BEHAVIOR OF GASES Chapter 14

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BEHAVIOR OF GASESChapter 14
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Importance of Gases

• Airbags fill with N2 gas in an accident.
• Gas is generated by the decomposition of sodium
  azide, NaN3.
• 2 NaN3(s) ---gt 2 Na(s) 3 N2(g)

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THREESTATES OF MATTER
Click picture above to view movie on states of
matter Click here for water production
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General Properties of Gases

• There is a lot of "free" space in a gas.
• Gases can be expanded infinitely.
• Gases occupy containers uniformly and completely.
• Gases diffuse and mix rapidly.

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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.
• Click for movie
• No Kinetic energy lost during collisions.
• All particles have same energy at same
  temperature.

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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. number of moles (n)

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Properties of Gases

• Gas properties can be modeled using math. Model
  depends on-
• V volume of the gas (L)
• T temperature (K)
• n amount (moles)
• P pressure (atm or kilopascal)

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Pressure

• Pressure of air is measured with a BAROMETER
  (developed by Torricelli in 1643)
• Barometer calibrated for column width and pool
  width/depth

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Pressure

• Hg rises in tube until gravitational force of Hg
  (down) balances the force of atmosphere (pushing
  up).
• P of Hg pushing down related to
• Hg density
• column height

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Pressure

• Column height measures Pressure of atmosphere
• 1 standard atm
• 760 mm Hg
• 76 cm Hg
• 760 torr
• 29.9 inches
• about 33 feet of water
• SI unit is PASCAL, Pa, where 1 atm 101.325 kPa

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Gas -Volume, Temp, Pressure

• Click to view movie

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1. Amount of Gas

• When we inflate a ball, 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

• Fewer molecules means fewer collisions.
• Gases naturally move from areas of high pressure
  to low pressure because there is empty space to
  move in - 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

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Expanding Gas Uses?

• The bombardier beetle uses decomposition of
  hydrogen peroxide to defend itself. The gas acts
  as a propellant.

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The Shuttle Uses a Solid Booster and Uncontrolled
Expanding Gases Can Be Disastrous
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• If you double the number of molecules

1 atm
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• If you double the number of molecules
• You double the pressure.

2 atm
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• As you remove molecules from a container

4 atm
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• As you remove molecules from a container the
  pressure decreases

2 atm
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• As you remove molecules from a container the
  pressure decreases
• Until the pressure inside equals the pressure
  outside
• Molecules naturally move from high to low pressure

1 atm
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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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Changing the Size of the Container

• In a smaller container molecules have less room
  to move.
• Hit the sides of the container more often.
• As volume decreases pressure increases. Think air
  pump

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• As the pressure on a gas increases

1 atm
4 Liters
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• As the pressure on a gas increases the volume
  decreases
• Pressure and volume are inversely related

2 atm
2 Liters
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Pressure and Volume Relationship
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What happens to the air in a divers lungs the
deeper they go?
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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 temperature at
  constant pressure is to increase the volume.

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Temperature

• Raising the temperature of a gas increases the
  pressure if the volume is held constant.
• The molecules hit the walls harder.
• The only way to increase the temperature at
  constant pressure is to increase the volume.

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300 K

• If you start with 1 liter of gas at 1 atm
  pressure and 300 K
• and heat it to 600 K one of 2 things happens

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600 K
300 K

• Either the volume will increase to 2 liters at 1
  atm

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600 K
300 K

• Or the pressure will increase to 2 atm.
• Or someplace in between

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Temperature and Volume Relation
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The Gas Laws

• Describe HOW gases behave.
• Can be predicted by theory.
• Amount of change can be calculated with
  mathematical equations.

