Gases

1
Gases

• Chapter 5

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Substances That Exist as a Gas

• Ionic compounds do not exist as gases at 25and 1
  atm, because cations and anions in an ionic
  compound are held together by strong
  electrostatic forces.

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Substances That Exist as a Gas

• The majority of molecular compounds are liquids
  or solids at 25and 1 atm.
• The stronger the attractive forces between the
  molecules (intermolecular forces) the less likely
  the material is a gas.

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Substances That Exist as a Gas under normal
atmospheric conditions
5
Properties of gases

• Gases assume the volume and shape of their
  container
• Gases are the most compressible of the states of
  matter
• Gases will mix evenly and completely when
  combined in the same container
• Gases have much lower densities than liquids or
  solids.

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Variables that Describe a Gas

• Pressure (P) measured in kilopascals
• Volume (V) measured in liters
• Temperature (T) - measured in Kelvin
• Number of moles (n)

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Deriving units of Pressure

• Velocity is change of distance with elapsed time
  vd/t
• The SI unit for velocity is m/s
• Acceleration is the change in velocity with time
  av/t
• The SI unit for velocity is m/s2

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Deriving units of Pressure

• Pressure is a force and is dependent on mass.
  According to Newtons second law
• force mass x acceleration
• The SI unit for force is the Newton, where N
  1 kg m/s2
• Finally, pressure is the force applied per unit
  area p f/a
• The SI unit for velocity is the pascal (Pa)
  defines as one Newton per square meter, or 1 Pa
  1 N/m2

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Atmospheric Pressure

• The gases in the atmosphere are subject to
  Earths gravitational pull.
• Air is denser at low altitudes, and less dense at
  high altitudes.
• The denser the air, the greater the pressure that
  it exerts.

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Atmospheric Pressure

• The force experienced by any area exposed to the
  Earths atmosphere is equal to the weight of the
  column of air above it. The actual value depends
  on location, temperature and weather conditions.

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Gas Pressure

• Barometer
• Measures atmospheric pressure
• Dependent on the weather
• Standard atmospheric pressure is equal to the
  pressure that supports a column of mercury
  exactly 760 mm high at 0C at sea level.

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Units of pressure

• Pascal (Pa)
• torr
• Millimeters mercury (mm Hg)
• Atmospheres (atm)
• 1 atm 760 mm Hg 760 torr 101.325 kPa

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Example 1

• The pressure outside a jet plane flying at high
  altitudes is considerably lower than standard
  atmospheric pressure. Therefore, the air inside
  of the planes cabin is pressurized to protect
  the passengers. What is the pressure in
  atmospheres if the barometer reading in the cabin
  is 688 mm Hg?

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Example 2

• The weatherman often reports the barometric
  pressure. The barometric pressure in San
  Francisco on a certain day was 732 mm Hg or 732
  torr. What is the pressure in kPa?

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Gas Pressure

• A manometer is a device used to measure the
  pressure of a fixed amount of gas separate from
  the atmosphere.

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Closed Manometer
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Open Manometer
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The Gas Laws

• Boyles Law
• Robert Boyle (1627-1691)
• Boyle studied the effect of pressure on the
  volume of a contained gas at constant temperature
• For a given mass of a gas at constant
  temperature, the volume of the gas varied
  inversely with pressure.

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Boyles Law

• Notice that for both conditions, the product of
  the pressure and volume was the same
• P1V1 100 mmHg x 10 L 1000 mmHgL
• P2V2 200 mmHg x 5 L 1000 mmHgL

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Boyles Law
PV k1
P2V2
P1V1
P3V3
21
Boyles Law
P k1 x 1/V
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Boyles Law

• P1V1 k1 P2V2
• Or
• P1V1 P2V2

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Example 3

• A child is given a balloon filled with 25 L of
  helium gas at 103 kPa. What will the volume of
  the balloon be if the child lets it go and it
  floats up to an altitude where the pressure is
  only 35 kPa?

