Chapter 14

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Chapter 14The Behavior of Gases
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Section 14.1The Properties of Gases

• OBJECTIVES
• Explain why gases are easier to compress than
  solids or liquids are.

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Section 14.1The Properties of Gases

• OBJECTIVES
• Describe the three factors that affect gas
  pressure.

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Compressibility

• Gases can expand to fill its container, unlike
  solids or liquids
• The reverse is also true
• They are easily compressed, or squeezed into a
  smaller volume
• Compressibility is a measure of how much the
  volume matter decreases under pressure

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Compressibility

• This is the idea behind placing air bags in
  automobiles
• In an accident, the air compresses more than the
  steering wheel or dash when you strike it
• The impact forces the gas particles closer
  together, because there is a lot of empty space
  between them

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Compressibility

• At room temperature, the distance between
  particles is about 10x the diameter of the
  particle
• Fig. 14.2, page 414
• How does the volume of the particles in a gas
  compare to the overall volume of the gas?

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Variables that describe a Gas

• The four variables and their common units
• 1. pressure (P) in kilopascals
• 2. volume (V) in Liters
• 3. temperature (T) in Kelvin
• 4. amount (n) in moles
• The amount of gas, volume, and temperature are
  factors that affect gas pressure.

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1. Amount of Gas

• When we inflate a balloon, we are adding gas
  molecules.
• Increasing the number of gas particles increases
  the number of collisions
• thus, the pressure increases
• If temperature is constant- doubling the number
  of particles doubles the pressure

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Pressure and the number of molecules are directly
related

• More molecules means more collisions.
• Fewer molecules means fewer collisions.
• Gases naturally move from areas of high pressure
  to low pressure because there is empty space to
  move into a spray can is example.

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Common use?

• Aerosol (spray) cans
• gas moves from higher pressure to lower pressure
• a propellant forces the product out
• whipped cream, hair spray, paint
• Fig. 14.5, page 416
• Is the can really ever empty?

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2. Volume of Gas

• In a smaller container, the molecules have less
  room to move.
• The particles hit the sides of the container more
  often.
• As volume decreases, pressure increases. (think
  of a syringe)

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3. Temperature of Gas

• Raising the temperature of a gas increases the
  pressure, if the volume is held constant.
• The molecules hit the walls harder, and more
  frequently!
• Fig. 14.7, page 417
• Should you throw an aerosol can into a fire?
  What could happen?
• When should your automobile tire pressure be
  checked?

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Section 14.2The Gas Laws

• OBJECTIVES
• Describe the relationships among the temperature,
  pressure, and volume of a gas.

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Section 14.2The Gas Laws

• OBJECTIVES
• Use the combined gas law to solve problems.

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The Gas Laws

• These will describe HOW gases behave.
• Gas behavior can be predicted by the theory.
• The amount of change can be calculated with
  mathematical equations.
• You need to know both of these the theory, and
  the math

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Robert Boyle(1627-1691)

• Boyle was born into an aristocratic Irish family
  
• Became interested in medicine and the new
  science of Galileo and studied chemistry. 
• A founder and an influential fellow of the Royal
  Society of London
• Wrote extensively on science, philosophy, and
  theology.

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1. Boyles Law - 1662
Gas pressure is inversely proportional to the
volume, when temperature is held constant.

• Pressure x Volume a constant
• Equation P1V1 P2V2 (T constant)

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Graph of Boyles Law page 418
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- Page 419
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Jacques Charles (1746-1823)

• French Physicist
• Part of a scientific balloon flight on Dec. 1,
  1783 was one of three passengers in the second
  balloon ascension that carried humans
• This is how his interest in gases started
• It was a hydrogen filled balloon good thing
  they were careful!

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2. Charless Law - 1787

• The volume of a fixed mass of gas is directly
  proportional to the Kelvin temperature, when
  pressure is held constant.
• This extrapolates to zero volume at a temperature
  of zero Kelvin.

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Converting Celsius to Kelvin

• Gas law problems involving temperature will
  always require that the temperature be in Kelvin.
  (Remember that no degree sign is shown with the
  kelvin scale.)
• Reason? There will never be a zero volume, since
  we have never reached absolute zero.

Kelvin ?C 273
C Kelvin - 273
and
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- Page 421
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Joseph Louis Gay-Lussac (1778 1850)

• French chemist and physicist
• Known for his studies on the physical properties
  of gases.
• In 1804 he made balloon ascensions to study
  magnetic forces and to observe the composition
  and temperature of the air at different
  altitudes.

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3. Gay Lussacs Law - 1802

• The pressure and Kelvin temperature of a gas are
  directly proportional, provided that the volume
  remains constant.

• How does a pressure cooker affect the time needed
  to cook food?
• Sample Problem 14.3, page 423

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4. The Combined Gas Law
The combined gas law expresses the relationship
between pressure, volume and temperature of a
fixed amount of gas.
Sample Problem 14.4, page 424
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• The combined gas law contains all the other gas
  laws!
• If the temperature remains constant...

