Gases

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Gases
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78 N2 (g) 21 O2 (g) 1 others
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-expand to fill the container in which they are
enclosed
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-are compressible
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General Properties of Gases
-expand to fill the container in which they are
enclosed
-are compressible
-they readily flow past one another
-they form homogeneous mixtures with other gases
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• These characteristics are a result of molecules
  being far apart.
• Gas molecules behave as if other gas molecules
  are not present.
• Molecules of liquids and solids are closer
  together and occupy much more of the available
  space.

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• Under ordinary conditions (pressure
  temperature) many molecular compounds exist as
  gases.
• Liquids and solids can exist as gas under
  different circumstances.
• These are called vapors

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The condition of a gas is determined by the
following properties
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Pressure
--results from gas molecules striking the
surface of a container --gases cause pressure on
all surfaces they contact
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Because of gravity, the air above us creates a
downward force.
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Mercury Barometers

• Glass tube more than 760 mm long and closed at
  one end.
• Invert into liquid mercury.
• Area in tube above mercury is a vacuum.
• Standard Atmospheric
• pressure is 760 mm Hg.

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Force
Pressure --------------
Area
ma
kg m s2
m2
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Units of Pressure Commonly Used And Conversion
Factors
1 atm 760 mm Hg 760 torr 101.3 kPa and 1
bar (105 Pa) 100 kPa
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1 atm 760 mm Hg 760 torr 101.3 kPa
Convert 0.357 atm to torr.
Convert 147.2 kPa to torr.
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Two devices used to measure atmospheric pressure
are the barometer and the manometer.
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http//www.chem.iastate.edu/group/Greenbowe/sectio
ns/projectfolder/flashfiles/gaslaw/manometer4-1.ht
ml
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Problem You read a barometer and find that
atmospheric pressure is 756.7 torr. A sample of
gas is placed in a vessel attached to an open
end-mercury manometer. The mercury in the
open-end arm is 24.4 mm higher than the mercury
in contact with the gas. What is the P of the
gas in atm?
1 atm
24.4 mm Hg
0.0321 atm
760 mm Hg
1 atm
756.7 torr
0.996 atm
760 torr
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Problem You read a barometer and find that
atmospheric pressure is 756.7 torr. A sample of
gas is placed in a vessel attached to an open
end-mercury manometer. The mercury in the
open-end arm is 24.4 mm higher than the mercury
in contact with the gas. What is the P of the
gas in atm?

0.0321 atm
1.028 atm
0.996 atm
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The Gas Laws

• 4 Variables needed to describe state of a gas
• Temperature (T)
• Pressure (P)
• Volume (V)
• Number of moles (n)

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Boyles Law(Pressure- Volume relationship)

• The volume of a fixed quantity of gas at a
  constant temperature is inversely proportional to
  the pressure.

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http//www.lerc.nasa.gov/WWW/K-12/airplane/aboyle.
html
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• Volume versus pressure graph shows inverse
  relationship.
• The Volume versus 1/P is a linear relationship.

V
V
P
1/P
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double
half
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Common way of expressing Boyles Law P1V1P2V2
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What will the volume be when the pressure is 6
atm?
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P1V1P2V2
What is the volume of the tank in L?
(21.5 atm)(50.0 L) (1.55 atm)V2
Volume of tank 693 L 50.0 L 643 L
P2 and V2
P1 and V1
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A sample of helium gas has a pressure of 2.69 x
103 torr 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 1.42 x103 torr.
What is the volume of the new container in L?
Assume constant temperature.
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P1V1P2V2
(3.54 atm)(23.1 L) (1.87 atm)V2
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Charles Law

• The Temperature-Volume relationship.
• The volume of a fixed amount of gas at a constant
  pressure is directly proportional to its absolute
  temperature.

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Directly Proportional
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A 2.45 L sample of nitrogen is collected at 273 K
and heated to 325 K. Calculate the volume of the
nitrogen gas at 325 K. Assume constant pressure.
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Note All temperatures must be converted to
Kelvin before solving gas law problems. Not
doing so will give you incorrect answers.
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Avogadro's Law

• The quantity-volume relationship
• The volume of a gas maintained at constant
  temperature and pressure is directly proportional
  to the number of moles of the gas.

