Gases

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Chapter 5

• Gases

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Ideal Gases
Ideal gases are imaginary gases that
perfectly fit all of the assumptions of the
kinetic molecular theory.

• Gases consist of tiny particles that are far
  apart
• relative to their size.

• Collisions between gas particles and between
• particles and the walls of the container are
• elastic collisions

• No kinetic energy is lost in elastic collisions

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Ideal Gases (continued)

• Gas particles are in constant, rapid motion.
  They
• therefore possess kinetic energy, the energy
  of
• motion

• There are no forces of attraction between gas
• particles

• The average kinetic energy of gas particles
• depends on temperature, not on the identity
• of the particle.

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The Nature of Gases

• Gases expand to fill their containers
• Gases are fluid they flow
• Gases have low density
• 1/1000 the density of the equivalent liquid or
  solid
• Gases are compressible
• Gases effuse and diffuse

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Pressure

• Pressure is caused by the collisions of molecules
  with the walls of a container
• Pressure is equal to force/unit area
• SI units N/meter2 1 Pascal (Pa)
• 1 atmosphere 101,325 Pa 101.325 kPa
• 1 atmosphere 1 atm 760 mm Hg 760 torr

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Measuring Pressure
The first device for measuring atmospheric pressur
e was developed by Evangelista Torricelli during
the 17th century.
The device was called a barometer

• Baro weight
• Meter measure

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An Early Barometer
The normal pressure due to the atmosphere at sea
level can support a column of mercury that is 760
mm high.
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Converting Celsius to Kelvin
Gas law problems involving temperature require
that the temperature be in KELVIN (K)!
Kelvin ?C 273
C Kelvin - 273
O K absolute zero 273 K OC 373 K 100C
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Standard Temperature and PressureSTP

• P 1 atmosphere, 760 torr
• T 0C, 273 Kelvin
• The molar volume of an ideal gas is 22.4
  liters at STP
• 22.4 L / mole of gas at 0C and 1 atm called
  the molar volume

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The Combined Gas Law
The combined gas law expresses the relationship
between pressure, volume and temperature of a
fixed amount of gas (of moles of gas are
constant)
PV k T
Boyles law, Gay-Lussacs law, and Charles law
are all derived from this by holding a variable
constant.
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Robert Boyle(1627-1691)

• Boyle was born into an aristocratic Irish family
  
• Became interested in medicine and the new
  science of Galileo and studied chemistry. 
• A founder and an influential fellow of the Royal
  Society of London
• Wrote prolifically on science, philosophy, and
  theology.

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Boyles Law
Pressure is inversely proportional to volume when
temperature is held constant. (Temperature and
of moles are constant)
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Why Dont I Get a Constant Value for PV k?

• Air is not made
• of ideal gases

2. Real gases deviate from ideal behavior at
high pressure
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Jacques Charles (1746-1823)

• French Physicist
• Conducted the first scientific balloon flight in
  1783

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Charless Law

• The volume of a gas is directly proportional to
  temperature, and extrapolates to zero at zero
  Kelvin
• (Pressure and of moles are constant)

• As temperature increases, volume increases
• As temp. decreases, volume decreases
• At absolute zero (O K), volume approaches zero,
  and KE approaches zero

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Avogadros Law

• For a gas at constant temperature and pressure,
  the volume is directly proportional to the number
  of moles of gas (at low pressures).
• V an
• a proportionality constant
• V volume of the gas
• n number of moles of gas

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Joseph Louis Gay-Lussac1778 - 1850

• French chemist and physicist
• Known for his studies on the physical properties
  of gases.
• In 1804 he made balloon ascensions to study
  magnetic forces and to observe the composition
  and temperature of the air at different
  altitudes.

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Gay Lussacs Law
The pressure and temperature of a gas
are directly related when the volume remains
constant (directly related).
(Volume constant)
As pressure increases, more collisions occur, and
a higher temperature. As pressure decreases,
fewer collisions and a lower temperature.
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Ideal Gas Law

• PV nRT
• P pressure in atm
• V volume in liters
• n moles
• R proportionality constant
• 0.08206 L atm/ molK
• T temperature in Kelvins

• Limitations of Ideal Gas Law
• Works well at low P and high T
• Most gases do not behave ideally above 1 atm
• Does not work well near the condensation
• conditions of a gas (becomes like a liquid)

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Examples

• A 47.3 L container containing 1.62 mol of He is
  heated until the pressure reaches 1.85 atm. What
  is the temperature?
• Kr gas in a 18.5 L cylinder exerts a pressure of
  8.61 atm at 24.8ºC What is the mass of Kr?
• A sample of gas has a volume of 4.18 L at 29ºC
  and 732 torr. What would its volume be at 24.8ºC
  and 756 torr?

