The Gaseous State

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The Gaseous State

• Pressure-Volume-Temperature Relationships for
  Gaseous Molecules
• Gaseous Diffusion

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Automobile Air Bag
Source Courtesy of Chrysler Corporation.
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Gas Pressure

• Force exerted per unit area of surface by
  molecules in motion.

P Force/unit area
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Mercury Barometer
Measurement of Gas Pressure
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Manometer
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Pressure Units

• Force exerted per unit area of surface by
  molecules in motion.

P Force/unit area

• 1 atmosphere 14.7 psi
• 1 atmosphere 760 mm Hg (torr)
• 1 atmosphere 101,325 Pascals
• 1 Pascal 1 kg/m.s2

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• Boyles Law
• Compressibility of Gases
• The volume of a sample of gas, at a given
  temperature, varies inversely with the applied
  pressure.

V a 1/P (constant moles and T)
or
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• Problem
• A sample of chlorine gas has a volume of 1.8 L at
  1.0 atm.
• If the pressure increases to 4.0 atm (at constant
• temperature), what would be the new volume?

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• Charless Law
• The volume occupied by any sample of gas at
  constant pressure is directly proportional to its
  absolute temperature.

V a T(K) (at constant moles and P)
or
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Linear Relationship of Gas Volume and Temperature
at Constant Pressure
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• Problem
• A sample of methane gas that has a volume of 3.8
  L at
• 5.0C is heated to 86.0C at constant pressure.
  What is
• its new volume?

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• Gay-Lussacs Law
• The pressure exerted by a gas at constant volume
  is directly proportional to its absolute
  temperature.

P a Tabs (constant moles and V)
or
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• Problem
• An aerosol can has a pressure of 1.4 atm at
  25C. What pressure would it have at 1200C,
  assuming the volume remained constant?

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• Combined Gas Law
• In the event that all three parameters, P, V,and
  T, are
• changing, their combined relationship is defined
  as follows

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• Problem
• A sample of carbon dioxide occupies 4.5 L at 30C
  and
• 650 mm Hg. What volume would it occupy at 800 mm
  Hg
• and 200C?

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The Ideal Gas Law

• From the individual gas laws, we see that volume
  varies in
• proportion to pressure, absolute temperature, and
  moles.

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The Ideal Gas Law

• Combining the three proportionalities, we can
  obtain the following relationship.

or
where R is the proportionality constant
referred to as the ideal gas constant.
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The Gas Constant, R

• The numerical value of R can be obtained using
  Avogadros law, which states that one mole of any
  gas at Standard Temperature and Pressure (STP)
  will occupy 22.4 liters (the Molar Volume).

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A Molar Volume of Gas
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Problem.How many grams of oxygen gas could
occupy the lungs of an adult with a lung capacity
of 3.80 L at 1 atm pressure and normal body
temperature, 37 oC?

• P 1.0 atm, V 3.8 L, T 37oC, n n mol of
  O2
• g grams of O2
• PV nRT, n PV
• RT
• n 1.0 x 3.8 mol 0.15 mol O2 x 32
  g O2 4.8 g O2
• 0.0821 x 310
  mol

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Problem.What pressure will be generated by 5.50
g of O2(g) in a 200 mL stoppered flask at 22 oC?

• P P atm, V 0.200 L, T 22oC (295K), n n
  mol of O2
• 5.50 g O2 x 1 mol O2 0.172 mol O2
• 32 g O2
• PV nRT, P nRT
• V
• P 0.172 x 0.0821 x 295
  20.8 atm
• 0.200
  

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Problem.What is the pressure generated by 91.3
g of O2 gas in a 8.0 Liter gas cylinder at 21 oC?

• P P atm, V 8.0 L, T 21oC, 91.3 g O2 x 1
  mol O2 2.85 mol O2 n mol
• 32 g
• Units must be in L, atm, mol and K
• PV nRT , P nRT 2.85 x 0.0821 x
  294
• 
  V 8.0
• P 8.61 atm

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Use of Ideal Gas Law to Determine Density and
Molecular Mass of gases
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Problem.What is the density of UF6 gas (in g/L)
at 100 oC and 1.0 atm?
Units must be in L, atm, mol and K
UF6 (MW 352 g/mol)

• density g g mol (n) g
• L V MW
• PV nRT
• PV g RT
• MW
• d g P. MW 1.0 x 352 11.5
  g/L
• V RT 0.0821 x 373

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Finding the Vapor Density of a Gas
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Problem.If 0.495 g of chloroform, CHCl3, fills
completely a 127 mL flask at 98 oC and 754 torr,
what is the molecular weight of chloroform?

