Gases

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Chapter 9

• Gases

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Gases and Gas Pressure

• Gases constituent atoms and molecules that have
  little attraction for one another
• Free to move in available volume
• Some properties of gases
• Mixtures are always homogenous
• Very weak attraction between gas molecules
• Identity of neighbor is irrelevant
• Compressible volume contracts when pressure is
  applied
• 0.10 of volume of gas is occupied by molecules
• Exert a measurable pressure on the walls of their
  container

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Gases and Gas Pressure

• Pressure force exerted per unit area
• SI unit equals Pascal (Pa)
• 1 Pa 1 N/m2 (1 N 1 (kgm)/s2)
• Alternative units
• Millimeters of mercury (mmHg)
• Atmosphere (atm)
• 1.0 atm 760 mmHg 101, 325 Pa
• 1.0 atm 760 torr

Pressure
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Atmospheric Pressure

• - pressure created from the mass of the
  atmosphere pressing down on the earths surface
• Standard atmospheric pressure at sea level 760
  mmHg

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Gases and Gas Pressure

• Barometer
• long thin mercury filled tube sealed at once end
  and inverted into a dish of mercury
• Downward pressure of Hg in column equals outside
  atmospheric pressure

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Measuring Pressure

• Manometer
• U-tube filled with mercury, with one end
  connected to the gas filled container and the
  other end open to the atmosphere.
• Pgas lt Patm liquid level in the arm connected to
  the gas-filled cylinder will be higher
• Pgas PHg Patm

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Measuring Pressure

• Pgas gt Patm liquid level in the arm connected to
  the gas filled cylinder will be lower
• Pgas Patm PHg
• (PHg the difference in the heights of the two
  mercury columns)

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Example

• What is the pressure of the gas inside the
  following apparatus (in mm Hg) if the outside
  pressure is 750 mm Hg? (1 cm Hg 10 mm Hg)

9
The Gas Laws

• Ideal Gas A gas whose behavior follows the gas
  laws exactly.
• The physical properties of a gas can be defined
  by four variables
• P pressure
• T temperature
• V volume
• n number of moles

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Pressure and Volume Boyles Law

• Showing the relationship between pressure and
  volume
• P x V k (constant value _at_ specific temp and
  constant moles of gas)
• k 1.40 x 103
• V 1/P (inverse relationship)

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Pressure and Volume Boyles Law

• Can predict a new volume of pressure is changed
• P1V1 k P2V2 ? P1V1 P2V2

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The Gas Laws
Boyles Law
(constant n and T)
PV k
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Example

• A sample of helium gas has a pressure of 3.54 atm
  in a container with a volume of 23.1 L. This
  sample is transferred to a new container and the
  pressure is measured to be 1.87 atm. Assume
  constant temperature.
• Will the volume of the gas increase of decrease?
• What will be the new volume of the gas?

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Volume and Temperature Charless Law

• Relationship between Volume and Temperature
• V bT (b is a constant)
• V / T b
• Can predict the new volume or temperature
• (V1/T1) (V2/T2)

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The Gas Laws
Charles Law
V a T
(constant n and P)
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Example

• A 2.0 L sample of air is collected at 298K and
  then cooled to 278 K. The pressure is held
  constant at 1.0 atm.
• Does the volume increase of decrease?
• Calculate the volume of the air at 278 K?

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Volume and Moles Avogadros Law

• Relationship between volume of gas and number
  moles of gas
• V is directly proportional to n
• V an or V / n a (a constant)
• Can predict the new volume or new moles of gas at
  constant pressure and temperature
• (V1/n1) (V2/n2)

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The Gas Laws
Avogadros Law
V a n
(constant T and P)
19
Example

• Consider two samples of nitrogen gas (composed N2
  molecules). Sample 1 contains 1.5 mol of N2 and
  has a volume of 36.7 L at 25oC and 1 atm. Sample
  2 has a volume of 16.0 L at 25oC and 1 atm.
  Calculate the number moles of N2 in sample 2

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Summary
Boyles Law Charles Law Avogadros Law
constant T n constant P n constant P T
V 1/P V T V n

PinitialVinitial PfinalVfinal
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9.3 The Ideal Gas law

• Different gasses show similar physical behavior
  (unlike solid or liquid)
• Relationship of variable gas laws
• Ideal gas behavior follows the gas laws exactly

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9.3 The Ideal Gas law

• Describes how the volume of a gas is affected by
  changes in pressure, temperature and moles.
• PV nRT

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9.3 The Ideal Gas Law
PV nRT
Ideal Gas Law
R is the gas constant and is the same for all
gases.
T 0 C (273.15 K)
Standard Temperature and Pressure (STP) for Gases
P 1 atm
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The Ideal Gas Law
What is the volume of 1 mol of gas at STP?
22.414 L
V

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Example

• A helium gas cylinder of the sort used to fill
  balloons have a volume of 43.8 L and pressure of
  1.51 x 104 kPa at 25.0oC. How many moles of
  helium are in the tank?
• What volume is occupied by 0.250 mol of carbon
  dioxide gas at 25.0oC and 371 torr?
• A 0.250 mol sample of argon gas has a volume of
  9.00L at a pressure of 875 mmHg. What is the
  temperature (in oC) of the gas?