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Standard Molar Volume
Equal volumes of all gases at the same
temperature and pressure contain the same number
of molecules. - Amedeo Avogadro
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Gas Density
so at STP (0C and 1atm)
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Density and the Ideal Gas Law
Combining the formula for density with the Ideal
Gas law, substituting and rearranging
algebraically
M Molar Mass g/mol P Pressure R Gas
Constant T Temperature in Kelvins m sample
mass
Can also be rearranged to solve for the Molar
Mass of the gas
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Examples

• What is the density of ammonia at 23ºC and 735
  torr?
• A compound has the empirical formula CHCl. A 256
  mL flask at 100.ºC and 750 torr contains .80 g of
  the gaseous compound. What is the empirical
  formula?

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Law of Combining Volumes
If reactants and products are at the same
conditions of temperature and pressure, then mole
ratios of gases are also volume ratios.
3 H2(g) N2(g) ?
2NH3(g)
3 moles H2 1 mole N2 ?
2 moles NH3
3 liters H2 1 liter N2 ?
2 liters NH3
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Gas Stoichiometry 2
How many liters of ammonia can be produced when
12 liters of hydrogen react with an excess of
nitrogen?
3 H2(g) N2(g) ?
2NH3(g)
12 L H2
L NH3
2
L NH3
8.0
L H2
3
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Gas Stoichiometry 3
How many liters of oxygen gas, at STP, can be
collected from the complete decomposition of 50.0
grams of potassium chlorate?
2 KClO3(s) ? 2 KCl(s) 3 O2(g)
50.0 g KClO3
1 mol KClO3
3 mol O2
22.4 L O2
122.55 g KClO3
2 mol KClO3
1 mol O2
L O2
13.7
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Gas Stoichiometry 4
How many liters of oxygen gas, at 37.0?C and
0.930 atmospheres, can be collected from the
complete decomposition of 50.0 grams of potassium
chlorate?
2 KClO3(s) ? 2 KCl(s) 3 O2(g)
50.0 g KClO3
1 mol KClO3
3 mol O2
n mol O2
0.612 mol O2
122.55 g KClO3
2 mol KClO3
16.7 L
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Examples

• Using the following reaction
• Calculate the mass of sodium hydrogen carbonate
  necessary to produce 2.87 L of carbon dioxide at
  25ºC and 2.00 atm.
• If 27 L of gas are produced at 26ºC and 745 torr
  when 2.6 L of HCl are added what is the
  concentration of HCl?

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Examples

• Consider the following reaction What
  volume of NO at 1.0 atm and 1000ºC can be
  produced from 10.0 L of NH3 and excess O2 at the
  same temperature and pressure?
• What volume of O2 measured at STP will be
  consumed when 10.0 kg NH3 is reacted?

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The Same reaction

• What mass of H2O will be produced from 65.0 L of
  O2 and 75.0 L of NH3 both measured at STP?
• What volume Of NO would be produced?
• What mass of NO is produced from 500. L of NH3 at
  250.0ºC and 3.00 atm?

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Examples

• Mercury can be achieved by the following
  reaction What volume of oxygen gas can
  be produced from 4.10 g of mercury (II) oxide at
  STP?
• At 400.ºC and 740 torr?

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Daltons Law of Partial Pressures

• For a mixture of gases in a container, the total
  pressure exerted is the sum of the pressures each
  gas would exert if it were alone.
• PTotal P1 P2 P3 . . .
• Ptotal (n1n2n3)(RT/V)

It is the total number of moles of particles that
is important, not the identity or composition of
the gases.
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Examples
3.50 L O2
1.50 L N2
4.00 L CH4
0.752 atm
2.70 atm
4.58 atm

• When these valves are opened, what is each
  partial pressure and the total pressure?

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This is particularly useful in calculating the
pressure of gases collected over water. Ptotal
Pgas A PH2O (depends of H2O temp)
KClO3(s) ? KCl(s) O2(g)
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Vapor Pressure

• Water evaporates!
• When that water evaporates, the vapor has a
  pressure.
• Gases are often collected over water so the
  vapor. Pressure of water must be subtracted from
  the total pressure.
• It must be given and is dependent on the water
  temperature.

