Chapter 10 Gases

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Chapter 10Gases
CHEMISTRY The Central Science 9th Edition
David P. White
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• HOMEWORK PRESSURE CONVERSIONS
• P 433 Q 9, 17, 21
• READ SECTION 10.3 P 404

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Characteristics of Gases

• Gases are highly compressible and occupy the full
  volume of their containers.
• When a gas is subjected to pressure, its volume
  decreases.
• Gases always form homogeneous mixtures with other
  gases.
• Gas molecules only occupy about 0.1 of the
  volume of their containers.
• Have extremely low densities.

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Pressure

• Pressure is the force acting on an object per
  unit area
• Gravity exerts a force on the earths atmosphere
• A column of air 1 m2 in cross section exerts a
  force of 105 N.
• The pressure of a 1 m2 column of air is 100 kPa.

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Atmospheric pressure is the weight of air per
unit of area.
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F m . amass of air column 10,000
kgacceleration due to gravity at the surface of
Earth 9.8 m/s2
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Atmosphere Pressure and the Barometer
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• Atmosphere Pressure and the Barometer
• SI Units 1 N 1 kg.m/s2 1 Pa 1 N/m2.
• Atmospheric pressure is measured with a
  barometer.
• If a vacated tube is inserted into a container of
  mercury open to the atmosphere, the mercury will
  rise 760 mm up the tube.
• Standard atmospheric pressure is the pressure
  required to support 760 mm of Hg in a column.

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Standard Pressure

• Normal atmospheric pressure at sea level.

• It is equal to
• 1.00 atm
• 760 torr (760 mm Hg)
• 101.325 kPa

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Units of Pressure

• 1 atm 760 mmHg 760 torr
• 1.01325 ? 105 Pa 101.325 kPa.
• Pascals
• 1 Pa 1 N/m2
• Bar
• 1 bar 105 Pa 100 kPa

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• Examples Convert the following pressures
• 658.2 mm Hg to kPa
• 1.85 atm to torr
• 337.3 kPa to atm

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• Examples Convert the following pressures
• 658.2 mm Hg to kPa 87.75 kPa
• 1.85 atm to torr 1410 torr
• 337.3 kPa to atm 3.329 atm

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Manometer

• Used to measure the difference in pressure
  between atmospheric pressure and that of a gas in
  a vessel.

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• Pressure and the Manometer
• The pressures of gases not open to the atmosphere
  are measured in manometers.
• A manometer consists of a bulb of gas attached to
  a U-tube containing Hg
• If Pgas lt Patm then Pgas Patm.- Ph
• If Pgas gt Patm then Pgas Patm Ph.

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Example The mercury in a manometer is 46 mm
higher on the open end than on the gas bulb end.
If atmospheric pressure is 102.2 kPa, what is the
pressure of the gas in the bulb?
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Example The mercury in a manometer is 46 mm
higher on the open end than on the gas bulb end.
If atmospheric pressure is 102.2 kPa, what is the
pressure of the gas in the bulb? 813 mm Hg 108 kPa
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GAS LAWS Section 3-4

• Boyles Law
• Charless Law
• Avogadros Law
• The ideal gas equation
• HOMEWORK PAGE 434 10.23 TO 10.41
• 41 IS A CHALLENGE QUESTION
• ODD ONLY

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The Gas Laws

• The Pressure-Volume Relationship Boyles Law
• Weather balloons are used as a practical
  consequence to the relationship between pressure
  and volume of a gas.
• As the weather balloon ascends, the volume
  increases.
• As the weather balloon gets further from the
  earths surface, the atmospheric pressure
  decreases.
• Boyles Law the volume of a fixed quantity of
  gas is inversely proportional to its pressure
  (assuming all other variables are unchanged).
• Boyle used a manometer to carry out the
  experiment.

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Boyles Law

• The volume of a fixed quantity of gas at
  constant temperature is inversely proportional to
  the pressure.