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The Gas Laws

• Charles's Law
• Jacques Charles (1746-1823)
• Charles studied the effect of temperature on the
  volume of a gas at constant pressure
• For a given mass of a gas at constant pressure,
  the volume of the gas varied directly with
  temperature.

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Charless Law

• Notice that for both conditions, the ratio of the
  volume and temperature was the same
• V1/T1 10L / 300 K 0.03 L/K
• V2/T2 20L / 600 K 0.03 L/K
• V1/T1 V2/T2

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Charless Law
Gas A
Gas B
-273.15 C
Gas C
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Example 4

• A child is given a balloon filled with 25 L of
  helium gas at 25 C. What will the volume of the
  balloon be if the child goes outside where the
  temperature is -15 C?

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The Gas Laws

• Gay-Lussac's Law
• Joseph Gay-Lussac (1778-1850)
• Gay-Lussac studied the effect of temperature on
  the pressure of a gas at constant volume
• For a given mass of a gas at constant volume, the
  pressure of the gas varied directly with
  temperature.

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Gay-Lussacs Law

• Notice that for both conditions, the ratio of the
  pressure and temperature was the same
• P1/T1 100 mm Hg / 300 K
• 0.3 mm Hg/K
• P2/T2 200 mm Hg / 600 K
• 0.3 mm Hg/K
• P1/T1 P2/T2

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Example 5

• You filled your bicycle tire to a pressure of 103
  kPa early in the morning when the temperature was
  only 17 C. What will be the pressure in the
  tire when the temperature outside reaches 35 C?

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Avogadros Hypothesis

• Equal volumes of gases at the same temperature
  and pressure contain equal numbers of particles.
• At STP, 1 mol (6.02 x 1023 particles ) of any gas
  occupies 22.414 L.

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The Gas Laws

• Avogadro's Law
• Amedeo Avogadro (1776-1856)
• Avogadro studied the effect of the amount of
  particles on the pressure of a gas at constant
  volume and temperature
• For a given mass of a gas at constant volume, the
  pressure of the gas varied directly with the
  number of particles.

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Avogadros Law

• Notice that for both conditions, the ratio of the
  pressure and temperature was the same
• P1/n1 100 mm Hg / 1 mole
• 100 mm Hg/mole
• P2/n2 200 mm Hg / 2 mole
• 200 mm Hg/mole
• P1/n1 P2/n2

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Avogadros Law

• Notice that for both conditions, the ratio of the
  pressure and temperature was the same
• P1/n1 100 mm Hg / 1 mole
• 100 mm Hg/mole
• P2/n2 200 mm Hg / 2 mole
• 200 mm Hg/mole
• P1/n1 P2/n2

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Example 6

• A rigid 50-L container is used as reaction
  vessel. When 3 moles of H2 and 1 mole of N2 are
  added the initial pressure is 198 kPa. What will
  be the pressure in the container when the
  reaction is complete?

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Avogadros Law

• Avogadro also studied the effect of the amount of
  particles on the volume of a gas at constant
  pressure and temperature
• For a given mass of a gas at constant pressure,
  the volume of the gas varied directly with the
  number of particles.

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Example 7

• When 3 L of H2 and 1 L of N2 are reacted at
  constant pressure, what will be the volume of the
  gas when the reaction is complete?

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I hear grumbling..

• Mrs. Rick, how are we supposed to memorize all
  of these equations?
• You dont! You only have to memorize one!

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The Combined Gas Law

• These four gas laws can be combined into a single
  expression

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The Combined Gas Law

• Any variable which is held constant can be
  factored out of the equation.
• The combined gas law enables you to perform
  calculations where none of the variables are
  constant.

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Example 8

• You are flying in a hot air balloon in the middle
  of the afternoon. The balloon has a volume of
  2.24 x 103 L at an altitude of 1 km where the
  temperature is 290 K and the pressure is 760 mm
  Hg. What would the volume be if the balloon
  ascended to 50 km where the pressure is 1.0 mm
  Hg, and the temperature is 260K?