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Example

• N2O can be produced by the following
  reaction what volume of N2O
  collected over water at a total pressure of 94
  kPa and 22ºC can be produced from 2.6 g of
  NH4NO3? ( the vapor pressure of water at 22ºC is
  21 torr)

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The Mole Fraction

• Ratio of moles of the substance to the total
  moles.
• symbol is Greek letter chi c
• c1 n1 P1 nTotal PTotal

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Examples

• The partial pressure of nitrogen in air is 592
  torr. Air pressure is 752 torr, what is the mole
  fraction of nitrogen?
• What is the partial pressure of nitrogen if the
  container holding the air is compressed to 5.25
  atm?

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Kinetic Molecular Theory

• Particles of matter are ALWAYS in motion
• Volume of individual particles is ? zero gases
  have lots of space in between particles lots of
  empty space
• Collisions between particles and walls of the
  container are elastic. (No loss of energy due to
  friction, heat, etc.)
• Collisions of particles with container walls
  cause pressure exerted by gas.
• Particles exert no IM forces on each other no
  H-bonding, dipole-dipole, or London forces
  (forces of attraction and repulsion)
• Average kinetic energy is approx. equal to the
  temperature of a gas.

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Kinetic Energy of Gas Particles
At the same conditions of temperature, all
gases have the same average kinetic energy.
The Meaning of Temperature
Kelvin temperature is an index of the random
motions of gas particles (higher T means greater
motion.)
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Root Mean Square Velocity

• Velocity of a gas is dependent on mass and
  temperature
• Velocity of gases is determined as an average
• M mass of one mole of a gas particles in kg
• R 8.3145 J/Kmol
• 1 J kgm2/s2

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Example

• Calculate the root mean square velocity of
  carbon dioxide at 25ºC.
• Calculate the root mean square velocity of
  hydrogen at 25ºC.
• Calculate the root mean square velocity of
  chlorine at 25ºC.

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Range of velocities

• The average distance a molecule travels before
  colliding with another is called the mean free
  path and is small (near 10-7)
• Temperature is an average. There are molecules of
  many speeds in the average.
• Shown on a graph called a velocity distribution

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Velocity

• Average increases as temperature increases.
• Spread increases as temperature increases.

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Diffusion
Diffusion describes the mixing of gases. The
rate of diffusion is the rate of gas mixing.
(movement from high conc. to low conc.)
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Diffusion

• The spreading of a gas through a room.
• Slow considering molecules move at 100s of
  meters per second.
• Collisions with other molecules slow down
  diffusions.
• Best estimate is Grahams Law.

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Effusion

• Effusion describes the passage of gas into an
  evacuated chamber.

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Effusion

• Passage of gas through a small hole, into a
  vacuum.
• The effusion rate measures how fast this happens.
• Grahams Law the rate of effusion is inversely
  proportional to the square root of the mass of
  its particles.

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Deriving

• The rate of effusion should be proportional to
  urms
• Effusion Rate 1 urms 1 Effusion Rate 2
  urms 2

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Grahams LawRates of Effusion and Diffusion
Effusion
Diffusion
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Examples

• A compound effuses through a porous cylinder 3.20
  time faster than helium. What is its molar mass?
• If 0.00251 mol of NH3 effuse through a hole in
  2.47 min, how much HCl would effuse in the same
  time?
• A sample of N2 effuses through a hole in 38
  seconds. what must be the molecular weight of gas
  that effuses in 55 seconds under identical
  conditions?

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Real Gases
Must correct ideal gas behavior when at high
pressure (smaller volume) and low temperature
(attractive forces become important).


corrected pressure
corrected volume
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Real Gases

• Volume
• Real gas molecules have volume
• Volume available is not 100 of the
• container volume
• n number of moles
• b constant taking into account
• real gas volume
• Pressure
• Molecules of real gases do experience
• forces
• a proportionality constant determined by
  observation of the gas

corrected pressure
corrected volume
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Example

• Calculate the pressure exerted by 0.5000 mol Cl2
  in a 1.000 L container at 25.0ºC
• Using the ideal gas law.
• Van der Waals equation
• a 6.49 atm L2 /mol2
• b 0.0562 L/mol