P1
V1
P2
x
V2
x

T1
T2
Boyles Law
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• The combined gas law contains all the other gas
  laws!
• If the pressure remains constant...

P1
V1
P2
x
V2
x

T1
T2
Charless Law
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• The combined gas law contains all the other gas
  laws!
• If the volume remains constant...

P1
V1
P2
x
V2
x

T1
T2
Gay-Lussacs Law
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Section 14.3Ideal Gases

• OBJECTIVES
• Compute the value of an unknown using the ideal
  gas law.

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Section 14.3Ideal Gases

• OBJECTIVES
• Compare and contrast real an ideal gases.

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5. The Ideal Gas Law 1

• Equation P x V n x R x T
• Pressure times Volume equals the number of moles
  (n) times the Ideal Gas Constant (R) times the
  temperature in Kelvin.
• R 8.31 (L x kPa) / (mol x K)
• The other units must match the value of the
  constant, in order to cancel out.
• The value of R could change, if other units of
  measurement are used for the other values (namely
  pressure changes)

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The Ideal Gas Law

• We now have a new way to count moles (amount of
  matter), by measuring T, P, and V. We arent
  restricted to only STP conditions
• P x V
• R x T

n
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Ideal Gases

• We are going to assume the gases behave
  ideally- in other words, they obey the Gas Laws
  under all conditions of temperature and pressure
• An ideal gas does not really exist, but it makes
  the math easier and is a close approximation.
• Particles have no volume? Wrong!
• No attractive forces? Wrong!

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Ideal Gases

• There are no gases for which this is true
  however,
• Real gases behave this way at a) high
  temperature, and b) low pressure.
• Because at these conditions, a gas will stay a
  gas!
• Sample Problem 14.5, page 427

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6. Ideal Gas Law 2

• P x V m x R x T M
• Allows LOTS of calculations, and some new items
  are
• m mass, in grams
• M molar mass, in g/mol
• Molar mass m R T P V

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Density

• Density is mass divided by volume
• m
• V
• so,
• m M P
• V R T

D
D

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Real Gases and Ideal Gases
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Ideal Gases dont exist, because

• Molecules do take up space
• There are attractive forces between particles
• - otherwise there would be no liquids formed

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Real Gases behave like Ideal Gases...

• When the molecules are far apart.
• The molecules do not take up as big a percentage
  of the space
• We can ignore the particle volume.
• This is at low pressure

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Real Gases behave like Ideal Gases

• When molecules are moving fast
• This is at high temperature
• Collisions are harder and faster.
• Molecules are not next to each other very long.
• Attractive forces cant play a role.

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Section 14.4Gases Mixtures and Movements

• OBJECTIVES
• Relate the total pressure of a mixture of gases
  to the partial pressures of the component gases.

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Section 14.4Gases Mixtures and Movements

• OBJECTIVES
• Explain how the molar mass of a gas affects the
  rate at which the gas diffuses and effuses.

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7 Daltons Law of Partial Pressures

• For a mixture of gases in a container,
• PTotal P1 P2 P3 . . .

• P1 represents the partial pressure or the
  contribution by that gas.
• Daltons Law is particularly useful in
  calculating the pressure of gases collected over
  water.

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• If the first three containers are all put into
  the fourth, we can find the pressure in that
  container by adding up the pressure in the first
  3

2 atm
1 atm
6 atm
3 atm
4
3
2
1
Sample Problem 14.6, page 434
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Diffusion is

• Molecules moving from areas of high concentration
  to low concentration.
• Example perfume molecules spreading across the
  room.

• Effusion Gas escaping through a tiny hole in a
  container.
• Both of these depend on the molar mass of the
  particle, which determines the speed.

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• Diffusion describes the mixing of gases. The
  rate of diffusion is the rate of gas mixing.
• Molecules move from areas of high concentration
  to low concentration.
• Fig. 14.18, p. 435

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• Effusion a gas escapes through a tiny hole in
  its container
• -Think of a nail in your car tire

Diffusion and effusion are explained by the next
gas law Grahams
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8. Grahams Law
RateA ? MassB RateB ? MassA

• The rate of effusion and diffusion is inversely
  proportional to the square root of the molar mass
  of the molecules.
• Derived from Kinetic energy 1/2 mv2
• m the molar mass, and v the velocity.

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Grahams Law

• Sample compare rates of effusion of Helium with
  Nitrogen done on p. 436
• With effusion and diffusion, the type of
  particle is important
• Gases of lower molar mass diffuse and effuse
  faster than gases of higher molar mass.
• Helium effuses and diffuses faster than nitrogen
  thus, helium escapes from a balloon quicker
  than many other gases!

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End of Chapter 14