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The Ideal Gas Law

• A single equation can be derived which describes
  the relationship between all four variables

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The Ideal Gas Law

• This equation relates two amounts at two
  different sets of conditions.
• It shows that the ratio of PV to Tn is constant
  for gases that behave ideally

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The Ideal Gas Law

• This constant value can be calculated based on
  some important facts about gases
• Molar volume 22.414L at STP
• STP is defined as 273.15K and 101.325 kPa

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The Ideal Gas Law

• We can use this information to solve for R, the
  ideal gas constant

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The Ideal Gas Law

• Rearranging the equation for R gives the usual
  form of the ideal gas law
• PV nRT
• The ideal gas law enables calculation of the
  number of moles of a gas given P,V, and T

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Example 9

• Compressed gases are stored and transported in
  steel cylinders. If a 250 L cylinder of N2 gas
  has an internal pressure of 2500 kPa at 25.0 C,
  what is the mass of nitrogen in the cylinder?

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Density Calculations

• Density is defined as mass/volume. The ideal gas
  law can be rearranged to solve for density.

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Density Calculations

• The number of moles of a gas, n, can be given by
• Where m is mass, and M is molar mass, therefore

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Density Calculations

• Density, D, is mass per unit volume, resulting in
  the following equation

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Example 10

• Calculate the density of carbon dioxide in grams
  per liter at 0.990 atm and 55C

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Example 11

• The density of dry air at 30.0 C, 720 mm Hg, is
  1.104 g/L. Calculate the average molecular
  weight of the air.

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Gas Stoichiometry

• Gas laws are used to calculate moles when
  conditions are not constant or not _at_ STP

• Remember the molar highway?
• When the reactants and/or products are gases we
  can use the relationships between amounts and
  volumes

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Example 12

• Calculate the volume of O2 (in Liters) required
  for the complete combustion of 7.64 L of
  acetylene (C2H2) at the same temperature and
  pressure.
• 2C2H2 (g) 5O2 (g) ? 4CO2 (g) 2 H2O (l)

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Example 13

• A 3.25 g sample of KClO3 is decomposed according
  to the equation
• 2KClO3(s) ? 2KCl(s) 3O2(g)
• Assuming 100 decomposition, what volume of O2
  should be collected at 22C,740 mm Hg?

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Daltons Law

• Gas pressure is dependent only on the number of
  gas particles in a container, and their kinetic
  energy.
• The total pressure of the system is the sum of
  the pressures due to all particles.

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Daltons Law
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Daltons Law

• The contribution each gas makes is called the
  partial pressure.
• In a mixture of gases, the total pressure is
  equal to the sum of the partial pressures
• Ptotal P1P2P3P4.

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Daltons Law
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Daltons Law

• The partial pressure of any component is equal to
  the mole fraction of that component times the
  total pressure.
• Because the sum of all mole fractions is equal to
  1

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Example 14

• You have three tanks of equal volume. One
  contains nitrogen at 200 kPa, the second contains
  oxygen at 500 kPa, and the third contains an
  unknown quantity of carbon dioxide. If the gases
  are combined into one tank, and the final
  pressure is 1100 kPa, what pressure is due to
  carbon dioxide?

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Example 15

• Oxygen gas generated by the decomposition of
  potassium chlorate is collected as shown. The
  volume of oxygen collected at 24C and 762 mmHg
  is 128 mL. Calculate the mass (in grams) of
  oxygen gas obtained.
• the vapor pressure of water at 24C is 22.4 mmHg

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Kinetic Molecular Theory of Gases

• Gas molecules are separated by great distances.
  They possess mass, but have negligible volume.
• Gas molecules are in constant, random motion.
  The collide frequently and elastically.
• Gas molecules exert no attractive or repulsive
  forces.
• The average kinetic energy of the molecules is
  proportional to the absolute temperature of the
  gas (K)

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Kinetic Molecular Theory of Gases

• Compressibility of gases
• Molecules can move into empty space
• Boyles Law
• Decreasing volume increases number density, which
  increases the number of collisions per area.
• Charles Law/Gay-Lussacs Law
• As the average KE increase, the rate of collision
  increases
• Avogadros Law
• At the same T,P, equal volumes of gas contain an
  equal number of particles, having an equal number
  of collision per area.

