Chapter 14 The Behavior of Gases

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Chapter 14 The Behavior of Gases

• Chemistry Honors

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The Behavior of GASES

• Beans beans the royal fruit the more you eat the
  more you toot

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Section 14.1The Properties of Gases

• OBJECTIVES
• Describe the properties of gas particles.

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Section 14.1The Properties of Gases

• OBJECTIVES
• Explain how the kinetic energy of gas particles
  relates to Kelvin temperature.

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THREE STATES OF MATTER
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Kinetic Theory Revisited

• 1. Gases consist of hard, spherical particles
  (usually molecules or atoms)
• 2. Small- so the individual volume is considered
  to be insignificant
• 3. Large empty space between them
• 4. Easily compressed and expanded
• 5. No attractive or repulsive forces
• 6. Move rapidly in constant motion

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Kinetic Theory Revisited

• Recall that the average kinetic energy of a
  collection of gas particles is directly
  proportional to the Kelvin temperature of the
  gas.

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We can measure gases in 4 ways
Measurement Unit
Amount of gas (n) Moles
Volume (V) Liters (L)
Temperature (T) K
Pressure (P) atm, kPa, Torr, mm Hg,
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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 temp. is constant- doubling the number of
  particles doubles 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 in too- 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, p. 416

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2. Volume of Gas

• In a smaller container, molecules have less room
  to move.
• 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!
• The only way to increase the volume at constant
  pressure is to increase the temperature.

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Result?

• Figure 14.7, p. 417
• Think of tire pressure
• measured when cold

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Pressure (P)
The force per unit area on a surface
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Pressure is caused by gas particles slamming into
the containers walls.
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Section 14.2The Gas Laws

• OBJECTIVES
• State a) Boyles Law, b) Charless Law, c)
  Gay-Lussacs Law, and d) the Combined Gas Law.

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Robert Boyle (1627-1691)"From a knowledge of His
work, we shall know Him"One of the founders of
the Royal Society in 1660, Robert Boyle was
sometimes called 'the son of the Earl of Cork and
the father of chemistry.' Although he spent most
of his life in Britain, Robert was born at
Lismore Castle in Co. Waterford Ireland, the
youngest of fourteen children.Robert was born
into a world in which the theories of Aristotle
and the beliefs of alchemy were paramount. He
made many great contributions in both physics and
chemistry, and we particularly remember him when
we learn Boyle's Law, which state that at
constant temperature, the volume of a gas is
inversely proportional to the pressure applied to
it. (V x p constant)
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Section 14.2The Gas Laws

• OBJECTIVES
• Apply the gas laws to problems involving a) the
  temperature, b) the volume, and c) the pressure
  of a contained gas.

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The Gas Laws

• These will describe HOW gases behave.
• Can be predicted by the theory.
• Amount of change can be calculated with
  mathematical equations.

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1. Boyles Law

• At a constant temperature, gas pressure and
  volume are inversely related.
• As one goes up the other goes down
• Formula to use P1 x V1 P2 x V2

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Boyles Law

• A bicycle pump is a good example of Boyles law.
• As the volume of the air trapped in the pump is
  reduced, its pressure goes up, and air is forced
  into the tire.

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A gas occupies a volume of 0.458 L at a pressure
of 1.01 kPa and temperature of 295 Kelvin.
Although the temperature stays the same, the
volume is increased to 0.477 L. What is the new
pressure?
0.970 kPa
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Examples

• A balloon is filled with 25 L of air at 1.0 atm
  pressure. If the pressure is changed to 1.5 atm
  what is the new volume?

P1V1 P2V2 1.0 atm x 25 L 1.5 atm x V2 1
atm x 25 L 16.7 L 1.5 atm
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• A balloon is filled with 73 L of air at 1.3 atm
  pressure. What pressure is needed to change the
  volume to 43 L?

P1V1 P2V2 1.3 atm x 73 L P2 x 43 L 1.3
atm x 73 L 2.21 atm 43 L
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2. Charless Law

• The volume of a gas is directly proportional to
  the Kelvin temperature, if the pressure is held
  constant.
• Formula to use V1/T1 V2/T2
• If one temperature goes up, the volume goes up!

