Transcript Slide 1

Chemistry: A Molecular Approach, 1st Ed.
Nivaldo Tro
Roy Kennedy
Massachusetts Bay Community College
Wellesley Hills, MA
2008, Prentice Hall
Mixtures of Gases
 when gases are mixed together, their molecules behave
independent of each other
 therefore, in certain applications, the mixture can be
thought of as one gas
Tro, Chemistry: A Molecular Approach
2
Partial Pressure
 the pressure of a single gas in a mixture of gases is called
its partial pressure
 we can calculate the partial pressure of a gas if
 the sum of the partial pressures of all the gases in the
mixture equals the total pressure
 Dalton’s Law of Partial Pressures
 because the gases behave independently
Tro, Chemistry: A Molecular Approach
3
Composition of Dry Air
Tro, Chemistry: A Molecular Approach
4
The partial pressure of each gas in a mixture can
be calculated using the ideal gas law
for two gases, A and B, mixed together
nA x R x T
nB x R x T
PA 
PB 
V
V
the temperatu re and volume of everything
in the mixture are the same
n total  n A  n B
n total x R x T
Ptotal  PA  PB 
V
Tro, Chemistry: A Molecular Approach
5
Example
 PHe=341 mmHg, PNe=112 mmHg, Ptot = 662 mmHg,
V = 1.00 L, T=298 K
Find the partial pressure of neon in a mixture with total
pressure 3.9 atm, volume 8.7 L, temperature 598 K, and
0.17 moles Xe.
Mole Fraction
the fraction of the total pressure that a single
gas contributes is equal to the fraction of the
total number of moles that a single gas
contributes
the ratio of the moles of a single
component to the total number of moles in
the mixture is called the mole fraction, c
for gases, = volume % / 100%
the partial pressure of a gas is equal to the
mole fraction of that gas times the total
pressure
Tro, Chemistry: A Molecular Approach
PA
nA

