The Gas Laws

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The Gas Laws

• Chapter 10

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Our Atmosphere

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

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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 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? (34.2 L)

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Gay-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?
  (11.3 atm)
• 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? (1.50
  L)

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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? (259 mL)

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Gas Density and Molar Mass

• Remember
• D mass Molar Mass mass
• volume moles

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Ex 1

• What is the density of carbon tetrachloride vapor
  at 714 torr and 125oC?
• 714 torr 0.939 atm
• 125 oC 398 K
• 1 mole of CCl4 154.0 g
• PV nRT
• V nRT
• P

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• V nRT
• P
• V (1 mole)(0.0821 L-atm/mol-K)(398K)
• 0.939 atm
• V 34.8 L
• D m 154.0 g 4.43 g/L
• v 34.8 L

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Ex 2

• The average molar mass of atmosphere of Titan
  (Saturns largest moon) is 28.6 g/mol. If the
  surface temperature is 95 K and the pressure 1.6
  atm, calculate the gas density of Titans
  atmosphere?
• (ANS 5.9 g/L)

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Ex 3

• A 936 mL flask masses 134.567 g empty. When it
  is filled with gas to a pressure of 735 torr at
  31.0oC, it is found to mass 137.456 g. What is
  the molar mass of the gas?
• 735 torr 0.967 atm
• 31.0 oC 304 K
• PV nRT
• n PV/RT

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• n (0.967 atm)(0.936 L)
• (0.0821 L-atm/mol-K)(304 K)
• n 0.0363 mol
• mass 137.456 g 134.567 g 2.89 g
• MM 2.89 g 79.6 g/mol
• 0.0363 mol

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Ex 4

• Calculate the average molar mass of dry air if it
  has a density of 1.17 g/L at 21oC and 740.0 torr.
• ANS 29.0 g/mol

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Gases and Reaction Stoichiometry Ex 1

• 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 Ex 2

• 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 Ex 3

• 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 Ex 4

• 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? (HINT Calculate
  the moles of each gas, then use PVnRT twice).
  (ANS 7.87 atm)

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Mole Fraction

• Mole fraction moles gas A XA
• total moles
• PA XAPtot

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Mole Fraction Ex 1

• A gas mixture contains 0.200 mol of oxygen and
  0.500 mole of nitrogen. If the total pressure is
  745 torr, what is the partial pressure of the two
  gases?
• XO2 0.200 mol 0.286
• 0.700 mol
• XN2 0.500 mol 0.714
• 0.700 mol

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• PO2 XO2Ptot
• PO2 (0.286)(745 torr) 213 torr
• PN2 XN2Ptot
• PN2 (0.714)(745 torr) 532 torr

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Ex 2

• The atmosphere of Titan is 82 mol nitrogen, 12
  mol argon, and 6 mol methane. Calculate the
  partial pressure of each gas if the total
  pressure on Titan is 1220 torr.
• PN2 (0.82)(1220 torr) 1000 torr
• PAr (0.12)(1220 torr) 150 torr
• PCH4 (0.06)(1220 torr) 73 torr

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Ex 3

• What is the mole fraction and mole percent of
  oxygen in exhaled air if PO2 is 116 torr and the
  Ptotal is 760 torr?
• PO2 XO2Ptot
• XO2 PO2/Ptot
• XO2 116 torr/760 torr 0.153 (15.3)

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Ex 4

• A mixture contains 2.15 g H2 and 34.0 g of O2.
  Calculate the partial pressure of each gas if the
  total pressure is 2.05 atm.
• ANS 1.03 atm H2 and 1.02 atm O2

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Gas Collection Over Water
Ptot Pgas PH2O
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Ex 1

• A sample of KClO3 is decomposed as shown. If 250
  mL of gas are collected at 26oC and 765 torr
  total pressure, calculate the partial pressure of
  O2.
• 2KClO3(s) ? 2KCl(s) 3O2(g)

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• Ptot PO2 PH2O
• PO2 Ptot - PH2O
• PO2 765 torr 25 torr 740 torr (0.974 atm)
• How many moles of gas were collected?
• n PV/RT
• n (0.974 atm)(0.250 L) 0.00992 mole
• (0.0821 L-atm/mol-K)(299K)

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• How many grams of KClO3 were decomposed?
• 2KClO3(s) ? 2KCl(s) 3O2(g)
• 0.00992 mol
• ANS 0.811 g KClO3

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Ex 2

• When a sample of NH4NO2 is decomposed, 511 mL of
  N2 are collected over water at 26oC and 745 torr
  total pressure. How many grams of NH4NO2 were
  decomposed?
• NH4NO2(s) ? N2(g) 2H2O(g)
• ANS 1.26 g

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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

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• Root Mean Square Speed of atoms/molecules
• m (3RT/M)1/2
• M molar mass (kg/mol)
• R 8.314 J/mol-K
• Calculate the rms speed of NH3 and HCl (25oC).

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• Grahams Law of Effusion 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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Real Gases

• Ideal Gas Equation Assumes
• Gas molecules have no volume
• Gas molecules do not attract one another
• Van der Waals Equation corrects for
• Volume of molecules Important at high pressures
• Molecular attraction Important at low
  temperatures (colder, stickier)

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• A gas has a volume of 800.0 mL at -23.00 C and
  300.0 torr. What would the volume of the gas be
  at 227.0 C and 600.0 torr of pressure?
• What is the volume at STP of 22 grams of CO2?
• 2.50 g of XeF4 gas is placed into an evacuated
  3.00 liter container at 80C. What is the
  pressure in the container?

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• The atmosphere of Jupiter is composed almost
  entirely of hydrogen (H2) and helium (He). If
  the average molar mass of Jupiters atmosphere is
  2.254 g/mole, calculate the percent composition.

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• The atmosphere of Mars is composed of CO2, N2 and
  1.6 Ar. If the average molar mass of the gases
  in Mars atmosphere is 43.28 g/mole, calculate
  the percentages of CO2 and N2.

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• PN2 0.389 atm, PH2 0.965, 0.496 (NH3)
• 68. a) XO2 0.239, XH2 0.612
• b) 0.303 atm (O2), 0.488(N2),1.25 (H2)
• a) 0.115 atm
• b) 0.206 atm
• c) Pt 0.321 atm