law PV = nRT
• R is called the universal gas constant
• R replaces all constants in the named laws
R = 8.314
Joules
mole K
= 0.0821 liter*atm
mole K
SI Units
most
used
SI unit is not used as much when actually working with gases
since SI unit V is the m3 which is too big to use in the lab
10
divide
stoichiometric
number
mass
compound
moles of
formula units,
molecules,
atoms,
or ions
number
formula units,
molecules,
atoms,
or ions
multiply
molar
mass
divide
molar
mass
multiply
molar
mass
divide
molar
mass
divide
Avogadro's
number
multiply
Avogadro's
number
divide
Avogadro's
number
multiply
Avogadro's
number
equivalents
volume
n= PV
RT V= nRT
P
A sample of nitrogen gas kept in a container of
volume 1.6 L and at a temperature of 36°C exerts
a pressure of 4.8 atm. Calculate the number of
moles of gas present.
11
Given that 5.5 moles of carbon monoxide gas are
present in a container of volume 23.4 L, what is the
pressure of the gas (in atm) if the temperature is
166°C?
.
A certain amount of gas at 37°C and at a pressure
of 0.60 atm is contained in a glass vessel. Suppose
that the vessel can withstand a pressure of 3.00
atm. How high can you raise the temperature of the
gas without bursting the vessel?
12
Molar Mass from Ideal Gas Law
• Molar Mass units grams/mole
• If you can measure a mass and a # moles
their ratio is the substance’s molar mass!
• Molar Mass = mass sample / # moles
• evaporate a liquid gas
• If you can measure P, V, T you can
calculate n!
• Condense the vapor and measure the
mass of the liquid
A quantity of gas weighing 14.20 g at 1482 torr and
44°C occupies a volume of 5.40 L. What is its molar
mass?
13
N2
H2O O2 N2
H2O
O2
N2
H2O
O2
N2
H2O
N2
N2
N2
N2
Air = N2 + O2 + H2O
Pressure each gas would
have by itself (same T and V)
PN2 PO2 PH2O
N2
H2O O2 N2
H2O
O2
N2
H2O
O2
N2
H2O
N2
N2
N2
N2
N2
H2O O2 N2
H2O
O2
N2
H2O
O2
N2
H2O
N2
N2
N2
N2
N2
H2O O2 N2
H2O
O2
N2
H2O
O2
N2
H2O
N2
N2
N2
N2
Partial
Pressure
written as P subscript
gas example partial
pressure of N2 is PN2
Daltons Law of
Partial Pressures
For a mixture of gases
Pgas (total) = Pgas1 + Pgas2 + Pgas3 …
For example air
Pair = PN2 + PO2 + PH2O … etc
+ + N2
H2OO2N2
H2O
O2
N2
H2O
O2
N2
H2O
N2
N2
N2
N2
N2
H2OO2N2
H2O
O2
N2
H2O
O2
N2
H2O
N2
N2
N2
N2
N2
N2
N2
N2 N2
N2
N2
N2
N2
N2
N2
N2 N2
N2
N2
N2
O2
O2O2
O2
O2O2
H2O
H2O
H2O
H2O
H2O
H2O
H2O
H2O=
14
Partial pressure CO2
and breathing rate
lungs release CO2
cell
cells put CO2 into blood
lungs
[CO2]
blood
cells
add
CO2
breathing
removes
CO2
CO2 levels are detected in the lower brain
Higher CO2 stimulates faster breathing
CO2 is an unwanted byproduct
of metabolism but CO2 is the gas
the brain monitors to determine
breathing rate not O2
When a cell uses more energy it releases more CO2
N2
H2OO2N2
H2O
O2
N2
H2O
O2
N2
H2O
N2
N2
N2
N2
N2
H2OO2N2
H2O
O2
N2
H2O
O2
N2
H2O
N2
N2
N2
N2
N2
N2
N2
N2 N2
N2
N2
N2
N2
N2
N2
N2 N2
N2
N2
N2
O2
O2O2
O2
O2O2
H2O
H2O
H2O
H2O
H2O
H2O
H2O
H2O
Mole Fraction ( )
• Ratio of moles of gases
• If expressed as %
aka molar percentage
N2 = moles N2
total moles gas sample N2
H2OO2N2
H2O
O2
N2
H2O
O2
N2
H2O
N2
N2
N2
N2
N2
H2OO2N2
H2O
O2
N2
H2O
O2
N2
H2O
N2
N2
N2
N2
N2
N2
N2
N2 N2
N2
N2
N2
N2
N2
N2
N2 N2
N2
N2
N2
=
mole fraction
of nitrogen
molar percentage N2 = x 100% moles N2
total moles gas sample
moles N2
total moles gas sample
Note this slide was out of order
15
Partial pressure O2
& scuba diving
Space
Earth’s atmosphere
Water
pressure
1.0 atm
90
meters!
pressure
9 atm
+ =10 atm!
if you breath air down partial
pressure of O2 is 10x higher!