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If 2.55 mol of helium gas occupies a volume of
59.5 L at a particular temperature and pressure,
what volume does 7.83 mol of helium occupy under
the same conditions?
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3 Gas Laws we know so far
We can combine the 3 laws to form a new equation
called the Ideal Gas Equation
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1
V
P
V
T
V
n
(
)
R
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(
)
n
T
V

R
Ideal Gas Equation
P
An ideal gas is a hypothetical gas whose
pressure, volume, and temperature is completely
described by the ideal-gas equation.
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• R is the gas constant
• Units are dependent upon units of P, V, n.
• T must always be expressed as absolute
  temperature (K).
• n is usually expressed in moles
• Units for V and P are usually liters and atm.

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Its important that you are able to algebraically
manipulate this equation to solve for all
variables. Write an equations for each variable
in notes (total of 5 equations).
PV nRT
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Its important that you are able to algebraically
manipulate this equation to solve for all
variable. In your notes, isolate each of the
variables as if you were going to solve for them.
What are the units for R?
PV nRT
Gas Constant is given on Exam!
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Ideal Gas Law and Boltzmanns Constant
Boltzmann constant defines the relation between
absolute temperature and the kinetic energy
contained in each molecule of an ideal gas.

•                                                 
                                                    
                                                    
  
• N number of molecules
• k Boltzmann constant 1.38066 x 10-23 J/K
• k R/NA
• NA Avogadro's number 6.0221 x 1023 /mol

If you take another form of the ideal gas
constant, 8.314 J /K /mol and divide it by
Avogadro's number, you get Boltzmanns constant.
No calculations on this one.
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Last year you learned that 1 mol of any gas
22.4 L at standard temperature and pressure
(STP). Now you will see where that is derived.
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STP

• Standard temperature and pressure.
• T 0C (273.15K) P 1 atm.
• Molar volume of an ideal gas at STP

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• The ideal gas equation does not always accurately
  describe gas behavior.
• Usually the difference between the ideal value
  and the real value is so small that we can ignore
  variations.

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• Calcium carbonate decomposes upon heating to give
  calcium oxide and CO2 gas. The carbon dioxide is
  collected in a 250 mL flask. The gas has a
  pressure of 1.3 atm. at 31C. How many moles of
  CO2 were generated?

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In order to solve, we must first sort out what we
are given and convert to the correct units.
P 1.3 atm
T 31 C (31 273)
304 K
V 250 ml 0.250 L
R 0.08206 L-atm-mol-1 K-1
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0.013 mol of CO2
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The equations for Boyles Law, Charless Law, and
Avogadros Law are not given on the exam. You
must be able to derive them from the ideal gas
equation by recognizing constants.
PV nRT
If the moles and the temperature are constant,
than the product of nRT is a constant.
PV nRT constant
Because the product of PV is a constant
P1V1 P2V2
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Problem
The gas pressure in an aerosol can is 1.5 atm at
25C. Assuming that the gas inside obeys the
ideal-gas equation, what would the pressure be if
the can were heated to 450 C?
Correct your units first. Then, isolate your
constants which will lead you to your equation.
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PV nRT
of moles and volume are both constant
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How to calculate grams and molar mass by
incorporating M g/mol into PVnRT. (Board)
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Extensions of Ideal Gas Equation
Using PV nRT, we can calculate
Density (d)
Molar Mass (M )
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m
M
n
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m
m
M
D


v
n

V
P
R
T
n
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m
m
D


n
v
M

V
P
R
T
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m
D


n
v
m

V
P
M
R
T
and there it is!!!
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O.K. A little slower this time!
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m
m
M
D