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Kinetic Molecular Theory of Gases

• At higher temperatures more molecules are moving
  at higher speeds

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Kinetic Molecular Theory of Gases

• The distribution of speeds for four gases at 300
  K. On average, the lighter molecules are moving
  faster.

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Kinetic Molecular Theory of Gases

• Root mean square speed is an average molecular
  speed
• For one mole of a gas KE 3/2 RT
• For one molecule
• Therefore

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Kinetic Molecule Theory

• most probable speed
• proportionality constant
• root mean square speed

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Example 16

• Calculate the root mean square speed of nitrogen
  molecules in m/s at 25C

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The Gas Laws

• Grahams Law
• Thomas Graham (1805-1869)
• Graham studied the diffusion of gases under the
  same conditions of temperature and pressure.
• Under the same conditions of temperature and
  pressure, rates of diffusion for gases are
  proportional to the square roots of their molar
  masses.

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time
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Grahams Law of Diffusion

• For two gases of differing molar mass

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Example 17

• Helium particles are much smaller than nitrogen
  particles. How much faster will they diffuse?

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Grahams Law

• Diffusion is the tendency for molecules to move
  toward areas of lower concentration until
  equilibrium is reached.
• Effusion is the process by which a gas escapes
  through a tiny hole in its container.

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Effusion of a gas
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Grahams Law

• Although effusion differs from diffusion in
  nature, the rate of effusion follows the same
  form as Grahams law of diffusion.

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Example 18

• A flammable gas composed of carbon and hydrogen
  effuse through a porous barrier in 1.50 min. If
  an equal volume of bromine gas effuses through
  the same barrier under the same conditions in
  4.73 min, what is the molar mass of the unknown
  gas?

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Deviation From Ideal Behavior

• The laws that we have discussed assume that gases
  behave in an ideal manner obeying the
  assumptions of Kinetic Theory.
• They Are Wrong!!

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Deviations from Ideal Behavior

• Assumptions of Kinetic theory
• Gas particles are not attracted to each other
• Particles have no volume
• Not True!!

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Deviations from Ideal Behavior

• Kinetic theory assumes gases are ideal.
• A truly ideal gas does not exist
• At many conditions (T,P) real gases behave
  ideally
• BUT, at low T or high P gases can condense or
  even become solids

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Deviations from Ideal Behavior

• What is an ideal gas?
• No attractive or repulsive forces
• Volume of particles is negligible
• Under what conditions do these laws apply?
• Low pressure
• High temperature

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Deviations from Ideal Behavior

• No gas behaves ideally at all temperatures and
  pressures.
• For an ideal gas, the ratio
• (PV)/(nRT)1
• Deviation indicates non-ideal behavior.

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Pressure Influence on Ideal behavior
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Deviations from Ideal Behavior

• Real gases take up slightly less space than
  predicted by the ideal gas law.
• Indicates attractive forces
• Less space between particles decreases volume.
• Results in a ratio lt 1

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Deviations from Ideal Behavior

• Real gas particles do have volume.
• Causes ratio gt1

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Deviations from Ideal Behavior

• Corrections can be made for the pressure and
  volume of a real gas
• The van der Waals equation uses constants a and b
  to adjust for the behavior of a real gas

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Van der Walls constants
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Example 19

• Given that 3.50 moles of NH3 occupy 5.20 L at
  47C, calculate the pressure of the gas (in atm)
  using the ideal gas law, and then the van der
  Waals equation.