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A. Boyles Law
PV k
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A. Boyles Law

• The pressure and volume of a gas are inversely
  related
• at constant mass temp

PV k
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A. Boyles Law
Click to view movie
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Boyles Law

• At a constant temperature pressure and volume are
  inversely related.
• As one goes up the other goes down
• P x V K (K is some constant)
• Easier to use P1 x V1P2 x V2
• Click for movie

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P
V
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Boyles Gas Law Problems

• A gas occupies 100. mL at 150. kPa. Find its
  volume at 200. kPa.

BOYLES LAW
GIVEN V1 100. mL P1 150. kPa V2 ? P2
200. kPa
WORK P1V1 P2V2
P?
V?
(150.kPa)(100.mL)(200.kPa)V2 V2 75.0 mL
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Examples

• A balloon is filled with 25 L of air at 1.0 atm
  pressure. If the pressure is change to 1.5 atm
  what is the new volume?
• A balloon is filled with 73 L of air at 1.3 atm
  pressure. What pressure is needed to change to
  volume to 43 L?

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B. Charles Law
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B. Charles Law

• The volume and absolute temperature (K) of a gas
  are directly related
• at constant mass pressure

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Charles Law
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B. Charles Law
Click for movie
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B. Charles Law

• The volume of a gas is directly proportional to
  the Kelvin temperature if the pressure is held
  constant.
• V K x T (K is some constant)
• V/T K
• V1/T1 V2/T2

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V
T
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Gas Law Problems

• A gas occupies 473 cm3 at 36C. Find its volume
  at 94C.

CHARLES LAW
GIVEN V1 473 cm3 T1 36C 309K V2 ? T2
94C 367K
WORK V1T2 V2T1
T?
V?
(473 cm3)(367 K)V2(309 K) V2 562 cm3
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Examples

• What is the temperature (ºC) of a gas that is
  expanded from 2.5 L at 25ºC to 4.1L at constant
  pressure.
• What is the final volume of a gas that starts at
  8.3 L and 17ºC and is heated to 96ºC?

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C. Gay-Lussacs Law
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C. Gay-Lussacs Law

• The pressure and absolute temperature (K) of a
  gas are directly related
• at constant mass volume

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C. Gay-Lussacs Law

• The temperature and the pressure of a gas are
  directly related at constant volume.
• P K x T (K is some constant)
• P/T K
• P1/T1 P2/T2

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P
T
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E. Gas Law Problems

• A gas pressure is 765 torr at 23C. At what
  temperature will the pressure be 560. torr?

GAY-LUSSACS LAW
GIVEN P1 765 torr T1 23C 296K P2 560.
torr T2 ?
WORK P1T2 P2T1
P?
T?
(765 torr)T2 (560. torr)(296K) T2 217 K
-56C
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Examples

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

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Too Much Pressure and Not Enough Volume!!!!
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Putting the pieces together

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

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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
Charles 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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D. Combined Gas Law
P T
V T
PV T
k
PV
P1V1T2 P2V2T1
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E. Gas Law Problems

• A gas occupies 7.84 cm3 at 71.8 kPa 25C. Find
  its volume at STP.

COMBINED GAS LAW
GIVEN V1 7.84 cm3 P1 71.8 kPa T1 25C
298 K V2 ? P2 101.325 kPa T2 273 K
WORK P1V1T2 P2V2T1 (71.8 kPa)(7.84 cm3)(273
K) (101.325 kPa) V2 (298 K) V2 5.09 cm3
P? T?
V?
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Examples

• A 15 L cylinder of gas at 4.8 atm pressure at
  25ºC is heated to 75ºC and compressed to 17 atm.
  What is the new volume?
• If 6.2 L of gas at 723 mm Hg at 21ºC is
  compressed to 2.2 L at 4117 mm Hg, what is the
  temperature of the gas?