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Stoichiometric Relationships with Gases

• The reaction used in the deployment of automobile
  airbags is the high temperature decomposition of
  sodium azide, NaN3, to produce N2 gas. How many
  liters of N2 at 1.15 atm and 30.0oC are produced
  by the decompostion of 45.0g NaN3?

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Examples

• Consider the reaction represented by the equation
  
• P4(s) 6 H2(g) ? 4H3(g)
• What is the amount of P4 is required to react
  with 5.39 L of hydrogen gas at 27.0oC and 1.25
  atm?

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Example

• Ammonia is commonly used as a fertilizer to
  provide a source of nitrogen for plants. A
  sample of NH3(g) occupies a volume of 5.00 L at
  STP. What moles will this sample occupy?

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Combine Gas Law

• is an expression obtained by mathematically
  combining Boyles and Charles law
• P1V1 P2V2 _at_ constant n
• T1 T2
• can predict P, V or T when condition is changed

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Examples

• A sample of diborane gas B2H6, a substance that
  bursts into flames when exposed to air, has a
  pressure of 0.454 atm at a temperature of -15oC
  and a volume of 3.48L. If condition are changed
  so that the temperature is 36oC and the pressure
  is 0.616 atm, what is the new volume of the
  sample?

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Examples

• Consider a sample of hydrogen gas of 63oC with a
  volume of 3.65L at a pressure of 4.55 atm. The
  pressure is changed to 2.75 atm and the gas is
  cooled to -35oC. Calculate the new volume of the
  gas

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13.6 Daltons Law of Partial Pressure

• A. Gas laws apply to mixtures of gases
• B. Dalton's law of partial pressure
• Ptotal P1 P2 P3 .. at constant V, T
• where P1, P2, .refer to the pressure of the
  individual gases in the mixture
• Mole Fraction (X)

or
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Partial Presssure

• C. Partial pressures refer to the pressure each
  individual gas would exert if it were alone in
  the container (P1, P2, )
• 1. Total pressure depends on the total molar
  amount of gas present
• Ptotal ntotal (RT/V)

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Examples

• A 2.0 L flask contains a mixture of nitrogen gas
  and oxgyen gas at 25.0oC. The total pressure of
  the gas mixture is 0.91 atm, and the mixture is
  known to contain 0.050 mol of N2. Calculate the
  partial pressure of oxygen and the moles of
  oxygen present

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Examples

• Mixture of helium and oxygen are use in the air
  tanks of underwater divers for deep dives. For a
  particular dive, 12.0L of O2 at 25.0oC and 1.0
  atm and 46.0 L of He at 25oC and 1.0 atm were
  both pumped into a 5.0 L tank. Calculate the
  partial pressure, moles fraction of each gas and
  the total pressure in the tank at 25.0oC

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The Kinetic Molecular Theory of Gas

• A. Model that can explain the behavior of gases
• .Assumptions
• 1. A gas consists of particles in constant
  random motion
• 2. Most of the volume of a gas is empty spaces
• 3. The attractive and repulsive forces between
  molecules of gases are negligible
• 4. The total kinetic energy of the gas
  particles is constant at constant T
• 5. Average Ek a T

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The Kinetic-Molecular Theory of Gases
molar mass
average speed
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The Kinetic-Molecular Theory of Gases
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Grahams Law Diffusion and Effusion of Gases

• Diffusion The mixing of different gases by
  molecular motion with frequent molecular
  collisions

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Grahams Law Diffusion and Effusion of Gases

• Effusion The escape of a gas through a pinhole
  into a vacuum without molecular collisions.

Grahams Law
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The Behavior of Real Gases
The volume of a real gas is larger than predicted
by the ideal gas law.
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The Behavior of Real Gases
Attractive forces between particles become more
important at higher pressures.
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The Behavior of Real Gases
van der Waals equation
Correction for intermolecular attractions.
n2
a
P
nRT

V - n
b
V2
Correction for molecular volume.
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examples

• Assume that you have 0.500 mol of N2 in a volume
  of 0.600L at 300K. Calculate the pressure in the
  atmosphere using both the ideal gas law and the
  van der Waals equation. For N2, a 1.35
  (L2atm)mol2, and b 0.0387 L/mol