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• The Pressure-Volume Relationship Boyles Law
• Mathematically
• A plot of V versus P is a hyperbola. T constant.
• Similarly, a plot of V versus 1/P must be a
  straight line passing through the origin.

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As P and V areinversely proportional

• A plot of V versus P results in a curve.

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• Examples
• A gas that occupies 2.84 L has a pressure of 88.6
  kPa. What would be the pressure of the gas
  sample if it only occupied 1.66 L (assuming the
  same temperature)?
• A 10.0-L sample of argon gas has a pressure of
  0.885 atm. At what volume would the sample have
  a pressure of 6.72 atm?

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• Examples
• A gas that occupies 2.84 L has a pressure of 88.6
  kPa. What would be the pressure of the gas
  sample if it only occupied 1.66 L (assuming the
  same temperature)?
• 152 kPa
• A 10.0-L sample of argon gas has a pressure of
  0.885 atm. At what volume would the sample have
  a pressure of 6.72 atm?
• 1.32 L

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• The Temperature-Volume Relationship Charless
  Law
• Charless Law the volume of a fixed quantity of
  gas at constant pressure increases as the
  temperature increases (assuming pressure
  constant).
• If we express T in Kelvin degrees, P constant

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• A plot of V versus T is a straight line.
• When T is measured in ?C, the intercept on the
  temperature axis is -273.15?C.
• We define absolute zero, 0 K -273.15?C.
• Note the amount of gas and pressure remain
  constant.

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Charless Law

• The volume of a fixed amount of gas at constant
  pressure is directly proportional to its absolute
  temperature.

A plot of V versus T will be a straight line.
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• Examples (remember to change T to K to use
  Charles Law!!!)
• A gas sample occupies a volume of 1.89 L at 25C.
  What would be the volume of the sample at 75C?
• A sample of carbon dioxide in a 5.00-L container
  has a temperature of 56.9C. At what temperature
  will this sample of CO2 occupy a volume of 3.00 L?

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• Examples
• A gas sample occupies a volume of 1.89 L at 25C.
  What would be the volume of the sample at 75C?
• 2.21 L
• A sample of carbon dioxide in a 5.00-L container
  has a temperature of 56.9C. At what temperature
  will this sample of CO2 occupy a volume of 3.00
  L?
• 198 K or -75C

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• The Quantity-Volume Relationship Avogadros
  Law
• Gay-Lussacs Law of combining volumes at a given
  temperature and pressure, the volumes of gases
  which react are ratios of small whole numbers.

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• Avogadros Hypothesis equal volumes of gas at
  the same temperature and pressure will contain
  the same number of molecules.
• Avogadros Law the volume of gas at a given
  temperature and pressure is directly proportional
  to the number of moles of gas.

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• Mathematically
• We can show that 22.4 L of any gas at 0?C contain
  6.02 ? 1023 gas molecules.

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The Ideal Gas Equation

• Consider the three gas laws.
• We can combine these into a general gas law

• Boyles Law

• Charless Law

• Avogadros Law

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The Ideal Gas Equation

• If R is the constant of proportionality (called
  the gas constant), then
• The ideal gas equation is
• R 0.08206 Latm/molK 8.314 J/molK

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• We define STP (standard temperature and pressure)
  0?C, 273.15 K, 1 atm.
• Volume of 1 mol of gas at STP is

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• Examples
• What is the volume of a 15.0-g sample of neon gas
  at 130.0 kPa and 39C?
• 14.8 L
• At what temperature will 2.85 moles of hydrogen
  gas occupy a volume of 0.58 L at 1.00 atm?
• 2.5 K or -270.7C

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• Relating the Ideal-Gas Equation and the Gas Laws
• If PV nRT and n and T are constant, then PV
  constant and we have Boyles law.
• Other laws can be generated similarly.
• In general, if we have a gas under two sets of
  conditions, then

