The Gas Laws

1
The Gas Laws

• Chapter 9

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Kinetic Molecular Theory

• A gas is composed of small particles (molecules)
  that are spaced widely apart.
• Compressible
• Low density - about a 1000 times less dense than
  a liquid
• The molecules of a gas are in rapid, constant
  motion
• Pressure the force of the molecules hitting the
  side of a container
• Fill a container (like a balloon) evenly.

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Kinetic Molecular Theory

• All collisions are elastic
• Molecules dont lose any energy when they
  collide.
• Gas molecules have little/no attractive force on
  one another.
• Too far apart
• Mix thoroughly unlike oil and water (too far
  apart for polar/non-polar forces to matter)

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Kinetic Molecular Theory

• The temperature of a gas is related to the
  average kinetic energy of the molecules.
• Kinetic energy energy in motion
• KE ½ mv2
• Grahams Law of Diffusion the higher the molar
  mass of a gas, the slower it moves
• v1 m2
• v2 m1

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Grahams Law Example

• At the same temperature, how much faster does an
  He atom move than an N2 molecule?
• (Ans 2.65 times faster)

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Grahams Law Example

• Which is faster (and by how much) Cl2 or O2?
• (Ans O2 is about 1.5 times faster)

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Our Atmosphere

• 99 N2 and O2
• 78 N2
• 21 O2
• 1 CO2 and the Noble Gases

8
Pressure

• Pressure Force
• Area
• (Needles, High Heels, Snow shoes)
• Caused by the collisions of gases against a
  container
• We live at about 1 atmosphere of pressure

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Barometer

• Torricelli (1643)
• Height of column stayed about 760 mm (760 torr)
• The higher the elevation, the lower the mercury
• Weather
• Rising pressure calm weather
• Dropping pressure storm (fast moving air)

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Units of Pressure

• All of the following are equal
• 760 mm Hg (760 torr)
• 29.9 inches Hg (weather reporting)
• 1 atmosphere (chemistry)
• 101.3 kPa (kiloPascals, physics)
• 760 mm 29.9 in 1 atmosphere 101.3 kPa

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Converting Pressures

• Examples
• Express 485 torr in atmospheres.
• Convert 2.4 atmospheres to mm Hg
• Convert 95.0 kPa to atmospheres and mm Hg.

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The Ideal Gas Law

• Combination of earlier work on gases.
• Assumes all gases follow the Kinetic Molecular
  Theory (fast moving molecules, no attraction
  between gases, etc)
• Works very well in situations close to Earths
  pressures and temperatures
• Does not work for extreme situations (Jupiters
  atmosphere is too cold and too dense)

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The Ideal Gas Law

• PV nRt
• P pressure in atmosphere
• V volume in Liters
• n number of moles
• T Temperature in Kelvin
• R gas constant
• R 0.0821 L-atm / mol-K

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The Ideal Gas Law

• Examples
• What is the pressure of a 1.45 mol sample of a
  gas in a 20.0 L container at 25oC?
• What volume will 5.00 grams of H2 occupy at
  10.0oC and 1 atmosphere of pressure?
• How many grams of O2 are needed to occupy a 500.0
  mL aerosol can at 20.0oC and 0.900 atmospheres?

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STP

• Standard Temperature Pressure
• Standard Temperature 0oC (273 K)
• Standard Pressure 1 atm
• 1 mole of a gas occupies 22.4 L at STP
• 1 mole or 22.4 L
• 22.4 L 1 mole

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STP

• Examples
• What volume will 0.180 moles of nitrogen gas
  occupy at STP?
• How many grams of chlorine (Cl2) gas are present
  in 50.0 L at STP?

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Comparing Two Situations

• Sometimes we want to know what happens when a gas
  is under different conditions
• Example What happens to a basketball if you
  pump it indoors, then take it out on a cold day?

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Comparing Two Situations

• P1V1 n1RT1 P2V2 n2RT2
• Solve both equations for R
• R P1V1 R P2V2
• n1T1 n2T2
• P1V1 P2V2
• n1T1 n2T2

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Comparing Two Situations

• See what you can cross out (what you are not
  told)
• Remember to convert to Kelvin and moles if needed.

