GAS LAWS

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GAS LAWS
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Kinetic Molecular Theory

• Particles in an ideal gas
• have no volume.
• have elastic collisions.
• are in constant, random, straight-line motion.
• dont attract or repel each other.
• have an average KE directly related to Kelvin
  temperature.

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Real Gases

• Particles in a REAL gas
• have their own volume
• attract and repel each other
• Gas behavior is most ideal
• at low pressures
• at high temperatures
• Most real gases act like ideal gases except
  under high pressure and low temperature.

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Characteristics of Gases

• Gases expand to fill any container.
• Take the shape and volume of their container.
• Gases are fluids (like liquids).
• Little to no attraction between the particles
• Gases have very low densities.
• lots of empty space between the particles

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Characteristics of Gases

• Gases can be compressed.
• lots of empty space between the particles
• Indefinite density
• Gases undergo diffusion.
• random motion
• scatter in all directions

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Pressure
Which shoes create the most pressure?
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Pressure- how much a gas is pushing
on a container.

• Atmospheric pressure- atmospheric gases push on
  everything on Earth
• UNITS AT SEA LEVEL
• 1 atm 101.3 kPa (kilopascal) 760 mmHg 760 torr
  

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Pressure

• Barometer
• measures atmospheric pressure

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Pressure

• Manometer
• measures contained gas pressure

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Temperature how fast the molecules
are moving

• Always use absolute temperature (Kelvin) when
  working with gases.

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STP
-OR-
12

• Volume how much space a gas occupies
• Units
• L, mL, cm3
• 1000 mL 1 L
• 1 mL 1 cm3

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BASIC GAS LAWS
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Charles Law

• T ? V (temperature is directly proportional to
  volume)
• T ? V? T? V?
• V1 V2
• T1 T2 T is always in K
• K C 273
• P and n constant

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Charles Law
(Pressure is held constant)
Timberlake, Chemistry 7th Edition, page 259
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Charles Law
Timberlake, Chemistry 7th Edition, page 254
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Charles Law
The egg out of the bottle
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ationsarts/pages/chem
18
Charles Law Problem

• Mrs. Rodriguez inflates a balloon for a party.
  She is in an air-conditioned room at 27.0oC, and
  the balloon has a volume of 4.0 L. Because she
  is a curious and intrepid chemistry teacher, she
  heats the balloon to a temperature of 57.0oC.
  What is the new volume of the balloon if the
  pressure remains constant?

• Given Unkown Equation
  
• Substitute and Solve

T1 27.0oC 273 300 K V1 4.0 L T2
57.0oC 273 330 K
P1V1 P2V2 T1 V1T2
V2 ? L
4.0 L V2 300 K 330K
4.4 L
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Charles Law Learning Check

• A 25 L balloon is released into the air on a warm
  afternoon (42º C). The next morning the balloon
  is recovered on the ground. It is a very cold
  morning and the balloon has shrunk to 22 L. What
  is the temperature in º C?

• Given Unkown Equation
  
• Substitute and Solve

V1 25 L T1 42 oC 273 315 K V2 22 L
P1V1 P2V2 T1 V1T2
T2 ? ºC
25 L 22 L 315 K T2
277.2 K -273 4.2 ºC
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Boyles Law

• P? V ? P? V ?
• P ? 1/V (pressure is inversely proportional to
  volume)
• P1V1 P2V2
• T and n constant

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Boyles Law
P1V1 P2V2
(Temperature is held constant)
Timberlake, Chemistry 7th Edition, page 253
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Boyles Law

• Marshmallows in a vacuum

Timberlake, Chemistry 7th Edition, page 254
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Mechanics of Breathing
Boyles Law
Timberlake, Chemistry 7th Edition, page 254
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Boyles Law Problem

• A balloon is filled with 30.L of helium gas at
  1.00 atm. What is the volume when the balloon
  rises to an altitude where the pressure is only
  0.25 atm?
• Given Unkown Equation
• Substitute and Solve

P1V1 P2V2 T1 T2
V1 30 L P1 1 atm P2 .25atm
V2 ? L

• V2 0.25 atm 30 L x 1.0 atm 120 L

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Boyles Law Learning Check

• A gas occupies 100. mL at 150. kPa. Find its
  volume at 200. kPa.
• Given Unkown Equation
• Substitute and Solve