• PV nRT Units must be in L, atm, mol
  and K
• 754 torr 754 atm 0.992 atm
  760
• PV g RT 127 mL 0.127 L
• MW
• MW g RT 0.495 x 0.0821 x 371 119.7
  g/mol
• PV 0.992 x 0.127

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Problem. A 15.5 gram sample of an unknown gas
occupied a volume of 5.75 L at 25C and a
pressure of 1.08 atm. Calculate its molecular
mass.

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Gases and Reaction Stoichiometry
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Problem. How many liters of oxygen can you
produce at 298 K and 1.02 atm from the reaction
of 0.0100 mol of KClO3?

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Problem.How many liters of CO(g) at 25 oC and
750 mm Hg are needed to reduce 1 kg of Fe2O3?
(Ans 466 L). Fe2O3(s) 3 CO(g) gt 2
Fe(s) 3 CO2(g)

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Problem.If an air-bag has a volume of 45.5L and
requires a N2 pressure of 828 mm Hg to function
at 22 oC, what mass of sodium azide, NaN3, must
decompose by the reaction 2 NaN3(s) ? 2 Na(s)
3 N2(g)

• P 828/760 atm, V 45.5 L, T 295
  K, n mol of N2(g)
• PV nRT, n PV 1.09 x 45.5 2.05
  mol
• RT
  0.0821 x 295
• 2 NaN3(s) ? 2 Na(s) 3 N2(g)
• 2.05 mol N2(g) x 2 mol NaN3 1.37 mol NaN3 x
  65 g NaN3 88.8 g
• 3 mol N2
  mol NaN3

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Partial Pressures of Gas Mixtures

• Daltons Law of Partial Pressures the sum of all
  the pressures of all the different gases in a
  mixture equals the total pressure of the mixture.
  

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Partial Pressures of Gas Mixtures

• The composition of a gas mixture is often
  described in terms of the mole fraction of its
  components

• The mole fraction, of a component gas is the
  fraction of moles of that component in the total
  moles of gas mixture.

The partial pressure of a component gas, A, is
then defined as
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Problem. Given a mixture of gases in the
atmosphere at 760 torr, what is the partial
pressure of N2 if its mole fraction, c, 0 .7808.

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Collection of Gas Over Water
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Problem.Suppose a 156 mL sample of H2 gas was
collected over water at 19oC and 769 mm Hg. What
is the mass of H2 collected?

• The vapor pressure of water at 19oC as 16.5 mm Hg.

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Kinetic-Molecular Theory

• Volume of particles is negligible
• Particles are in constant motion
• No inherent attractive or repulsive forces
• The average kinetic energy of a collection of
  particles is proportional to the temperature (K)

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Molecular Speeds Diffusion and Effusion

• The root-mean-square (rms) molecular speed, u, is
  a type of average molecular speed, equal to the
  speed of a molecule having the average molecular
  kinetic energy. It is given by the following
  formula

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Maxwells Distribution of Molecular Speeds
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Molecular Speeds Diffusion and Effusion
Diffusion is the transfer of a gas through space
or another gas over time. Effusion is the
transfer of a gas through a membrane or orifice
into a vacuum. From the equation for the rms
velocity of gases, the following relationship
exists between the rate of effusion and molecular
mass.
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• Grahams law The rate of effusion or diffusion
  is
• inversely proportional to the square root of its
• molecular mass.

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Problem.How much faster would H2 gas effuse
through an opening than methane, CH4?

• H2 gas effuses through an opening 2.8 times as
  fast as methane, CH4?

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Problem.It takes 16.6 min for a 10.0-mL
sample of an unknown gas to effuse through a
pinhole. A 10.0-mL sample of helium, He, required
5.00 min. What is the molecular weight of the
unknown gas?
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Real Gases
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Effect of Intermolecular Attractions on Gas
Pressure
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Pressure-volume Product of Gases at Different
Pressures
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Problem.If sulfur dioxide were an ideal
gas, the pressure at 0C exerted by 1.000 mol
occupying 22.41 L would be 1.000 atm. Use the van
der Waals equation to estimate the real
pressure. For SO2 a 6.865 L2.atm/mol2 b
0.05679 L/mol

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