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Boyles Law

• Boyles Law Apparatus Demo
• Boyles Law The pressure and volume of a gas
  are inversely related
• Bicycle pump example
• Piston down low volume, high pressure
• Piston up high volume, low pressure

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Boyles Law

• Example
• The volume of a cars cylinder is 475 mL at 1.05
  atm. What is the volume when the cylinder is
  compressed and the pressure is 5.65 atm?
• P1V1 P2V2
• n1T1 n2T2

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Boyles Law

• Collapses to
• P1V1 P2V2
• (Answer 88.3 mL)

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Boyles Law

• Example
• A weather balloon has a volume of 40.0 liters on
  the surface of the earth at 1.00 atm. What will
  be the volume at 0.400 atm as it rises?
• P1V1 P2V2
• n1T1 n2T2

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Charles Law

• Charles Law The temperature and volume of a gas
  are directly related
• HOTTER BIGGER
• A gas increases in volume 1/273rd per degree
  celsius
• Can be used to find absolute zero
• Temperature must be in Kelvin

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Charles Law

• A basketball has a volume of 12.0 L when blown up
  at 25.00 oC. What will be the volume if it is
  taken outside on a day when it is only 5.00 oC?
• P1V1 P2V2
• n1T1 n2T2

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Charles Law

• Collapses to
• V1 V2
• T1 T2

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Charles Law

• 2. If a tire contains 30.0 L of air at 10.0 oC,
  what volume will it occupy when it is driven and
  warms up to 50.0 oC?

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Guy-Lussacs Law

• Gay-Lussacs Law The temperature and pressure
  of a gas are directly related.
• Temperature must be in Kelvin
• Gas in a spray can has a pressure of 5.00 atm at
  25.0 oC. What will be the pressure at 400.0 oC?
• P1V1 P2V2
• n1T1 n2T2

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Avagadros Law

• Avagadros Law The volume of a gas is directly
  proportional to the moles present
• MORE BIGGER
• A balloon has a volume of 1.00 L when 50.0 grams
  of N2 are in the balloon. What is the volume if
  an additional 25.0 grams of N2 are added?

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Putting it all together

• Often you change more than one thing at a time.
• Ex In a car, volume, temperature, and pressure
  may change.
• 1. The volume of 0.0400 mol of a gas is 500.0 mL
  at 1.00 atm and 20.0 oC. What is the volume at
  2.00 atm and 30.0oC?

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Gases and Reaction Stoichiometry

• What mass of Al is needed to produce 50.0 L of H2
  at STP?
• 2Al(s) 6HCl(aq) ? 2AlCl3(aq) 3H2(g)
• (ANS 40.2 g Al)

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Gases and Reaction Stoichiometry

• What volume of NO gas measured at 0.724 atm and
  25oC will be produced from the reaction of 19.5 g
  of O2?
• 4NH3(g) 5O2(g) ? 4NO(g) 6H2O(l)
• (Ans 16.4 L)

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Gases and Reaction Stoichiometry

• Car safety bags are inflated through the
  decomposition of NaN3. How many grams of NaN3
  are needed to produce 36.0 L of N2 at 1.15 atm
  and 26.0oC?
• 2NaN3(s) ? 2Na(s) 3N2(g)
• (Ans 72 g)

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Gases and Reaction Stoichiometry

• 4. How many liters of H2 and N2 at 1.00 atm and
  15.0oC are needed to produce 150.0 grams of NH3?
• N2(g) 3H2(g) ? 2NH3(g)

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Daltons Law of Partial Pressures

• John Dalton Daltons Atomic Theory
• Daltons Law the total pressure of a gas is
  equal to the sum of the partial pressures
• Ptot PA PB PC PD ..
• Patm PN2 PO2 Prest
• 1 atm 0.78atm 0.21atm 0.01atm

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Daltons Law of Partial Pressures

• 1. Three gases are mixed in a 5.00 L container.
  In the container, there are 255 torr of Ar, 228
  torr of N2, and 752 torr of H2. What is the
  total pressure?

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Daltons Law of Partial Pressures

• On a humid day, the partial pressure of water in
  the atmosphere is 18 torr.
• If the total pressure is 766 torr, what are the
  pressures of all of the other gases?
• If the atmosphere is 78 N2 and 21 O2, what are
  their pressures on this humid day?

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Daltons Law of Partial Pressures

• 3. What is the total pressure (in atm) exerted
  by a mixture of 12.0 g of N2 and 12.0 g of O2 in
  a 2.50 L container at 25.0oC?