Transcript Slide 1

Chapter 5
Gases
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
2
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)
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
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
4
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
5
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
6
Molecular Speed vs. Molar Mass

in order to have the same average kinetic energy, heavier molecules must
have a slower average speed
7
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
8
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
9
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
10
Graham’s Law of Effusion
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 
1
MM
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
11

Molar Massgas B
Molar Massgas A
Examples

Determine how much faster Helium atoms moves, on average, than a
carbon dioxide molecule at the same temperature

Calculate the molar mass of a gas that effuses at a rate 0.462 times N2
Ideal vs. Real Gases



Real gases often do not behave like ideal gases at high pressure or
low temperature
Ideal gas laws assume
1) no attractions between gas molecules
2) gas molecules do not take up space
◦
based on the kinetic-molecular theory
at low temperatures and high pressures these assumptions are not
valid
13
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
nRT
V
 nb
P
14
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
15
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
16
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
17
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




18
Example
sample of 3.50 moles of NH3 gas occupies 5.20 L at 47oC. Calculate the
pressure of the gas (in atm) using
◦ A) the ideal gas equation
◦ B) the van der Waals equation
a = 4.17 atm •L2/mol2 b = 0.0371 L/mol
A
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
20
Mountain Climbing & Partial Pressure
our bodies are adapted to
breathe O2 at a partial pressure
of 0.21 atm
 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
21