Ch. 11 Properties of Gases

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Ch. 11 Properties of Gases

• Brady Senese, 5th Ed

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Index

• 10.1. Familiar properties of gases can be
  explained at the molecular level
• 10.2. Pressure is a measured property of gases
• 10.3. The gas laws summarize experimental
  observations
• 10.4. Gas volumes are used in solving
  stoichiometry problems
• 10.5. The ideal gas law relates P, V, T, and the
  number of moles of gas, n
• 10.6. In a mixture each gas exerts its own
  partial pressure
• 10.7. Effusion and diffusion in gases leads to
  Graham's law
• 10.8. The kinetic molecular theory explains the
  gas laws
• 10.9. Real gases don't obey the ideal gas law
  perfectly

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Properties of Gases

• What is the shape of the air in a balloon?
• Gases have an indefinite shape
• What is the volume of the gas in the balloon?
• They have an indefinite volume

4
How Does a Molecular Model Explain This?

• gases completely fill their containers
• Gases are in constant random motion
• gases have low density and are easy to compress
• gas molecules are very far apart
• gases are easy to expand
• gas molecules dont attract one another strongly

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What Is Pressure?

• The force of the collisions of the gas
  distributed over the surface area of the
  container walls Pforce/area
• units 1 atmosphere (atm) 760 mm Hg (torr)
  1.01325(105) Pascal (Pa) 14.7 psi1013 millibar
  (mb)
• measured with a barometer
• Pgdh
• ddensity of the liquid
• g gravitational acceleration
• hheight of the column supported
• Why use Mercury?

6
Learning Check Pressure Units

• Convert 675 mm Hg to atm.

Known 675 mmHg
Unknown atm
Conversion factor?
760 mmHg 1 atm
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Learning Check

• What happens to gas pressure when you raise the
  temperature?

If the container can expand in response to the force In a rigid walled container

Pressure increases because the faster moving
molecules hit the walls of the container with
greater force
No change in pressure is observed because the
area increased.
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Learning Check

• What happens to gas pressure when you increase
  the number of molecules in the container?

If a container can expand In a rigid walled container

pressure increases because more molecules hit the
walls of the container, thus exert a greater
force on the container
No pressure change is observed.
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Absolute Zero

• Temperature of a gas at which pressure and volume
  are zero
• It is not possible to have a gas with a V 0
• molecular volume doesnt change but the total
  volume decreases
• extrapolation is necessary due to condensation

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Ideal Gases

• Their behavior is predicted by the gas laws
• There are NO ideal gases
• However, most gases behave ideally at atmospheric
  P or lower and room T or higher
• You need to know when they are not useful

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Combined Gas Law

• Boyles Law
• Charles Law
• Gay-Lussacs Law
• Thus combining this information
• And therefore, for any 2 conditions

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Combined Gas Law

• Used for calculating the effects of changing
  conditions
• works if the Temperature is in Kelvin, but P and
  V can be any units so long as the units cancel
• Learning Check
• If a sample of air occupies 500. mL at STP, what
  is the volume at 85 C and 560 torr?

890 mL
Standard Temperature (273.15K) and Pressure (1
atm)
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Learning Check

• A sample of oxygen gas occupies 500.0 mL at 722
  torr and 25 ºC. Calculate the temperature in ºC
  if the gas has a volume of 2.53 L at 491 mm Hg.
• .

T2581 C
T2853.90 K
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Learning Check

• A sample of helium gas occupies 500.0 mL at 1.21
  atm Calculate the volume of the gas if the
  pressure is reduced to 491 torr

936 mL
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Your Turn!

• 22.4 L of He at 25 ºC are heated to 200.ºC. What
  is the resulting volume?
• 22.4 L
• 179 L
• 43.1 L
• not enough information given

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Molar Volume

• The volume of one mole of any gas at STP is 22.4
  L.
• Identity of the gas doesnt matter
• Molar mass of the gas doesnt matter
• Corollary equal volumes of any gas contain the
  same number of particles as long as the T and P
  are the same

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Bringing It Together

• Avogadro n directly proportional to V
• Boyle P indirectly proportional to V
• Charles T directly proportional to V
• Gay-Lussac T directly proportional to P
• Combining these variables into one equation
  results in the Ideal Gas Law.
• R is the constant of proportionality (the ideal
  or universal gas constant) its value is
  0.082057 Latm/molK

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Ideal Gas Law

• Used to describe a sample of gas under one set of
  conditions
• The units have to be
• P in atm or torr
• V in L
• n in mol
• T in K
• R 0.082057 Latm/molK 62.36 Ltorr/molK

PV nRT
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Your Turn!

• 12.2 g of Ne are placed into a 5.0 L flask at 25
  ºC. What is the pressure of the gas?
• 3.0 atm
• 60. atm
• 0.25 atm
• None of these

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Learning Check

• How many liters of N2(g) at 1.00 atm and 25.0 C
  are produced by the decomposition of 150. g of
  NaN3? 2NaN3(s) ? 2Na(s) 3N2(g)

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Gas Density

• The number of moles may be related to both the
  mass (m) of the gas sample and the molar mass
  (MM) of the gas involved
• Thus we may rewrite the Ideal Gas Law as
• Further, since dm/V, we can rewrite the equation
  in terms of density

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Learning Check

• What is the molar mass of a gas with a density of
  6.7 g/L at -73.ºC and a pressure of 36.7 psi?