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• Examples
• A gas sample occupies a volume of 0.685 L at 38C
  and 0.775 atm. What will be the temperature of
  the sample if it occupies 0.125 L at 1.25 atm?
• 91.6 K or -181.6C
• A sample of nitrogen gas in a 2.00 L container
  has a pressure of 1800.6 mmHg at 25C. What
  would be the pressure on the sample in a 1.00 L
  container at 125C?
• 4810 mm Hg

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Section 10-5

• Ideal Gas Equation Problems
• Gas Densities and Molar Mass
• Volumes of gases in chemical reactions
• HW
• 38 ideal gas equation
• 43-45-46 concepts
• 47-49-50 density and molar mass
• 52-54 to 56 Stoichiometry with gases

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Further Applications of the Ideal-Gas Equation

• Gas Densities and Molar Mass
• Density has units of mass over volume.
• Rearranging the ideal-gas equation with M as
  molar mass we get

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• Examples
• What is the density of nitrogen gas at 35C and
  1.50 atm?

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• Examples
• What is the density of nitrogen gas at 35C and
  1.50 atm?
• 1.67 g/L

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• The molar mass of a gas can be determined as
  follows
• OR
• The cat paws throw dirt over the P
• Volumes of Gases in Chemical Reactions
• The ideal-gas equation relates P, V, and T to
  number of moles of gas.
• The n can then be used in stoichiometric
  calculations.

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• Examples
• 4.83 g of a gas occupy a 1.50 L flask at 25C and
  112.4 kPa. What is the molar mass of the gas?
• 71.0 g/mol

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STOICHIOMETRY PROBLEMS
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• If an air bag has a volume of 36 L and is filled
  up with Nitrogen at a pressure of 1.15 atm at a
  temperature of 26C, how many grams of NaN3 must
  be decomposed

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• 2 Na N3 (s)? 2 Na (s) 3 N2
• (73.2 g)

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• How many L of NH3 at 850 0C and 5 atm are
  required to react wih 32 g of O2?
• 4NH3 5 O2 -gt4NO 6 H2 O
• (14.7 L )

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Section 10-6

• Gas Mixtures and Partial Pressures
• Partial Pressures and Mole Fraction
• Collecting Gases over Water
• HW page 436 Q 55 and 56 collecting gas over
  water
• 1057 to 67 odd numbers (red)

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Gas Mixtures and Partial Pressures

• Since gas molecules are so far apart, we can
  assume they behave independently.
• Daltons Law in a gas mixture the total pressure
  is given by the sum of partial pressures of each
  component
• Each gas obeys the ideal gas equation

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• Combining the equations
• Partial Pressures and Mole Fractions
• Let ni be the number of moles of gas i exerting a
  partial pressure Pi, then
• where ?i is the mole fraction (ni/nt).

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• Examples
• Hydrogen gas is added to a 2.00-L flask at a
  pressure of 5.6 atm. Oxygen gas is added until
  the total pressure in the flask measures 8.4 atm.
  What is the mole fraction of hydrogen in the
  flask? What the pp of Oxygen?
• 2 .35 moles of argon and 2.75 moles of neon are
  placed in a 15.0-L tank at 35C. What is the
  total pressure in the flask? What is the
  pressure exerted by neon?

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• Examples
• Hydrogen gas is added to a 2.00-L flask at a
  pressure of 5.6 atm. Oxygen gas is added until
  the total pressure in the flask measures 8.4 atm.
  What is the mole fraction of hydrogen in the
  flask?
• 0.67 2.8 atm
• 1.35 moles of argon and 2.75 moles of neon are
  placed in a 15.0-L tank at 35C. What is the
  total pressure in the flask? What is the
  pressure exerted by neon? Ptot 6.91 atm
• PNe 4.63 atm

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• Collecting Gases over Water
• It is common to synthesize gases and collect them
  by displacing a volume of water.
• To calculate the amount of gas produced, we need
  to correct for the partial pressure of the water

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Collecting Gases over Water
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Example - 150.82 mL of an unknown gas is
collected over water at 27C and 1.032 atm. The
mass of the gas is 0.1644 g. What is the molar
mass of the gas? The vapor pressure of water at
27C is 26.74 torr
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Section 10-7 and 10-8