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The Fourth Part

• Avagadros Hypothesis
• click for movie
• V is proportional to number of molecules at
  constant T and P
• V is proportional to moles
• One mole 6.02 x 1023 particles
• One mole 22.4 L at STP movie
• V K n ( n ) is the number of moles
• Gets put into the Ideal Gas Law

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Ideal Gases

• Remember in this chapter we assume the gases
  behave ideally.
• Ideal gases dont really exist, but assuming it
  makes the math easier. So we get a close
  approximation.
• Particles have no volume.
• No attractive forces.
• However, real gases do behave like ideal gases at
  high temperature and low pressure.

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Ideal Gases

• There are no gases for which this is true.
• However, real gases do behave like ideal gases at
  high temperature and low pressure.

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The Ideal Gas Law

• 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

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The Ideal Gas Law

• R 0.0821 (L atm)/(mol K) or
• R 62.4 (L mm Hg)/(K mol)
• We now have a new way to count moles. By
  measuring T, P, and V. We arent restricted to
  STP.
• n PV/RT

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Examples

• How many moles of air are there in a 2.0 L bottle
  at 19ºC and 747 mm Hg?
• What is the pressure exerted by 1.8 g of H2 gas
  exert in a 4.3 L balloon at 27ºC?

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Density

• The Molar mass of a gas can be determined by the
  density of the gas.
• D mass m Volume
  V
• Molar mass mass m Moles
  n
• n PV RT

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Molar Mass Formulas

• Molar Mass m (PV/RT)
• Molar mass m RT V
  P
• Molar mass DRT P

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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
• For example

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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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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?
• 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?

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B. Daltons Law

• The total pressure of a mixture of gases equals
  the sum of the partial pressures of the
  individual gases.

When a H2 gas is collected by water displacement,
the gas in the collection bottle is actually a
mixture of H2 and water vapor.
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B. Daltons Law

• Hydrogen gas is collected over water at 22.5C.
  Find the pressure of the dry gas if the
  atmospheric pressure is 94.4 kPa.

The total pressure in the collection bottle is
equal to atmospheric pressure and is a mixture of
H2 and water vapor.
GIVEN PH2 ? Ptotal 94.4 kPa PH2O 2.72 kPa
WORK Ptotal PH2 PH2O 94.4 kPa PH2 2.72
kPa PH2 91.7 kPa
Look up water-vapor pressure for 22.5C.
Sig Figs Round to least number of decimal places.
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B. Daltons Law

• A gas is collected over water at a temp of 35.0C
  when the barometric pressure is 742.0 torr. What
  is the partial pressure of the dry gas?

The total pressure in the collection bottle is
equal to barometric pressure and is a mixture of
the gas and water vapor.
GIVEN Pgas ? Ptotal 742.0 torr PH2O 42.2
torr
WORK Ptotal Pgas PH2O 742.0 torr PH2
42.2 torr Pgas 699.8 torr
Look up water-vapor pressure for 35.0C.
Sig Figs Round to least number of decimal places.
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Diffusion

• Molecules moving from areas of high concentration
  to low concentration.
• 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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GAS DIFFUSION AND EFFUSION

• effusion is the movement of molecules through a
  small hole into an empty container.

• diffusion is the gradual mixing of molecules of
  different gases.

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Grahams Law

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

Chem Express
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Grahams Law

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

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C. Grahams Law

• Diffusion
• Spreading of gas molecules throughout a container
  until evenly distributed.
• Effusion
• Passing of gas molecules through a tiny opening
  in a container

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C. Grahams Law

• Speed of diffusion/effusion
• Kinetic energy is determined by the temperature
  of the gas.
• At the same temp KE, heavier molecules move
  more slowly.
• Larger m ? smaller v

KE ½mv2
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C. Grahams Law

• Grahams Law
• Rate of diffusion of a gas is inversely related
  to the square root of its molar mass.
• The equation shows the ratio of Gas As speed to
  Gas Bs speed.

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C. Grahams Law

• Determine the relative rate of diffusion for
  krypton and bromine.

The first gas is Gas A and the second gas is
Gas B. Relative rate mean find the ratio
vA/vB.
Kr diffuses 1.381 times faster than Br2.
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C. Grahams Law

• An unknown gas diffuses 4.0 times faster than O2.
  Find its molar mass.