V1 100. mL 0.100 L P1 150. kPa P2
200. kPa
P1V1 P2V2 T1 T2
V2 ? L

• V2 x 200. kPa 0.100 L x 150. kPa 75.0 mL
• 0.0750 L

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AVOGADROS LAW

• V?n? V?n?
• V? n (direct)
• V1 V2
• n1 n2
• T P Constant

V
n
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Avogadros Law Problem

• A 3.0 liter sample of gas contains 7.0 moles.
  How much gas will there be, in order for the
  sample to be 2.3 liters? P T do not change
• Given Unkown Equation
• Substitute and Solve

P1V1 P2V2 n1T1 n2T2
V1 3.0 L n1 7.0 mol V2 2.3 L
n2 ? mol
3.0 L 2.3 L 7.0 mol n2 mol
5.4 mol
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Gay-Lussacs Law

• P1 P2
• T1 T2
• V n constant
• Direct relationship
• P?T? P?T ?

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Gay-Lussac Law

• Collapsing Barrel

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Gay-Lussac Law

• Tank car implosion

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COMBINED IDEAL GAS LAW

• P1V1 P2V2
• n1T1 n2T2
• If P, V, n, or T are constant then they cancel
  out of the equation.
• n usually constant (unless you add or remove
  gas), so
• P1V1 P2V2
• T1 T2

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Combined Gas Law Problem

• Ms. Evans travels to work in a hot air balloon
  from the Rocky Mountains. At her launch site,
  the temperature is 5.00 C, the atmospheric
  pressure is 0.801 atm, and the volume of the air
  in the balloon is 120.0 L. When she lands in
  Plano, the temperature is 28.0 C and the
  atmospheric pressure is 101.3 kPa. What is the
  new volume of the air in the balloon?

• Given Unkown Equation
• Substitute and Solve

T1 5.0oC 273 278 K P1 0.801 atm V1 120.0
L T2 28.0oC 273 301 K P2 101.3 kPa 1 atm

V2 ? L
V1 x P1 V 2 x P2 T 1 T
2

• V2 x 1 atm 120.0 L x 0.801 atm 104 L
• 301K 278 K

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Combined Gas Law Learning Check

• Nitrogen gas is in a 7.51 L container at 5.?C and
  0.58 atm. What is the new volume of the gas at
  STP?

• Given Unkown Equation
• Substitute and Solve

T1 5.0oC 273 278 K P1 0.58 atm V1 7.51
L T2 273 K P2 1 atm
V2 ? L
V1 x P1 V 2 x P2 T 1 T
2

• V2 x 1.0 atm 7.51L x 0.58 atm 4.3 L
• 273 K 278 K

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Ideal Gas Law (Pivnert)

• PVnRT
• R The Ideal Gas Constant
• R 0.0821 (Latm) R
  62.4 (Lmm Hg)
• (molK)
  (molK)
• R 8.31 (LkPa)
• (molK)
• V has to be in Liters, n in Moles, T in Kelvin,
• P can be in atm, kPa or mmHg
• Choose which R to used based on the units of
  your pressure.
• P V n R T
• (atm) (L) (moles) (Latm/molK)
  (K)
• (kPa) (L) (moles) (LkPa/molK)
  (K)
• mm Hg (L) (moles) (LmmHg/molK) (K)

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Ideal Gas Law Problem

• A rigid steel cylinder with a volume of 20.0 L is
  filled with nitrogen gas to a final pressure of
  200.0 atm at 27.0 oC. How many moles of gas does
  the cylinder hold?

• Given Unkown
  Equation
  
  
• Substitute and Solve

V 20.0 L P 200.0 atm T 27.0oC 273 300 K
PVnRT R .0821 atm L/K Mole
moles of nitrogen?

• n 0821 atm L/K Mole x 300 K 200.0 atm x
  20.0L 162 moles

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Ideal Gas Law Learning Check

• A balloon contains 2.00 mol of nitrogen at a
  pressure of 0.980 atm and a temperature of 37?C.
  What is the volume of the balloon?