v
n

V
P
R
T
n
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m
m
D


n
v
M

V
P
R
T
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m
D


n
v
m

V
P
M
R
T
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m

n
M
Will be given on AP Exam!
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Sample Problem
What is the density of carbon tetrachloride vapor
at 714 torr and 125C?
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What is the density of carbon tetrachloride vapor
at 714 torr and 125C?
4.43 g/L
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Starting with the ideal gas equation, try the
practice exercise on page 367. Make sure you show
in your notes how you manipulated the ideal gas
equation to solve for density.
5.9 g/L
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Can be rearranged to find Molar Mass
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Partial Pressure
Pressure exerted by a particular component of a
mixture of gases.
Dalton's Law of Partial Pressures
The total pressure (Pt) of a gas mixture is equal
to the sum of the individual pressures
Each gas behaves independently of the others!
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Same volume and temperature for each!
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Since each gas behaves independently, we can say
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Read sample exercise 10.10 on page 383 and try
the practice below the sample.
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Relating amount of a gas to partial pressures
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rearrange
Let
X1
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78 of air molecules are N2
Therefore, its mole fraction equals
X1 0.78
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Read sample exercise 10.11 on page 384 and try
the practice below the sample.
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Collecting Gases Over Water
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We must consider the vapor pressure!
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The gas is collected and pressures inside and
outside are equalized by raising or lowering the
bottle so that water levels inside and outside of
the bottle are equal. Because we must account
for the gas pressure and the pressure from the
water vapor, the total pressure equals Ptotal
Pgas PH2O So Pgas Patm PH2O
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The pressure resulting from water vapor depends
upon temperature. The higher the temperature,
the higher the vapor pressure. This value is
usually obtained from a data table of vapor
pressures for given temperatures. PH2O _at_ 26C
25 torr
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Read sample exercise 10.12 on page 385 and try
the practice below the sample.
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Combined Gas Law
Given on the AP Exam. Must manipulate equation
to solve for one variable. This is to be used
when given a scenario when several properties of
a gas change. Can also use this to derive
Boyles Law and Charless Law.
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A 5.00 L air sample at a temperature of -50.0ºC
has a pressure of 802.8 torr. What will be the
new pressure in atm if the temperature is raised
to 102C and the volume expands to 7.00 L?
V1 5.00 L V2 7.00 L
T1 -50.0 ºC 223K T2 102 ºC 375 K
P1 802.8 torr 1.056 atm P2 ???????
1.26 atm
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Why do gases behave the way they do?
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Kinetic-Molecular Theory
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Kinetic Molecular Theory
This describes what actually happens to the
molecules as experimental conditions change!
pressure
temperature
volume
moles
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http//wps.prenhall.com/wps/media/objects/439/4499
69/Media_Portfolio/Chapter_12/Kinetic_Energy_in_a_
Gas.MOV
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--Gas molecules move in straight line paths in
all directions and at all speeds.
--the size of a gas molecule is negligible in
comparison to the distance between molecules.
(mostly empty space)
--intermolecular forces are weak or negligible.
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--energy can be transferred between molecules
during collisions, but the average kinetic energy
is constant at constant temperature.
--collisions between molecules are perfectly
elastic. (No kinetic energy is lost)
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--the average kinetic energy of gas molecules is
proportional to the absolute temperature (Kelvin).
--absolute temperature of a gas is a measure of
average kinetic energy
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--the pressure of a gas results from the
collisions with the wall of the container.
--the magnitude of the pressure is determined by
how often and how hard the molecules strike.
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It was previously stated that --absolute
temperature of a gas is a measure of the average
kinetic energy
To calculate average KE of a gas
(Given on AP Exam)
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As usual, we must always use the correct units so
canceling occurs!
1 Joule
If we refer to the kinetic energy per mole,
R 8.31 J mol -1 K -1 Same as previous R,
different units
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It was previously stated that absolute temp. of
a gas is a measure of the average kinetic energy
Notice Mass and velocity are not mentioned in
the statement above.
Reason All gas particles in a sample possess
the same KE regardless of size.
If this is the case, what must be true of m and v
in order for the equation above to be valid?
Larger molecules must move more slowly than
smaller molecules.
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Main idea of Kinetic Molecular Theory of
Gases --at the same temperature, molecules of all
gases have the same average translational kinetic
energy.
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We also stated that --gas molecules move in
