Chapter 8 Gases

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Chapter 8Gases

• The Gas Laws of Boyle, Charles and Avogadro
• The Ideal Gas Law
• Gas Stoichiometry
• Daltons Laws of Partial Pressure
• The Kinetic Molecular Theory of Gases
• Effusion and Diffusion
• Collisions of Gas Particles with the Container
  Walls
• Intermolecular Collisions
• Real Gases
• Chemistry in the Atmosphere

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States of Matter
Solid Liquid Gas We start with gases because
they are simpler than the others.
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Pressure (force/area, PaN/m2) A pressure of
101.325 kPa is need to raise the column of Hg 76
cm (760 mm). standard pressure 760 mm Hg 760
torr 1 atm 101.325 kPa
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P1V1 P2V2 (fixed T,n)
Boyles Law
V x P const
1662
Charles Law
V1 / V2 T1 / T2 (fixed P,n)
V / T const
1787
V / n const
(fixed P,T)
Avogadro
1811
n number of moles
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Boyles Law Pressure and Volume
The product of the pressure and volume, PV, of a
sample of gas is a constant at a constant
temperature PV k Constant (fixed T,n)
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Boyles Law The Effect of Pressure on Gas Volume
Example The cylinder of a bicycle pump has a
volume of 1131 cm3 and is filled with air at a
pressure of 1.02 atm. The outlet valve is sealed
shut, and the pump handle is pushed down until
the volume of the air is 517 cm3. The
temperature of the air trapped inside does not
change. Compute the pressure inside the pump.
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Charles Law T vs V
At constant pressure, the volume of a sample of
gas is a linear function of its temperature. V
bT
T(C) 273C(V/Vo)
When V0, T-273C
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Charles Law T vs V
The Absolute Temperature Scale
Kelvin temperature scale
T (Kelvin) 273.15 t (Celsius)
Gas volume is proportional to Temp
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Charles Law The Effect of Temperature on Gas
Volume
V vs T
V1 / V2 T1 / T2 (at a fixed pressure and for
a fixed amount of gas)
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• Avogadros law (1811)
• V an
• n number of moles of gas
• a proportionality constant
• For a gas at constant temperature and pressure
  the volume is directly proportional to the number
  of moles of gas.

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P1V1 P2V2 (at a fixed temperature)
Boyles Law
V kP -1
Charles Law
V1 / V2 T1 / T2 (at a fixed pressure)
V bT
(at a fixed pressure and temperature)
V an
Avogadro
n number of moles
PV nRT ideal gas law
an empirical law
V nRTP-1
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Example At some point during its ascent, a sealed
weather balloon initially filled with helium at a
fixed volume of 1.0 x 104 L at 1.00 atm and 30oC
reaches an altitude at which the temperature is
-10oC yet the volume is unchanged. Calculate the
pressure at that altitude .
n1 n2
V1 V2
P2 P1T2/T1 (1 atm)(263K)/(303K)
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STP (Standard Temperature and Pressure)
For 1 mole of a perfect gas at OC (273K) (i.e.,
32.0 g of O2 28.0 g N2 2.02 g H2)
nRT 22.4 L atm PV
At 1 atm, V 22.4 L
STP standard temperature and pressure 273 K
(0o C) and 1 atm
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PV nRT
The Ideal Gas Law
What is R, universal gas constant?
the R is independent of the particular gas studied
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PV nRT ideal gas law constants
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Example What mass of Hydrogen gas is needed to
fill a weather balloon to a volume of 10,000 L,
1.00 atm and 30 C?
1) Use PV nRT nPV/RT. 2) Find the number of
moles. 3) Use the atomic weight to find the mass.
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Example What mass of Hydrogen gas is needed to
fill a weather balloon to a volume of 10,000 L,
1.00 atm and 30 C?
n PV/RT (1 atm) (10,000 L) (293 K)-1 (0.082
L atm mol-1 K-1)-1 416 mol (416 mol)(1.0 g
mol-1) 416 g
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Use volumes to determine stoichiometry.
Gas Stoichiometry
The volume of a gas is easier to measure than the
mass.
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Gas Density and Molar Mass
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Gas Density and Molar Mass
Example Calculate the density of gaseous hydrogen
at a pressure of 1.32 atm and a temperature of
-45oC.
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Example Fluorocarbons are compounds containing
fluorine and carbon. A 45.6 g sample of a
gaseous fluorocarbon contains 7.94 g of carbon
and 37.7 g of fluorine and occupies 7.40 L at STP
(P 1.00 atm and T 273 K). Determine the
molecular weight of the fluorocarbon and give its
molecular formula.
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Example Fluorocarbons are compounds of fluorine
and carbon. A 45.60 g sample of a gaseous
fluorocarbon contains 7.94 g of carbon and 37.66
g of fluorine and occupies 7.40 L at STP (P
1.00 atm and T 273.15 K). Determine the
approximate molar mass of the fluorocarbon and
give its molecular formula.
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Mixtures of Gases
Daltons Law of Partial Pressures The total
pressure of a mixture of gases equals the sum of
the partial pressures of the individual gases.
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Mole Fractions and Partial Pressures
The mole fraction of a component in a mixture is
define as the number of moles of the components
that are in the mixture divided by the total
number of moles present.
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Example A solid hydrocarbon is burned in air in a
closed container, producing a mixture of gases
having a total pressure of 3.34 atm. Analysis of
the mixture shows it to contain 0.340 g of water
vapor, 0.792 g of carbon dioxide, 0.288 g of
oxygen, 3.790 g of nitrogen, and no other gases.
Calculate the mole fraction and partial pressure
of carbon dioxide in this mixture.
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2NH4ClO4 (s) ? N2(g) Cl2 (g) 2O2 (g) 4 H2
(g)
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The Kinetic Molecular Theory of Gases

• The Ideal Gas Law is an empirical relationship
  based on experimental observations.
• Boyle, Charles and Avogadro.
• Kinetic Molecular Theory is a simple model that
  attempts to explain the behavior of gases.