• Kinetic-Molecular Theory
• Application to the Gas Laws
• Molecular Effusion Grahams Law
• Diffusion and Mean Free Path
• HW P 437 69 to 79 odd only and 80

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• LABORATORY BOOKS THEY ARE IN!
• 30 BOTH BOOKS MUST GET LAB BOOK BY MONDAY
  TUESDAY FIRST LAB
• FOR TUESDAY MUST STUDY LAB 8
• DETERMINING THE MOLAR MASS OF A GAS
• AND DO PRELAB QUESTIONS

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Kinetic Molecular Theory

• Theory developed to explain gas behavior.
• Theory of moving molecules.
• Assumptions
• 1.-Gases consist of a large number of molecules
  in continuous, random motion.
• 2.-Volume of individual molecules negligible
  compared to volume of container.
• 3.-Intermolecular forces (forces between gas
  molecules) are negligible (no attraction or
  repulsion between molecules)

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4.- Energy can be transferred between molecules
during collisions, but AVERAGE kinetic energy
DOES NOT CHANGE at constant temperature (When
molecules collide one speeds up the other slows
down) 5.-Average kinetic energy of molecules is
proportional to the ABSOLUTE temperature. At a
given temperature molecules of all gases have
same average KE
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Kinetic molecular theory gives us an
understanding of pressure and temperature on the
molecular level.
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• Pressure
• of a gas results from the number of
  collisions per unit time on the walls of
  container.
• Magnitude of pressure given by how often and how
  hard the molecules strike against the walls.

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Temperature

• MOLECULAR MOTION INCREASES WITH TEMPERATURE
• Molecules at 1 T at a given moment have a wide
  range of speed
• At higher temperature a larger fraction of
  molecules have a higher speed.
• Gas molecules have an average kinetic energy.
• Each molecule has a different energy.

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• If 2 different gases are at same T their
  molecules have the same Average Kinetic Energy.
• If T increases their motion increases too.
• MOLECULAR MOTION INCREASES WITH T
• Individual molecules move at different speeds but
  the average kinetic energy is one at each
  temperature.
• When particles collide, the momentum is
  conserved. That means that one particle will move
  faster but the other will slow down to conserve
  the total amount of energy in the system.

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• The diagram shows the distribution of molecular
  speeds for a sample of gas at different
  temperatures.
• Increasing T increases both the most probable
  speed
• ( curve maximum) and rms speed (u) root mean
  square-
• At higher T, a larger fraction of molecules move
  a greater speeds.
• The peak shows the most probable speed ( speed
  of the largest number of molecules.
• 400m/s is approximately 1000miles/hour

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• KE ½ mass x speed2
• Root mean square is an statistical expression
  that is close to the mean.
• Example , the average between 4 different speeds
• V1,v2,v3, v4 vav ¼ (v1v2v3v4)
• u average ke of a collection of molecules

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• As kinetic energy increases, the velocity of the
  gas molecules increases.
• Root mean square speed, u, is the speed of a gas
  molecule having average kinetic energy. For one
  molecule
• Average kinetic energy, ?, is related to root
  mean square speed

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• m is the mass of the molecules
• u is the root mean square speed
• T is proportional to the speeds of the particles.
• The root mean square or rms speed temperature and
  molecular mass are related by the Maxwells
  equation.

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• Application to Gas Laws
• As volume increases at constant temperature, the
  average kinetic energy of the gas remains
  constant. Therefore, u is constant. However,
  volume increases so the gas molecules have to
  travel further to hit the walls of the container.
  Therefore, pressure decreases.
• If temperature increases at constant volume, the
  average kinetic energy of the gas molecules
  increases. Therefore, there are more collisions
  with the container walls and the pressure
  increases.

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Effusion

• The escape of gas molecules through a tiny hole.

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Diffusion

• The spread of one substance throughout a space
  or throughout a second substance.
• Spread of a gas.