straight line paths in all directions and at all
speeds.
In other words, Although we consider the
average kinetic energy and average speed when
dealing with a collection of gas molecules,
individual gas molecules move at different
speeds.
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The speed of an individual molecule, possessing
an average kinetic energy, is described as the
Root Mean Square Molecular Speed Urms
The speed of a molecule is directly proportional
to the absolute temperature, and indirectly
proportional to the molar mass.
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The speed of a molecule is indirectly
proportional to the molar mass.
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Calculate the rms speed of nitrogen gas particles
in a tank that has a temperature of 27 C.
517 m s-1
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Dealing with the units! (What a mess!)
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Finally
and
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Diffusion
VS.
Effusion
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Diffusion
Movement of particles from an area of high
concentration (high partial pressure) to an area
of low concentration (low partial pressure)
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Effusion
The escape of particles through a tiny hole into
an evacuated space.
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What will effect the likelihood of a molecule
hitting the hole? Speed and Mass Therefore, we
must consider urms.
We can use this equation to come up with a new
equation that compares the rates of effusion of
two gases in a porous container.
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We can use this equation to come up with a new
equation that compares the rates of effusion of
two gases in a porous container.
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Compares the rate of effusion of two different
gases under identical conditions.
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Graham's Law of Effusion
At constant temperature and pressure, the
effusion rate of a gas is inversely proportional
to the square root of its molar mass.
r1 rate of effusion of gas 1 M1 molar
mass of gas 1 r2 rate of effusion of gas 2
M2 molar mass of gas 2
All units cancel giving a ratio.
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Conceptually, the equation tells you that larger
molecules will effuse more slowly than smaller
particles.
Mathematically, the equation provides the ratio
of effusion rates between gas 1 and 2. If ratio gt
1, gas 1 effuses quicker than gas 2 If ratio lt 1,
gas 2 effuses quicker than gas 1
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Conceptual Question (Appeared on a previous AP
Exam) Equal numbers of moles of He, O2, and CO2
are placed in a glass vessel with a pinhole sized
leak in it at room temperature. The gases are
allowed to effuse for a brief period of time.
Rank order the gases remaining in the container,
from the gas with the highest partial pressure to
the gas with the lowest partial pressure.
Answer
CO2 gt O2 gt He Explanation to follow
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CO2 gt O2 gt He
Which of the 3 has the highest molar mass? CO2
gt O2 gt He Which will have the highest rate of
effusion? He gt O2 gt CO2 Which will be more
plentiful in the container after effusion? CO2 gt
O2 gt He Which will contribute the most to the
pressure after effusion?
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Conceptual Question 2 Which balloon will be
smaller after 1 hour Hydrogen filled
balloon? Helium filled balloon?
Hydrogen
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Mathematical Question Two gases, SO2 and NO2, are
placed in a container at a constant temperature
and pressure. Calculate the ratio of effusion
rates of the molecules. Hint Its always best to
label the lightest gas as M1 (this simplifies the
math)
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Let NO2 r1 since it has lower molar mass
1.18
NO2 effuses at a rate 1.18 times greater than SO2.
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Mathematical Question Calculate the ratio of
effusion rates of helium (He) and neon (Ne) gases
from the same container and at the same
temperature and pressure.
2.25
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Real Gases Deviations from Ideal Behavior
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When discussing the kinetic molecular theory, we
stated that
--the size of a gas molecule is negligible in
comparison to the distance between molecules.
True! In most cases, because the particles in a
gas are very far apart! Do the molecules
themselves take up volume?
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we also stated that
--because the molecules are very far apart,
intermolecular forces between gas molecules are
weak or negligible.
Again, True! In most cases!
What 2 conditions do you think might cause these
statements to be false?
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High Pressure
Low Temperature
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Small fraction of gas molecules in corner! (Far
apart, small attractive forces ? Ideal Gas)
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More particles concentrated in small
area! (Closer together ? attractive forces occur
? deviation from ideal Gas)
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Far apart!
Decrease Temperature
Closer together!
More attraction between molecules. Deviation from
ideal gas!
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Van der Waals equation --Modification of ideal
gas relationship
Correction for volume deviation.
Correction for molecular attraction deviation.
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Equation is given on AP Exam, but in a different
form.
Constant associated with molecular forces.
(units L2.atm/mol2)
Constant Measure of actual volume occupied by 1
mol of gas molecules (units L.mol-1).
Will be given in mini data table or within
question.
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Sample Problem on Board