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Charless original balloon
Warm air is less dense than cooler air
Modern long-distance balloon
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What will be the volume of a gas sample at 309 K
if its volume at 215 K is 3.42 L? Assume that
pressure is constant.
4.92 L
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Examples

• What is the temperature of a gas expanded from
  2.5 L at 25 ºC to 4.1L at constant pressure?
• V1 V2 2.5 L
  4.1 L
• T1 T2 298 K T2
• Temperature must be in K
• T2 488.7 K or 215.7 C

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• What is the final volume of a gas that starts at
  8.3 L and 17 ºC, and is heated to 96 ºC?
• V2 10.6 L

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3. Gay-Lussacs Law

• The temperature and the pressure of a gas are
  directly related, at constant volume.
• Formula to use P1/T1 P2/T2
• If one temperature goes up, the pressure goes up!

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Gay-Lussacs Law Pressure and Temperature

• When a gas is heated at constant volume, the
  pressure increases.

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A balloon with a pressure of 0.900 atm is heated
from 105 K to 155 K. If volume is held
constant, what is the new pressure?
1.33 atm
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Examples

• What is the pressure inside a 0.250 L can of
  deodorant that starts at 25 ºC and 1.2 atm if the
  temperature is raised to 100 ºC?
• P2 1.5 atm
• At what temperature will the can be above have a
  pressure of 2.2 atm?
• T2 546.3 K

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4. Combined Gas Law

• The Combined Gas Law deals with the situation
  where only the number of molecules stays
  constant.
• Formula (P1 x V1)/T1 (P2 x V2)/T2
• This lets us figure out one thing when two of the
  others change.

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Combined Gas Law

• The good news is that you dont have to remember
  all three gas laws! Since they are all related
  to each other, we can combine them into a single
  equation. BE SURE YOU KNOW THIS EQUATION!

No, its not related to R2D2
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Combined Gas Law

• If you should only need one of the other gas
  laws, you can cover up the item that is constant
  and you will get that gas law!

P1
V1
P2
Boyles Law Charles Law Gay-Lussacs Law
V2
T2
T1
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Combined Gas Law Problem

• A sample of helium gas has a volume of 0.180 L,
  a pressure of 0.800 atm and a temperature of
  29C. What is the new temperature(K) of the gas
  at a volume of .090 L and a pressure of 3.20 atm?

Set up Data Table P1 0.800 atm V1 .180
L T1 302 K P2 3.20 atm V2 .090 L
T2 ??
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Calculation

• P1 0.800 atm V1 .180 L T1 302 K
• P2 3.20 atm V2 .090 L T2
  ??
• P1 V1 P2 V2
• P1 V1 T2 P2 V2 T1
• T1 T2
• T2 P2 V2 T1
• P1 V1
• T2 3.20 atm x .090 L x 302 K
  0.800 atm x .180 L

604 K
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The gas in a 0.010 L container has a pressure of
1.39 atmospheres. When the gas is transferred to
a 0.017 L container at the same temperature, what
is the pressure of the gas?
0.818 atm
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Example

• A 15 L cylinder of gas at 4.8 atm pressure and 25
  ºC is heated to 75 ºC and compressed to 17 atm.
  What is the new volume?
• V2 4.9 L

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• If 6.2 L of gas at 723 mm Hg and 21 ºC is
  compressed to 2.2 L at 4117 mm Hg, what is the
  final temperature of the gas?
• T2 594 K or 321 C

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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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Tips for Gas Law Problems

• 1) Determine which gas law you need
• Pressure and volume Boyles
• Temperature and volume Charles
• Temperature and Pressure Gay-Lussacs
• Temperature, pressure, and volume Combined
• 2) Identify your variables. Be sure you put the
  proper numbers together
• 3) Change all variables into the correct units
• Temperature must be K
• Pressure units must match
• Volume units must match
• 4) Put numbers into the gas law equation and solve

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And now, we pause for this commercial message
from STP
OK, so its really not THIS kind of STP STP in
chemistry stands for Standard Temperature and
Pressure
Standard Pressure 1 atm (or an
equivalent) Standard Temperature 0 deg C (273 K)
STP allows us to compare amounts of gases between
different pressures and temperatures
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STP
Standard Temperature and Pressure 0C and 1 atm
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Section 14.3Ideal Gases

• OBJECTIVES
• Distinguish between ideal and real gases.