44 g/mol MM
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Learning Check

• What is the density of NO2 at 200 C and 600.
  torr?

0.9 g/L
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Your Turn!

• What is the density of Helium gas at 35 ºC and
  1.2 atm?
• 5.1 g/L
• 0.20 g/L
• 2.34 g/L
• None of these

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Learning Check

• A sample of fluorine gas occupies 275 mL at 945
  torr and 72 ºC. What is the mass of the sample?

PV nRT
0.459 g mass
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Learning Check

• Determine the molecular weight of a gas if 1.053
  g of the gas occupies a volume of 1.000L at 25 C
  and 752 mm Hg (The Dumas Method)

PV nRT
26.0 g/mol mass
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Your Turn!

• What is the molar mass of a sample of gas if 2.22
  g occupies a volume of 5.0 L a 35 ºC and 769 mm
  Hg?
• 1.3 g/mol
• 0.015 g/mol
• 0.090 g/mol
• None of these

11 g/mol
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Daltons Law

• The partial pressure of a gas is the pressure
  that the gas would exert if it were in the
  container by itself

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Collecting A Gas By Water Displacement

• Collected gas pressure must be corrected for
  water vapor
• PtotalPgas VPwater (see Table 10.2)

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PTotal P1 P2 P3 .
Learning Check

• Pump 520 mm Hg N2 and 250 mm Hg O2 into an empty
  gas cylinder. What is the overall pressure of
  the mixture?

Pt520 mm Hg 250 mm Hg770 mm Hg
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PTotal P1 P2 P3 .
Learning Check

• 32.5 mL of Hydrogen gas is collected over water
  at 25 ºC and 755 torr. What is the pressure of
  dry hydrogen gas?
• VP25ºC  23.76 mmHg)

Correct Pt to find the Pdry gas 755-23.76
torr731.24 torr
731 torr Phydrogen
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Mole Fraction, X

• Each gas molecule contributes a fraction of the
  total pressure
• Xathe mole fraction of substance a
• na the moles of component a
• nt the total number of moles of gas in the
  mixture
• Application The partial pressure contributed by
  the component gas a is a fraction of the total
  pressure

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Learning Check

• What is the mole fraction of N2 in the
  atmosphere? 1.000atm Air .7808 atm N2 .2095
  atm O2 .0093 atm Ar .00036 atm CO2

.7808 Xnitrogen
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Diffusion vs. Effusion

• When the partition is removed, blue molecules
  diffuse to mix
• The molecules effuse through a pinhole into an
  area of lower pressure

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Grahams Law Of Effusion

• Relates the velocity (rate at which the gas
  moves through a given space) to the molecular
  mass of the gas.
• The greater the molecular mass of the gas, the
  slower its velocity.

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Your Turn!

• The average kinetic energy of all gas molecules
  is the same at the same temperature. Compared to
  lighter atoms at the same temperature, heavier
  atoms on average
• move faster
• move slower
• move at the same average velocity

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Your Turn!

• Three balloons are filled with equal volumes of
  the gases CH4, H2, and He. After 5 hours the
  balloons look like the picture.
• Which is the He balloon?

C
A
B
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Learning Check

• If it is observed that Br2 travels 5.0 cm/s in a
  container, if a sample of an unknown gas travels
  at half the speed, what is the molecular mass of
  the unknown gas?

MM 640 g/mol
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Kinetic Molecular Theory Explains Gas Behaviors

• Gases consists of an extremely large number of
  very tiny particles that
• are in constant, random motion
• occupy a negligible portion of the total volume
  of the sample-their individual contribution may
  be ignored
• collide elastically with themselves and the walls
  of the container
• move in straight lines between collisions,
  neither attracting nor repelling each other

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Kinetic Molecular Theory-Irregularities

• The volume of a gas molecule is negligible
• NO! Under conditions of extremely high pressure,
  gases are closer, their relative size is a factor
• Gas molecules collide elastically
• NO! Under conditions of extremely low
  temperatures, gases move more slowly and
  intermolecular attractions are more significant

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Real Gases

• van der Waals equation accounts for deviations
  from ideal behavior by correcting assumptions
• particle volume is not negligible!
• particles do interact!
• van der Waals constants, a b, are specific to
  the substance

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van der Waals Constants
TABLE 10.3 TABLE 10.3 Van der Waals Constants Van der Waals Constants Van der Waals Constants Van der Waals Constants
Substance   a (L2 atm mol-2)     b (L mol-1)     Substance     a (L2 atm mol-2)     b (L mol-1)  
Noble gases     Other Gases    
He     0.03421     0.02370     H2      0.02444     0.02661  
Ne     0.2107     0.01709   O2      1.360     0.03183  
Ar     1.345     0.03219   N2      1.390     0.03913  
Kr     2.318     0.03978   CH4      2.253     0.04278  
Xe     4.194     0.05105   CO2      3.592     0.04267  
      NH3      4.170     0.03707  
      H2O     5.464     0.03049  
      C2H5OH     12.02     0.08407