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Roy KennedyMassachusetts Bay Community College
Wellesley Hills, MA2008, Prentice Hall
Chemistry: A Molecular Approach, 1st Ed.
Nivaldo Tro
Mixtures of Gaseswhen 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 Pressurethe 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 pressureDalton’s Law of Partial Pressuresbecause the gases behave independently
Tro, Chemistry: A Molecular Approach 3
Composition of Dry Air
Tro, Chemistry: A Molecular Approach 4
Tro, Chemistry: A Molecular Approach 5
V
T x R x n P P P
n n n
same theare mixture in the
everything of volumeand re temperatutheV
T x R x n P
V
T x R x n P
togethermixed B, andA gases, for two
totalBAtotal
BAtotal
BB
AA
ExamplePHe=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.
Tro, Chemistry: A Molecular Approach 7
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
total
A
total
A
n
n
P
P
the ratio of the moles of a single component to the total number of moles in the mixture is called the mole fraction,
for gases, = volume % / 100%
total
AA n
n
the partial pressure of a gas is equal to the mole fraction of that gas times the total pressure
totalAA PP
Deep Sea Divers & Partial Pressure
its also possible to have too much O2, a condition called oxygen toxicityPO2 > 1.4 atmoxygen toxicity can lead to muscle spasms, tunnel vision,
and convulsionsits also possible to have too much N2, a condition
called nitrogen narcosisalso known as Rapture of the Deep
when diving deep, the pressure of the air divers breathe increases – so the partial pressure of the oxygen increasesat a depth of 55 m the partial pressure of O2 is 1.4 atmdivers 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
Tro, Chemistry: A Molecular Approach 9
Mountain Climbing & Partial Pressureour bodies are adapted to breathe
O2 at a partial pressure of 0.21 atmSherpa, 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 hypoxiaunconsciousness or death
climbers of Mt Everest carry O2 in cylinders to prevent hypoxiaon top of Mt Everest, Pair = 0.311 atm,
so PO2 = 0.065 atm
Tro, Chemistry: A Molecular Approach 10
ExampleFind 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 Gasesgases are often collected by having them
displace water from a containerthe problem is that since water evaporates,
there is also water vapor in the collected gasthe 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
Tro, Chemistry: A Molecular Approach 14
Examples1.02 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.
Tro, Chemistry: A Molecular Approach 16
Reactions Involving Gasesthe 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 mole A mole B P, V, T of Gas B
ExamplesHow 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)
Tro, Chemistry: A Molecular Approach 18
Properties of Gasesexpand to completely fill their containertake the shape of their containerlow density
much less than solid or liquid statecompressiblemixtures of gases are always homogeneousfluid
Tro, Chemistry: A Molecular Approach 19
Kinetic Molecular Theorythe 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 directionlike billiard balls
Tro, Chemistry: A Molecular Approach 20
Kinetic Molecular Theorythere is a lot of empty space
between the particlescompared to the size of the
particlesthe average kinetic energy of the
particles is directly proportional to the Kelvin temperatureas you raise the temperature of the
gas, the average speed of the particles increases
Tro, Chemistry: A Molecular Approach 21
Because the gasmolecules have enough kineticenergy to overcomeattractions, theykeep moving aroundand spreading outuntil they fill the container.
As a result, gasestake the shape andthe volume of thecontainer they are in.
Tro, Chemistry: A Molecular Approach 22
Because there is a lot of unoccupied space in the structureof a gas, the gas molecules can be squeezed closer together
Tro, Chemistry: A Molecular Approach 23
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 24
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 pressurealso higher density
Tro, Chemistry: A Molecular Approach 25
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 26
Dalton’s Law & Pressuresince 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 27
Calculating Gas Pressure
Tro, Chemistry: A Molecular Approach 28
Kinetic Energy and Molecular Velocitiesaverage kinetic energy of the gas molecules
depends on the average mass and velocityKE = 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 velocitieslighter particles will have a faster average velocity
than more massive particles
Tro, Chemistry: A Molecular Approach 29
Molecular Speed vs. Molar Massin order to have the same average kinetic
energy, heavier molecules must have a slower average speed
Tro, Chemistry: A Molecular Approach 30
Temperature vs. Molecular Speedas the absolute
temperature increases, the average velocity increasesthe distribution
function “spreads out,” resulting in more molecules with faster speeds
Tro, Chemistry: A Molecular Approach 31
Mean Free Pathmolecules 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 32
Diffusion and Effusionthe 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
MM
1 rate
Tro, Chemistry: A Molecular Approach 33
Effusion
Tro, Chemistry: A Molecular Approach 34
Graham’s Law of Effusionfor two different gases at the same temperature, the ratio of their rates of effusion is given by the following equation:
A gas
B gas
B gas
A gas
MassMolar
MassMolar
rate
rate
35
Ideal vs. Real Gases Real gases often do not behave like ideal
gases at high pressure or low temperature
Ideal gas laws assume1) no attractions between gas molecules2) gas molecules do not take up space based on the kinetic-molecular theory
at low temperatures and high pressures these assumptions are not valid
Tro, Chemistry: A Molecular Approach 36
The Effect of Molecular Volumeat 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 volumeb is called a van der Waals constant and is
different for every gas because their molecules are different sizes
bnP
nRTV
Tro, Chemistry: A Molecular Approach 37
Real Gas Behaviorbecause 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 38
The Effect of Intermolecular Attractionsat low temperature, the attractions between
the molecules is significantthe 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 attractionsa is called a van der Waals constant and is
different for every gas because their molecules are different sizes 2
V
n
V
nRTP
a
Tro, Chemistry: A Molecular Approach 39
Real Gas Behaviorbecause 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 40
Van der Waals’ Equationcombining the equations to
account for molecular volume and intermolecular attractions we get the following equationused for real gasesa and b are called van der Waal
constants and are different for each gas
nRTn-VV
nP
2
ba
Tro, Chemistry: A Molecular Approach 41
Real Gasesa plot of PV/RT vs. P for 1 mole of a gas shows
the difference between real and ideal gasesit 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 42
PV/RT Plots