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• Molecular Effusion and Diffusion
• As kinetic energy increases,(T) the velocity of
  the gas molecules increases.
• Average kinetic energy of a gas is related to its
  mass
• (KE)
• Consider two gases at the same temperature both
  have same KE therefore the lighter gas molecules
  have to have higher speeds (rms speed u) than
  the heavier gas.
• Mathematically (M is molecular mass)

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• The lower the molar mass, M, the higher the speed
  of the molecules (rms speed).

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• Calculate the rms speed for O2 molecules at 25 0 C

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Convert mass to kgunits of speed m/sanswer 482
m/s approximately 1100 miles /hour
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• Grahams Law of Effusion
• As kinetic energy increases, the velocity of the
  gas molecules increases.
• Effusion is the escape of a gas through a tiny
  hole (a balloon will deflate over time due to
  effusion).
• The rate of effusion can be quantified.

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• Consider two gases with molar masses M1 and M2,
  the relative rate of effusion is given by
• Only those molecules that hit the small hole will
  escape through it.
• Therefore, the higher the rms the more likelihood
  of a gas molecule hitting the hole.

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• Consider two gases with molar masses M1 and M2,
  the relative rate of effusion is given by
• Only those molecules that hit the small hole will
  escape through it.
• Therefore, the higher the rms the more likelihood
  of a gas molecule hitting the hole.

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• Examples For each pair of gases, determine
  which will effuse faster, and by how much it will
  be faster.
• CH4 and Xe
• Cl2 and N2
• F2 and He

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• Examples For each pair of gases, determine
  which will effuse faster, and by how much it will
  be faster.
• CH4 and Xe 2.8607
• Cl2 and N2 1.59095
• F2 and He 3.08027

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• Diffusion and Mean Free Path
• Diffusion of a gas is the spread of the gas
  through space.
• Diffusion is faster for light gas molecules.
• Diffusion is significantly slower than rms speed
  (consider someone opening a perfume bottle it
  takes while to detect the odor but rms speed at
  25?C is about 1150 mi/hr).
• Diffusion is slowed by gas molecules colliding
  with each other.

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• Average distance of a gas molecule between
  collisions is called mean free path.
• At sea level, mean free path is about 6 ? 10-6
  cm.

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• Tetrafluoroethylene C2F4 effuses through a
  barrier at a rate of 4.6 x 10 -6 mol/h. An
  unknown gas, consisting only of boron and
  hydrogen, effuses at a rate
• of 5.8 x 10 -6 mol/h under the same
  conditions. What is the molar mass of the unknown
  gas?
• Use Grahams Law
• M 63g/mol

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SECTION 10-9

• REAL GASES DEVIATIONS FROM IDEAL BEHAVIOR
• VAN DER WAALS EQUATION
• HW 10.8
• 10.81,85,95,97

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Real Gases Deviations from Ideal Behavior

• From the ideal gas equation, we have
• For 1 mol of gas, PV/RT 1 for all pressures.
• BUT REAL GASES DO NOT BEHAVE IDEALLY SPECIALLY AT
  HIGH PRESSURES!!!
• In a real gas, PV/RT varies from 1 significantly.
• The higher the pressure the more the deviation
  from ideal behavior (For Plt10 atm we could use
  ideal-gas equation)

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• As the pressure on a gas increases, the molecules
  are forced closer together.
• As the molecules get closer together, the volume
  of the gas molecules begin to be significant, and
  the volume of the gases is greater that what is
  predicted by the ideal gas equation.
• Also at the higher the pressure, the attraction
  between gas particles begins to manifest and less
  particles hit the walls of the container,
  therefore there is a reduction in the Pressure
  due to the molecular attractions

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• From the ideal gas equation, we have
• As temperature increases, the gases behave more
  ideally.
• The assumptions in kinetic molecular theory show
  where ideal gas behavior breaks down
• the molecules of a gas have finite volume
• molecules of a gas do attract each other.

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• As the gas molecules get closer together, the
  smaller the intermolecular distance.

