Gas Laws

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Gas Laws
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Kinetic Theory

• True for ideal gases.
• 1. Gas molecules dont attract or repel each
  other
• 2. Particles are smaller than the space between
  them
• They dont have volume

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Kinetic Theory

• 3. Constant Random motion
• 4. No kinetic energy is lost when molecules
  collideelastic collision
• All gases have same energy at a particular
  temperature.
• Actual gases dont really obey all of these
  assumptionsBut its close enough!!

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B. Real Gases

• Particles in a REAL gas
• have their own volume
• attract each other
• Gas behavior is most ideal
• at low pressures
• at high temperatures
• in nonpolar atoms/molecules

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C. Characteristics of Gases

• Gases expand to fill any container.
• random motion, no attraction
• Gases are fluids (like liquids).
• no attraction
• Gases have very low densities.
• no volume lots of empty space

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C. Characteristics of Gases

• Gases can be compressed.
• no volume lots of empty space
• Gases undergo diffusion effusion.
• random motion

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The Gas Laws

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

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E. Pressure
Which shoes create the most pressure?
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E. Pressure

• Barometer
• measures atmospheric pressure

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E. Pressure

• Manometer
• measures contained gas pressure

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E. Pressure

• KEY UNITS AT SEA LEVEL
• 101.325 kPa (kilopascal)
• 1 atm
• 760 mm Hg
• 760 torr
• 14.7 psi

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F. STP
STP
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The effect of adding gas.

• Doubling the the number of gas particles doubles
  the pressure.
• (of the same volume at the same temperature).

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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.

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• If you double the number of molecules

1 atm
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• If you double the number of molecules
• When we blow up a balloon we are adding gas
  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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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.

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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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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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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.

6 atm
1 atm
2 atm
3 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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Boyles Law

• At a constant temperature pressure and volume are
  inversely related.
• As one goes up the other goes down
• P1 x V1P2 x V2

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Think about it mathematicallyPressure and Volume
are INVERSELY proportional

• P1 x V1P2 x V2
• Pressure is 2 atm at 10L and increases to 4 atm.
• (2 atm)(10L) (4 atm)(X)

• 20 (4) (X)

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P
V
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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?
• 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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Charles Law

• The volume of a gas is directly proportional to
  the Kelvin temperature if the pressure is held
  constant.
• V1 V2
• T1 T2

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Think about it mathematically Volume and
Temperature are DIRECTLY proportional

• V1 V2
• T1 T2
• Volume is 4L and Temp is 8K and Temp is lowered
  to 4K. What does the volume have to be????
• 4 ?
• 8 4
• What number does it take to keep both sides equal

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V
T
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Examples

• What is the temperature 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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Gay Lussacs Law

• The temperature and the pressure of a gas are
  directly related at constant volume.
• P1 P2
• T1 T2

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P
T
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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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Putting the pieces together

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

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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 1.7
  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 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-Lussac Law
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The Fourth Part

• Avagadros Hypothesis
• Volume is proportional to number of molecules (or
  moles) at constant T and P.
• V is proportional to moles.
• Gets put into the combined gas Law

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• P1 x V1 P2 x V2
• T1x n1 T2x n2

• For an ideal gas at STP
• P101KPa
• T273K
• V22.4L
• n1mole

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These numbers are constant, so put them into the
equation!!!
P2 x V2
101.3KPa
22.4L
x

273K
x
1 mol
T2 x n
The left side 8.31 KPa x L K x mole
Lets assign it a letter-----R---------called
the ideal gas constant
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What if we use a different number for standard
pressure?

• Instead of 101.3KPa use 1atm

1 atm
x
22.4L
P2 x V2

1 mole
273K
n2xT2
x
So R .0821 atm x L mole x K
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What if we use a different number for standard
pressure?

• Instead of 101.3KPa use 760mHg

x
22.4L
P2 x V2
760 mm

1 mole
273K
n2xT2
x
So R 62.4mmHg x L mole x K
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So..

• R P x V
• n x T
• Too hard to memorizerearrange the letters
• P x V n x R x T The Ideal Gas Law

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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

• 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 gram formula mass of a gas can be determined
  by the density of the gas.
• Or Density can be determined by using gfm and the
  ideal gas law
• D mass m
• Volume V
• Molar Mass grams m moles
  n
• n PV
• RT
  
• Therefore .

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

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Density Examples

• What is the density of a O2 at 800mmHg and 35oC?
• What is the gram formula mass of a gas with a
  density of 5.68g/L at 70oC and 1.86atm? What gas
  is it?

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Molar mass(Molecular WT)

• PV nRT n g/Molar mass
• PV (g/MM)RT
• MM (gRT)(PV)

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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

• Use the Ideal Gas Law n PV/RT
• If you want to find how much gas - use moles to
  figure out volume.
• For Example

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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 with excess H2SO4?

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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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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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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.