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The Kinetic Molecular Theory of Gases
1. A pure gas consists of a large number of
identical molecules separated by distances that
are large compared with their size. The volumes
of the individual particles can be assumed to be
negligible (zero).
2. The molecules of a gas are constantly moving
in random directions with a distribution of
speeds. The collisions of the particles with the
walls of the container are the cause of the
pressure exerted by the gas.
3. The molecules of a gas exert no forces on one
another except during collisions, so that between
collisions they move in straight lines with
constant velocities. The gases are assumed to
neither attract or repel each other. The
collisions of the molecules with each other and
with the walls of the container are elastic no
energy is lost during a collision.
4. The average kinetic energy of a collection of
gas particles is assumed to be directly
proportional to the Kelvin temperature of the gas.
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Pressure and Molecular Motion
Pressure ? (impulse per collision) x (frequency
of collisions with the walls)

• frequency of collisions
• ? speed of molecules (u)

• impulse per collision
• ? momentum (m u)

• frequency of collisions
• ? number of molecules per unit
  volume (N/V)

P ? (m u) (N/V) u
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Pressure and Molecular Motion
P ? (m u) (N/V) u
PV ? Nmu2
Correction The molecules have a distribution of
speeds.
Mean-square speed of all molecules
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Pressure and Molecular Motion
Make some substitutions

1. 1/2m kinetic energy (KEave) of one
   molecule.
2. KE is proportional to T (KEave RT)
3. Divide by 3 (3 dimensions)
4. N nNa (molecules moles x molecules/mole)

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The Kinetic Molecular Theory of Gases
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Speed Distribution
Temperature is a measure of the average kinetic
energy of gas molecules.
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Velocity Distributions Distribution of Molecular
Speeds
ump uavg urms 1.000 1.128 1.225
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Example
At a certain speed, the root-mean-square-speed
of the molecules of hydrogen in a sample of gas
is 1055 ms-1. Compute the root-mean square speed
of molecules of oxygen at the same temperature.

• Strategy
• Find T for the H2 gas with a urms 1055 ms-1

2. Find urms of O2 at the same temperature
H2 about 4 times velocity of O2
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Gaseous Diffusion and Effusion
Diffusion mixing of Gases
e.g., NH3 and HCl
Effusion rate of passage of a gas through a tiny
orifice in a chamber.
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Example A gas mixture contains equal numbers of
molecules of N2 and SF6. A small portion of it is
passed through a gaseous diffusion apparatus.
Calculate how many molecules of N2 are present in
the product of gas for every 100 molecules of SF6.
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Real Gases

• Ideal Gas behavior is generally conditions of low
  pressure and high temperature

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Real Gases

• Kinetic Molecular Theory model
• assumed no interactions between gas particles and
  
• no volume for the gas particles
• 1873 Johannes van der Waals
• Correction for attractive forces in gases (and
  liquids)
• Correction for volume of the molecules

Pcorrected Vcorrected nRT
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The Person Behind the Science
Johannes van der Waals (1837-1923)

• Highlights
• 1873 first to realize the necessity of taking
  into account the volumes of molecules and
• intermolecular forces (now generally called "van
  der Waals forces") in establishing the
  relationship between the pressure, volume and
  temperature of gases and liquids.
• Moments in a Life
• 1910 awarded Nobel Prize in Physics

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• Significant Figures
• Zeros that follow the last non-zero digit
  sometimes are counted.
• E.g., for 700 g, the zeros may or not be
  significant.
• They may present solely to position the decimal
  point
• But also may be intended to convey the precision
  of the measurement.
• The uncertainty in the measurement is on the
  order of /- 1 g or /- 10g or perhaps /- 100 g
• It is impossible to tell which without further
  information.
• If you need 2 sig figs and want to write 40 use
  either
• Four zero decimal point 40. or
• 4.0 x 101

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The Person Behind the Science
Lord Kelvin (William Thomson) 1824-1907
When you can measure what you are speaking
about and express it in numbers, you know
something about it but when you cannot measure
it, when you cannot express it in numbers, you
knowledge is of a meager and unsatisfactory kind
it may be the beginning of knowledge but you
have scarcely, in your thoughts advanced to the
stage of science, whatever the matter may be.
Lecture to the Institution of Civil
Engineers, 3 May 1883
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The Person Behind the Science
Evangelista Torricelli (1608-1647)

• Highlights
• In 1641, moved to Florence to assist the
  astronomer Galileo.
• Designed first barometer
• It was Galileo that suggested Evangelista
  Torricelli use mercury in his vacuum experiments.
  
• Torricelli filled a four-foot long glass tube
  with mercury and inverted the tube into a dish.
• Moments in a Life
• Succeed Galileo as professor of mathematics in
  the University of Pisa.
• Asteroid (7437) Torricelli named in his honor

Barometer P g x d x h