The first gas is Gas A and the second gas is
Gas B. The ratio vA/vB is 4.0.
Square both sides to get rid of the square root
sign.
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C. Grahams Law

• A molecule of oxygen gas has an average speed of
  12.3 m/s at a given temp and pressure. What is
  the average speed of hydrogen molecules at the
  same conditions?

Put the gas with the unknown speed as Gas A.
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Ideal Gases dont exist

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

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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.
• Collisions are harder and faster.
• Molecules are not next to each other very long.
• Attractive forces cant play a role.

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You may need to review Chapter 12 click for movie
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At STP

• At STP determining the amount of gas required or
  produced is easy.
• 22.4 L 1 mole
• For example How many liters of O2 at STP
  are required to produce 20.3 g of H2O?

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Not At STP

• Chemical reactions happen in MOLES.
• If you know how much gas - change it to moles
• Use the Ideal Gas Law n PV/RT
• If you want to find how much gas - use moles to
  figure out volume V nRT/P

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A. Gas Stoichiometry

• Moles ? Liters of a Gas
• STP - use 22.4 L/mol
• Non-STP - use ideal gas law
• Non-STP
• Given liters of gas?
• start with ideal gas law
• Looking for liters of gas?
• start with stoichiometry conversions.

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B. Gas Stoichiometry Problem

• What volume of CO2 forms from 5.25 g of CaCO3
  at 103 kPa 25ºC?

CaCO3 ? CaO CO2
5.25 g
? Lnon-STP
Looking for liters Start with stoich and
calculate moles of CO2.
1 mol CaCO3 100.09g CaCO3
5.25 g CaCO3
1 mol CO2 1 mol CaCO3
0.0525 mol CO2
Plug this into the Ideal Gas Law to find liters.
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B. Gas Stoichiometry Problem

• What volume of CO2 forms from 5.25 g of CaCO3
  at 103 kPa 25ºC?

WORK PV nRT (103 kPa)V(.0525mol)(8.314
L?kPa/mol?K)
(298K) V 1.26 L CO2
GIVEN P 103 kPa V ? n 0.0525 mol T 25C
298 K R 8.314 L?kPa/mol?K
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B. Gas Stoichiometry Problem

• How many grams of Al2O3 are formed from 15.0 L of
  O2 at 97.3 kPa 21C?

4 Al 3 O2 ? 2 Al2O3
15.0 L non-STP
? g
WORK PV nRT (97.3 kPa) (15.0 L) n (8.314
L?kPa/mol?K) (294K) n 0.597 mol O2
GIVEN P 97.3 kPa V 15.0 L n ? T 21C
294 K R 8.314 L?kPa/mol?K
Given liters Start with Ideal Gas Law and
calculate moles of O2.
NEXT ?
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B. Gas Stoichiometry Problem

• How many grams of Al2O3 are formed from 15.0 L of
  O2 at 97.3 kPa 21C?

4 Al 3 O2 ? 2 Al2O3
15.0L non-STP
? g
Use stoich to convert moles of O2 to grams Al2O3.
2 mol Al2O3 3 mol O2
0.597 mol O2
101.96 g Al2O3 1 mol Al2O3
40.6 g Al2O3
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Example 1

• HCl(g) can be formed by the following reaction
• 2NaCl(aq) H2SO4 (aq) 2HCl(g) Na2SO4(aq)
• What mass of NaCl is needed to produce 340 mL of
  HCl at 1.51 atm at 20ºC?

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Example 2

• 2NaCl(aq) H2SO4 (aq) 2HCl(g) Na2SO4
  (aq)
• What volume of HCl gas at 25ºC and 715 mm Hg will
  be generated if 10.2 g of NaCl react?

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Too Little Pressure and Too Little Volume!!!!
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What is a Turbocharger?