Physical States of Matter

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Physical States of Matter

• Solid fixed shape
• Liquid conforms to container shape
• (fixed volume)
• Gas fills container

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What else is special about the gas phase?

• Gas volume changes greatly with P
• Gas volume changes greatly with T
• Gases have relatively low viscosity
• - Flow freely (pipes, through leaks/holes)
• Most gases have relatively low densities
• - Ex. O2 density 1.3 g/L
• Gases are miscible

http//www.grc.nasa.gov
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What is Pressure?

• Pressure (P) Force / Area
• Typically external P internal P
• What happens if external P gt internal P?

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How do we measure pressure?

• Barometer measures atmospheric pressure

• Manometer measures pressure of gas in an
  experiment

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Units of Pressure

• Millimeter of mercury
• mm Hg
• Torr
• bar (meterology, chemistry, physics)
• psi, pounds per square inch (engineering)

• pascal
• Pa
• 1 Pa 1 N/m2
• 103 Pa 1 kPa

• atmosphere
• atm

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Converting Units of Pressure
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Gas Laws

• Four variables P, T, V, n
• Any one can be determined from other three
• Hold two constant change one measure one
• Boyles Law (V P)
• Charless Law (V T)
• Avogadros Law (V n)

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Boyles Law

• The volume occupied by a gas is inversely related
  to its pressure.

PV constant
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Charless Law

• The volume occupied by a fixed amount of gas is
  directly related to its absolute Kelvin
  temperature.

V / T constant
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Combining Charless and Boyles Laws

• At constant volume, pressure is directly related
  to temperature

P / T constant
Combined Gas Law 2 variables change find
effect on third
PV/ T constant
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Avogadros Law

• The volume occupied by a gas is directly
  proportional to the amount (mol) of gas
• (fixed T P)

V / n constant
At fixed T P, equal volumes of any ideal gas
contain equal numbers of particles (or mols).
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Gas Behavior at STP

• STP
• Standard Temperature Pressure
• 0 C (273.15 K) and 1 atm (760 torr)
• Standard Molar Volume 22.4141 L or 22.4 L

Fig. 5.8
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Ideal Gas Law

• Combine
• Boyles Law
• Charless Law
• Avogadros Law

PV nRT
Solve at STP
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Solving Gas Law Problems

• Units must be consistent T is always in Kelvin
• Identify what variables are held constant
• Identify what variables are changing
• Predict direction of change to check answer
• (did you expect the variable to increase or
  decrease?)
• Rearrange ideal gas law to solve

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• A sample of gas occupies 105 ml at 0.903 atm. If
  temperature remains constant, what is the volume
  (in L) at 26.3 kPa?

Initial n T P V
Final n T P V
constant constant 0.903 atm 105 ml
constant constant
26.4 kPa ? ml
0.2605 atm
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• A tank filled with methane at 23 C and 0.991 atm
  is fitted with a safety valve that opens if
  internal pressure exceeds 1.00 x 103 torr. When
  the tank is placed in boiling water at exactly
  100 C, will the safety valve open?

Initial n T P V
Final n T P V

• constant
• 23 C 296. 15 K
• 0.991 atm
• constant

• constant
• 100 C 373.15 K

? torr constant
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Further Applications of the Ideal Gas LawThe
Density of a Gas

• One mole of any gas occupies nearly the same
  volume at a given temperature and pressure
• volume is constant
• Each gas has a molar mass
• Density mass / volume
• Density depends on molar mass of gas

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Further Applications of the Ideal Gas LawThe
Density of a Gas

• Rearrange to isolate Density (mass / volume)

• Density of gas is directly proportional to its
  molar mass
• Density of gas is inversely proportional to the
  temperature

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Further Applications of the Ideal Gas LawMolar
Mass of a Gas

• Rearrange to isolate molar mass

Volatile easily evaporates
Fig. 5.11
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Further Applications of the Ideal Gas LawThe
Partial Pressure of a Gas (Mixture of Gases)

• Each gas in a mixture acts like it is the only
  gas present
• No chemical reactions
• Totally miscible (homogeneous solution)

Daltons Law of Partial Pressures When water
vapor added to pure air. Phumid air Pdry
air Padded water vapor Each gas exerts a
partial pressure as if it were by itself.
Ptotal P1 P2 P3
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Further Applications of the Ideal Gas LawThe
Partial Pressure of a Gas (Mixture of Gases)

• In a tank filled with nitrogen gas and hydrogen
  gas

The pressure each gas contributes is based on its
mole fraction
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Ideal Gas Law Reaction Stoichiometry

• If 117 g NaCl reacts with excess acid, what
  volume of gas forms at STP? Molar mass NaCl
  58.45 g/mol

At STP, 1 mol gas 22.4 L
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Kinetic-Molecular Theory

• Postulate 1 Particle Volume
• Each individual gas particle is tiny compared to
  size of a container
• Lots of space between each molecule

• Postulate 2 Particle Motion
• Constant, random, straight-line (until collision
  with wall or each other)

• Postulate 3 Particle Collisions
• Collisions are elastic (energy exchanged, but not
  lost)
• Total kinetic energy (Ek) is constant
• No attractive or repulsive forces

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Kinetic Energy

• Total Ek is constant
• Total Ek refers to average Ek for sample
• Temperature is a measure of Ek

Fig. 5.14
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Molecular View of Gas Law

• Origin of Pressure
• Any moving object exerts a force when it hits
  something
• As each gas particle hits a surface, it exerts a
  tiny force
• Pressure is a cumulative effect

• 2. Boyles Law
• Gas sample is mostly empty space
• Exert P on sample
• gas molecules get closer together V?
• Decrease V
• Gas molecules have less space to move without
  hitting walls
• P (exerted by gas) ?

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Molecular View of Gas Law

• 3. Daltons Law of Partial Pressures
• Add gas
• ? of molecules ? of collisions ? P

• 4. Charless Law
• ? T, average Ek ?
• Molecules hit walls more frequently with more
  energy
• P on walls of container ?
• V must increase to restore P

• 5. Avogadros Law
• Increase of molecules (n) increase of
  collisions
• P on walls of container ?
• V must increase to restore P

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Relationship between Ek and T

• Why do equal numbers of molecules of two
  different gases occupy the same volume?

Average Ek is the same larger mass molecules
must be moving more slowly
same of gas molecules --gt same P --gt same V
(at constant T)
(Fig. 5.19)
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Relationship between Ek and T
Average Ek is the same larger mass molecules
must be moving more slowly
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Effusion Diffusion

• Effusion gas escaping from container through a
  tiny hole

Diffusion movement of one gas through another
Grahams Law of Effusion
Gas with lower molecular mass - most probable
speed is bigger - more molecular escape per time
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Effusion Diffusion
Diffusion movement of one gas through another
Fig. 5.20
Typically, diffusion is much slower than effusion
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Mean Free Path Collision Frequency

• Mean free path
• average distance a molecule travels before
  hitting another molecule
• affects diffusion
• Collision Frequency
• most probable speed
• mfp
• units collisions / s

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Real or Ideal?

• Gases have volumes associated with them
• (not just points in space)
• All collisions are not elastic
• Attractive/repulsive forces do exist in samples

Deviations from ideal behavior do occur,
especially under extreme conditions For 1 mol
of gas P gt 10 atm PV/RT lt 1 P gt gt 10
atm PV/RT gt 1
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Van der Waals Equationadjustments for real gases

• Adjust measured P up (intermolecular attractions)
• Adjust measured V down (molecular volume)

a and b are experimentally determined constants
(positive numbers)
What if a b 0?