• Given Unkown
  Equation
  
  
• Substitute and Solve

n 2.00 mol P 0.980 atm T 37.0oC 273 310 K
PVnRT R .0821 atm L/K Mole
V in L?

• 0.980 atm x V 2.00 mol x .0821 atm L/K Mole x
  310 K 51.9 L

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Daltons Law of Partial Pressure

• The total pressure of a mixture of gases is equal
  to the sum of the partial pressures of the
  component gases.
• Ptotal Pgas 1 Pgas 2 Pgas 3

A metal container holds a mixture of 2.00 atm of
nitrogen, 1.50 atm of oxygen and 3.00 atm of
helium. What is the total pressure in the
canister?
6.5 atm
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• Welcome to Mole Island

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Welcome to Mole Island
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Welcome to Mole Island
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Gas Stoichiometry

• Moles ? Liters of a Gas
• 2C4H10 (g) 13O2(g) ? 8CO2(g) 10H2O(g)

2 mol 13 mol ? 8 mol
10 mol
2 L 13 L ? 8 L
10 L
RecallThe coefficients in a chemical reaction
represent molar amounts of substances taking
part in the reaction.
Avogadros principle states that one mole of any
gas occupies 22.4 L at STP.
Thus when gases are involved, the coefficients in
a balanced chemical equation represent not only
molar amounts but also relatives volumes
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ationsarts/pages/chem
42
Gas Stoichiometry Problem

• In the following combustion reaction, what volume
  of methane (CH4) is needed to produce 26 L of
  water vapor?
• CH4 (g) 2O2(g) ? CO2(g)
  2H2O(g)

x L ?
26 L
1 mol ?
2 mol
1 L ?
2 L
x L
26 L
1L 2L
x 13 L
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ationsarts/pages/chem
43
Gas Stoichiometry use ideal gas law
PVnRT

• Looking for grams or moles of gas?
• Step 1 start with ideal gas law to find moles of
  gas
• Step 2 1change to grams of gas

Grams/mol? 1) Use Ideal Gas Law
2) Do stoichiometry calculations
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ationsarts/pages/chem
44
Example 1

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

4 Al(s) 3 O2(g) ? 2 Al2O3(s)

• Given Unkown
• V O2 15.0 L O2 grams of
  Al2O3? R .0821 atm L/K Mole
• P O2 97.3 kPa 0.9605 atm
• T O2 21oC 273 294 K
• Step 1 Calculate moles of O2
• n PV 0.9605 atm x 15.0 L
  0.5969 mol O2
• RT 0.0821 atm L/K Mole 294 K

Given liters Start with Ideal Gas Law and
calculate moles of O2.
Use stoich to convert moles of O2 to grams Al2O3.
Step 2 Calculate mass of Al2O3 0.5969 mol O2 X
mol Al2O3 0.3979 mol Al2O3 3moleO2 2
mole Al2O3
0.3979 mol Al2O3 x 101.96 g Al2O3
1 mol Al2O3
41 g Al2O3
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ationsarts/pages/chem
45
Gas Stoichiometry use ideal gas law
PVnRT

• Looking for volume of gas?
• Step 1 start with stoichiometry conversion to
  find moles of gas
• Step 2 use ideal gas law to find the volume

Liters ? 1) Do stoichiometry calculations
2) Use Ideal Gas Law
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ationsarts/pages/chem
46
Example 2

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

CaCO3 ? CaO CO2

• Given Unkown PVnRT
• m 5.25 g CaCO3 volume of CO2?
  R .0821 atm L/K Mole
• P 101.3 kPa 1 atm
  T 25.0oC 273 298 K
• Step 1 Calculate moles of CO2
• 5.25 g CaCO3 x 1 mole CaCO3 0.0525 mol CaCO3
• 100 g CaCO3
• 1 mole CO2 1mole CaCO3 0.0525 mol CO2

Looking for liters Start with stoich and
calculate moles of CO2.
Plug this into the Ideal Gas Law to find volume.
Step 2 Calculate volume of CO2 V nRT 0.0525
mol CO2 x .0821 atm L/K Mole x 298 K 1.28 L
P 1 atm