Ptotal n total
nA
cA 
n total
PA  cA  Ptotal
7
Deep Sea Divers & Partial Pressure
 its also possible to have too much O2, a condition called
oxygen toxicity
 PO2 > 1.4 atm
 oxygen toxicity can lead to muscle spasms, tunnel vision, and
convulsions
 its also possible to have too much N2, a condition called
nitrogen narcosis
 also known as Rapture of the Deep
 when diving deep, the pressure of the air divers breathe
increases – so the partial pressure of the oxygen increases
 at a depth of 55 m the partial pressure of O2 is 1.4 atm
 divers that go below 50 m use a mixture of He and O2 called heliox
that contains a lower percentage of O2 than air
Tro, Chemistry: A Molecular Approach
8
Mountain Climbing & Partial Pressure
 our bodies are adapted to breathe O2
at a partial pressure of 0.21 atm
 Sherpa, people native to the Himalaya
mountains, are adapted to the much lower
partial pressure of oxygen in their air
 partial pressures of O2 lower than 0.1
atm will lead to hypoxia
 unconsciousness or death
 climbers of Mt Everest carry O2 in
cylinders to prevent hypoxia
 on top of Mt Everest, Pair = 0.311 atm,
so PO2 = 0.065 atm
Tro, Chemistry: A Molecular
Approach
9
Partial Pressure & Diving
Tro, Chemistry: A Molecular Approach
10
Example
 Find the mole fractions and partial pressures in a 12.5 L tank with
24.2 g He and 4.32 g O2 at 298 K
 A diver breathes a heliox mixture with an oxygen mole fraction
of 0.050. What must the total pressure be for the partial pressure
of oxygen to be 0.21 atm?
Collecting Gases
 gases are often collected by having them displace
water from a container
 the problem is that since water evaporates, there is
also water vapor in the collected gas
 the partial pressure of the water vapor, called the
vapor pressure, depends only on the temperature
 if you collect a gas sample with a total pressure of
758.2 mmHg* at 25°C, the partial pressure of the
water vapor will be 23.78 mmHg – so the partial
pressure of the dry gas will be 734.4 mmHg
 Table 5.4*
Tro, Chemistry: A Molecular Approach
12
Vapor Pressure of Water
Tro, Chemistry: A Molecular Approach
13
Collecting Gas by Water Displacement
Tro, Chemistry: A Molecular Approach
14
Examples
 1.02 L of O2 collected over water at 293 K with a total pressure
of 755.2 mmHg. Find mass O2.
 0.12 moles of H2 is collected over water in a 10.0 L container at
323 K. Find the total pressure.
Reactions Involving Gases
 the principles of reaction stoichiometry from
Chapter 4 can be combined with the gas laws for
reactions involving gases
 in reactions of gases, the amount of a gas is often
given as a volume
 the ideal gas law allows us to convert from the
volume of the gas to moles; then we can use the
coefficients in the equation as a mole ratio
 when gases are at STP, use 1 mol = 22.4 L
P, V, T of Gas A
Tro, Chemistry: A Molecular
Approach
mole A
16
mole B
P, V, T of Gas B
Examples
 How many grams of H2O form when 1.24 L H2 reacts
completely with O2 at STP?
O2(g) + 2 H2(g) → 2 H2O(g)
 What volume of O2 at 0.750 atm and 313 K is
generated by the thermolysis of 10.0 g of HgO?
2 HgO(s)  2 Hg(l) + O2(g)
Properties of Gases
 expand to completely fill their container
 take the shape of their container
 low density
 much less than solid or liquid state
 compressible
 mixtures of gases are always homogeneous
 fluid
Tro, Chemistry: A Molecular
Approach
18
Kinetic Molecular Theory
 the particles of the gas (either atoms or
molecules) are constantly moving
 the attraction between particles is negligible
 when the moving particles hit another particle
or the container, they do not stick; but they
bounce off and continue moving in another
direction
 like billiard balls
Tro, Chemistry: A Molecular
Approach
19
Kinetic Molecular Theory
 there is a lot of empty space between the
particles
 compared to the size of the particles
 the average kinetic energy of the particles is
directly proportional to the Kelvin
temperature
 as you raise the temperature of the gas, the
average speed of the particles increases
Tro, Chemistry: A Molecular
Approach
20
Gas Properties Explained –
Indefinite Shape and Indefinite Volume
Because the gas
molecules have
enough kinetic
energy to overcome
attractions, they
keep moving around
and spreading out
until they fill the
container.
Tro, Chemistry: A Molecular
Approach
As a result, gases
take the shape and
the volume of the
container they
are in.
21
Gas Properties Explained Compressibility
Because there is a lot of unoccupied space in the structure
of a gas, the gas molecules can be squeezed closer together
Tro, Chemistry: A Molecular
Approach
22
Gas Properties Explained –
Low Density
Because there is a lot of
unoccupied space in the
structure of a gas, gases
do not have a lot of mass
in a given volume, the
result is they have low
density
Tro, Chemistry: A Molecular
Approach
23
Density & Pressure
 result of the constant movement of the
gas molecules and their collisions with the
surfaces around them
 when more molecules are added, more
molecules hit the container at any one
instant, resulting in higher pressure
 also higher density
Tro, Chemistry: A Molecular
Approach
24
Gas Laws Explained –
Dalton’s Law of Partial Pressures
 Dalton’s Law says that the total pressure of a mixture of
gases is the sum of the partial pressures
 kinetic-molecular theory says that the gas molecules are
negligibly small and don’t interact
 therefore the molecules behave independent of each other,
each gas contributing its own collisions to the container
with the same average kinetic energy
 since the average kinetic energy is the same, the total
pressure of the collisions is the same
Tro, Chemistry: A Molecular
Approach
25
Dalton’s Law & Pressure
 since the gas molecules
are not sticking together,
each gas molecule
contributes its own force
to the total force on the
side
Tro, Chemistry: A Molecular
Approach
26
Calculating Gas Pressure
Tro, Chemistry: A Molecular
Approach
27
Kinetic Energy and
Molecular Velocities
 average kinetic energy of the gas molecules depends on
the average mass and velocity
 KE = ½mv2
 gases in the same container have the same temperature,
the same average kinetic energy
 if they have different masses, the only way for them to
have the same kinetic energy is to have different average
velocities
 lighter particles will have a faster average velocity than more
massive particles
Tro, Chemistry: A Molecular
Approach
28
Molecular Speed vs. Molar
Mass
 in order to have the same average kinetic energy, heavier
molecules must have a slower average speed
Tro, Chemistry: A Molecular
Approach
29
Temperature vs. Molecular
Speed
 as the absolute temperature
increases, the average velocity
increases
 the distribution function
“spreads out,” resulting in
more molecules with faster
speeds
Tro, Chemistry: A Molecular
Approach
30
Mean Free Path
 molecules in a gas travel in
straight lines until they collide
with another molecule or the
container
 the average distance a molecule
travels between collisions is
called the mean free path
 mean free path decreases as the
pressure increases
Tro, Chemistry: A Molecular
Approach
31
Diffusion
and
Effusion
 the process of a collection of molecules spreading out
from high concentration to low concentration is called
diffusion
 the process by which a collection of molecules escapes
through a small hole into a vacuum is called effusion
 both the rates of diffusion and effusion of a gas are
related to its rms average velocity
 for gases at the same temperature, this means that the rate
of gas movement is inversely proportional to the square
root of the molar mass
rate 
Tro, Chemistry: A Molecular
Approach
32
1
MM
Effusion
Tro, Chemistry: A Molecular
Approach
33
Graham’s
Law
of
Effusion
 for two different gases at the same temperature, the ratio of
their rates of effusion is given by the following equation:
rategas A
rategas B
Tro, Chemistry: A Molecular
Approach
34