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• The smaller the distance between gas molecules,
  the more likely attractive forces will develop
  between the molecules.
• Therefore, the less the gas resembles and ideal
  gas.
• As temperature increases, the gas molecules move
  faster and further apart.
• Also, higher temperatures mean more energy
  available to break intermolecular forces.
• Then an increase in T helps the gases behave more
  ideally

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Real Gases Deviations from Ideal Behavior

• Therefore, the higher the temperature, the more
  ideal the gas.
• The T increase helps the molecules break the
  forces of attractions.

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• The van der Waals Equation
• We add two terms to the ideal gas equation one
  to correct for volume of molecules and the other
  to correct for intermolecular attractions
• The correction terms generate the van der Waals
  equation
• where a and b are empirical constants.

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Real Gases Deviations from Ideal Behavior

• The van der Waals Equation
• General form of the van der Waals equation

Corrects for molecular volume
Corrects for molecular attraction
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• The constant b adjusts the volume, since gas
  particles do have volume the total volume that
  the particles have to move in is less than the
  whole container. That is why b is substracting V,
  and the units are L/mol
• ( V-n b)
• The constant a accounts for the attraction
  between molecules which increases with the square
  of the number of molecules per unit of Volume.
• Units for a L2 atm/mol2
• It indicates HOW STRONGLY THE MOLECULES ATTRACT
  EACH OTHER!!!

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• If 1.00 mol of an ideal gas is confined to a 2.4
  L at 0.0 C, it would exert a pressure of 1.00
  atm. Use the Van Der Waals equation and the
  contants for Cl2 to estimate the pressure
  exerted by 1 mol of Cl2 in 22.4 L at 0.0 C

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• Monday October 18 PRACTICE QUESTIONS unit 10
  DUE
• Tuesday October 18. Experiment 8
• Determining the Molar Volume of a Gas.
• MUST BRING LAB NOTEBOOK (a marble book) AND LAB
  BOOK
• KNOW THE PROCEDURE!!! You have to know what are
  you going to do BEFORE walking into the lab room.

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• Barometric Pressure for Friday at 130 PM
• inches of Hg
• Convert to atm!!!
• Literature value for density of Hydrogen gas
  0.0899g/L
• NOTEBOOK
• LEAVE 2 FIRST PAGES FOR A TABLE OF CONTENTS For
  each lab that is written up, copy the title and
  page numbers where lab report begins and ends.
• FOLLOW GUIDELINES. NUMBER PAGES
• INDICATE FULL NAME OF PARTNERS IN THE EXPERIMENT
• ANSWER ALL POSTLAB QUESTIONS. COPY THE QUESTIONS
• BE NEAT!!!

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• LAB QUIZ
• Q 1 to 3 were covered in lab
• 4 What reaction takes place ? Write the molecular
  equation and the net ionic equation. Indicate
  the spectator ion

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5. A reaction of .056 g of Mg with excess HCl
generated 62.0 mL of H2 (g). The gas was
collected over water at 250C. The barometric
pressure was 768 mm of Hg and the vapor pressure
of water at 250C is 23.8 mm of Hg.a) Find the
pressure for H2
.
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• b) What would be the volume of H2 at STP

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• c) How many ml of HCl 2 M are needed to
  completely react with the amount of Mg?

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• Question 54 Stoichiometry problem with gases
• the following UNBALANCED eq.
• C5H12 (l) O2 -gt CO2 (g) H2O
• What volume of Oxygen gas measured at 23o C and
  .980 atm is needed to react with 2.50 g of C5H12
  ?
• What volume of each product is produced under
  the same conditions?

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• When 2 gases reactants react the partial pressure
  of them is proportional to their number of moles.
• A B -gt C
• 5 mol of A and when reaction ended 3 mol of C
  formed.
• How many mol of A are left without reacting
• How many mol of B were present considering 100
  yield.
• If total pressure of the container is 900mm Hg,
  find the pp of each gas after the reaction