PO2 = 2.1 atm!
if you breath trimix 10/70
PO2 = 1.0 atm!
(10% of 10 atm)
trimix 10/70 is a mixture of
gases used for extremely
deep dives. It has 10% O2
to reduce P02
breathing high
PO2 can be toxic
scuba divers breath
trimix to decrease PO2
O2 is 21% of air so
21% of 1.0 atm is
PO2 = 0.21 atm
K2 is the second
highest mountain
in world 28,251 ft
Patm = 0.33 atm
If you breathe air on top of K2 PO2 is reduced b/c all pressure is lower
P02 = 0.07 atm
is reduced to about 1/3 of what we have at sea level
but if you breathe pure O2 instead of air on top of K2
100% O2 means Ptotal = PO2
P02 = 0.33 atm
(mountain climbers are being almost suffocated !)
Mountain climbers breathe pure O2 to increase PO2
Life requires a certain range of PO2 not % O2
Partial pressure and
mountain climbing
16
Density of a gas
• D= m / V
• Density is intensive
• Imagine 1 mole as the sample size
• Mass of 1 mole of a gas is its Molar Mass
• Volume of 1 mole of gas depends on T
and P
• V= RT/P
• Density = Molar Mass / RT /P
A sample of air contains only nitrogen and oxygen
gases whose partial pressures are 0.60 atm and
0.10 atm, respectively. Calculate the total pressure
and the mole fractions of the gases.
17
A mixture of gases contains CH4, C2H6, and C3H8.
If the total pressure is 2.50 atm and the numbers
of moles of the gases present are 0.21 mole for
CH4, 0.36mole for C2H6, and 0.16 mole for C3H8,
calculate the partial pressures of the gases.
A 2.5-L flask at 25°C contains a mixture of three
gases, N2, He, and Ne, at partial pressures of 0.12
atm for N2, 0.18 atm for He, and 0.46 atm for Ne.
(a) Calculate the total pressure of the mixture.
(b) Calculate the volume in liters at STP occupied
by He and Ne if the N2 is removed selectively.
18
Calculate the density of argon gas at 300
K and a pressure 1.1 atm.
Kinetic Molecular Theory
• Model to explain properties
of gases
• 3 postulates of KMT
1) Gas particles small compared to distance between them
2) Average kinetic energy proportional to the Kelvin temperature
3) Collisions are all elastic
(no KE turned into heat in collisions)
Ludwig Boltzmann
19
KMT and pressure
• In Kinetic Molecular Theory the force part of
pressure is due to collisions of gas molecules.
Area
Force created by constant collisions of gas particles
P = Force
Area
increase
pressure
Boyles Law
when a gas is compressed into smaller
volume collisions with wall become
more frequent increasing the pressure
smaller volume
higher pressure
(same temp)
(PV=constant)
revisited
20
KMT and Temperature
• Kinetic energy of a gas is proportional to
Kelvin temperature
• At higher temperatures gas molecules
move more quickly
As temperature increases two effects
• More frequent collisions with walls
• More energetic collisions with walls
Charles’ Law
When cooled the gas molecules slow down
collide less often and not as hard.
This causes the volume to shrink
under the applied pressure.
smaller volume
lower temperature
(same pressure)
decrease
temperature
revisited (V/T = constant)
21
Boltzmann Speed/Energy
Distribution
Ludwig Boltzmann
• Increasing temperature
increases average speed
• Higher speeds = higher energy
- kinetic energy = ½mv2
higher
temperature
% m
ole
cu
les
with
a s
pe
ed
0 300 600 900 1200
speed (m/s)
lower
temperature
50% 50%
average
speed
• Superior teaching
increases students understanding
• Better understanding higher MCAT scores
Boltzmann Energy Distribution
like the Hicks Grade Distribution
other
classes
Hicks’
class
% s
tud
en
ts
with
a s
co
re
0 10 20 30 40 45
MCAT Score
Charles Hicks
class averages
on MCAT
medical school
MCAT requirement class
Hicks’
lesser
instructors
20%
4%
% students with
required grade
20% 4%
22
0 300 600 900 1200
speed (m/s)
% m
ole
cu
les
with
a s
pe
ed
0 300 600 900 1200
speed (m/s)
% m
ole
cu
les
with
a s
pe
ed
Boltzmann Speed/Energy
Distribution
• Higher speeds = higher energy
• Reactions have energy
requirements
higher
temperature
% m
ole
cu
les
with
a s
pe
ed
0 300 600 900 1200
speed (m/s)
lower
temperature
Every speed has a kinetic energy
KE = ½mv2
higher
temperature
lower
temperature
55%
80% 20%
45%
At the higher temperature larger
% of molecules have enough
kinetic energy to react
Ludwig BoltzmannLudwig Boltzmann
20% have
enough
energy
80% don’t
have enough
energy
55% have
enough
energy
45% don’t
have enough
energy
Reaction requires
this speed (energy)
or greater
23
two different molecules at the same temperature.
Which molecule is heavier?
molecule 1
molecule 2