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Ideal Gases

• We are going to assume the gases behave
  ideally- obeys the Gas Laws under all temp. and
  pres.
• An ideal gas does not really exist, but it makes
  the math easier and is a close approximation.
• Particles have no volume.
• No attractive forces.

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Ideal Gases

• There are no gases for which this is true
  however,
• Real gases behave this way at high temperature
  and low pressure.

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5. The Ideal Gas Law

• Equation P x V n x R x T
• Pressure times Volume equals the number of moles
  times the Ideal Gas Constant (R) times the
  temperature in Kelvin.
• This time R does not depend on anything, it is
  really constant
• R 8.31 (L x kPa) / (mol x K) or
• 0.0821 (L x atm) / (mol x K)

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Ideal Gas Law
The mother of all gas laws. It includes
everything!
PV nRT
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PV nRT
P pressure (atm) V volume (L) n moles
(mol) R Gas Constant T Temperature (Kelvin)
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Using PV nRT

• P Pressure V Volume
• T Temperature N number of moles
• R is a constant, called the Ideal Gas Constant.
  Depending what your pressure unit is determines
  which of the 3 gas constants you need to use.
• R 8.314 R .0821
• R 62.4

L kPa Mol K
L kPa Mol K
L mm Hg Mol K
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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 STP conditions
• P x V
• R x T

n
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If the pressure exerted by a gas at 0.00C in a
volume of 0.0010 L is 5.00 atm, how many moles
of gas are present?
2.2 x 10-4 moles
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Examples

• How many moles of air are there in a 2.0 L bottle
  at 19 ºC and 747 mm Hg?
• n P x V
• R x T
• n 747 mmHg x 2 L .0820 moles air
  
• 62.4 L mmHg x 292 K
• 
  mole K

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• What is the pressure exerted by 1.8 g of H2 gas
  in a 4.3 L balloon at 27 ºC?
• P 5.10
• You have to get moles from the 1.8 g of H2 by
  multiplying by the molar mass of H2

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Ideal Gases dont exist

• Molecules do take up space
• There are attractive forces
• 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 their volume.
• This is at low pressure

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Real Gases behave like Ideal gases when...

• When molecules are moving fast
• 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 14.4Gas MoleculesMixtures and
Movements

• OBJECTIVES
• Calculate a) moles, b) masses, and c) volumes of
  gases at STP.

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Avagadros Hypothesis
Equal volumes of gas (at same T and P) contain
the same amount of particles
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1 mole 6.02 x 1023 particles
1 mole 22.4 L
Only works at same T and P
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6. Daltons Law of Partial Pressures

• The total pressure inside a container is equal to
  the partial pressure due to each gas.
• The partial pressure is the contribution by that
  gas.
• PTotal P1 P2 P3

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• We can find out the pressure in the fourth
  container.
• By adding up the pressure in the first 3.

2 atm
1 atm
3 atm
6 atm
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A balloon contains O2 and N2 gas. If the partial
pressure of the O2 is 0.75 atm and the partial
pressure of the N2 is 0.55 atm, what is the total
pressure of the balloon?
1.30 atm
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Table of Vapor Pressures for Water
3.56 kPa
1.40 kPa
5.65 kPa
31.2 kPa
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Examples

• What is the total pressure in a balloon filled
  with air if the pressure of the oxygen is 170 mm
  Hg and the pressure of nitrogen is 620 mm Hg?
• Ptotal 170 mm Hg 620 mm Hg
• Ptotal 790 mm Hg

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In a second balloon the total pressure is 1.3
atm. What is the pressure of oxygen if the
pressure of nitrogen is 720 mm Hg? First
Convert 720 mm Hg to atm 720 mm Hg x 1 atm
.95 atm 760 mm Hg PTotal
1.3 - .95 PTotal .35 atm
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Diffusion

• 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.
• Depends on the speed of the molecule.

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Grahams Law

• Heavier molecules move slower at the same temp.
  (by Square root)
• Heavier molecules effuse and diffuse slower
• Helium effuses and diffuses faster than air -
  escapes from balloon.

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Grahams Law
Gases with smaller masses move faster than gases
with large masses
(like a kid in Walmart)
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H2 moves faster than N2.
Which of the following gases moves the fastest?
O2 CO2 NH3
Cl2 I2 H2O
Ar N2 Br2