Molar Massgas B
Molar Massgas A
Ideal vs. Real Gases


Real gases often do not behave like ideal gases at
high pressure or low temperature
Ideal gas laws assume
1)
2)


no attractions between gas molecules
gas molecules do not take up space
based on the kinetic-molecular theory
at low temperatures and high pressures these
assumptions are not valid
35
The Effect of Molecular
Volume
 at high pressure, the amount of space occupied by the
molecules is a significant amount of the total volume
 the molecular volume makes the real volume larger than the
ideal gas law would predict
 van der Waals modified the ideal gas equation to account for
the molecular volume
 b is called a van der Waals constant and is different for every
gas because their molecules are different sizes
Tro, Chemistry: A Molecular
Approach
36
nRT
V
 nb
P
Real Gas Behavior
 because real molecules take
up space, the molar volume
of a real gas is larger than
predicted by the ideal gas
law at high pressures
Tro, Chemistry: A Molecular
Approach
37
The Effect of Intermolecular
Attractions
 at low temperature, the attractions between the molecules
is significant
 the intermolecular attractions makes the real pressure less
than the ideal gas law would predict
 van der Waals modified the ideal gas equation to account
for the intermolecular attractions
 a is called a van der Waals constant and is different for every
gas because their molecules are different sizes
nRT  n 
P
 a 
V
V
Tro, Chemistry: A Molecular
Approach
38
2
Real Gas Behavior
 because real molecules
attract each other, the molar
volume of a real gas is
smaller than predicted by the
ideal gas law at low
temperatures
Tro, Chemistry: A Molecular
Approach
39
Van der Waals’
Equation
 combining the equations to
account for molecular volume and
intermolecular attractions we get
the following equation
 used for real gases
 a and b are called van der Waal
constants and are different for each
gas
2

 P  a n    V - nb   nRT


V




Tro, Chemistry: A Molecular
Approach
40
Real
Gases
 a plot of PV/RT vs. P for 1 mole of a gas shows the
difference between real and ideal gases
 it reveals a curve that shows the PV/RT ratio for a real gas is
generally lower than ideality for “low” pressures – meaning
the most important factor is the intermolecular attractions
 it reveals a curve that shows the PV/RT ratio for a real gas is
generally higher than ideality for “high” pressures – meaning
the most important factor is the molecular volume
Tro, Chemistry: A Molecular
Approach
41
PV/RT Plots
Tro, Chemistry: A Molecular
Approach
42