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1 The Gaseous State of Matter Chapter 12 Hein and Arena Dr. Eugene Passer Chemistry Department Bronx Community College © John Wiley and Company Version 1.1
1
The Gaseous State of MatterChapter 12
Hein and Arena
Dr. Eugene Passer
Chemistry Department
Bronx Community College
© John Wiley and Company
Version 1.1
2
The Kinetic-
Molecular Theory
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The Kinetic-Molecular Theory
• KMT is based on the motions of gasparticles.
• A gas that behaves exactly as outlinedby KMT is known as an ideal gas.
• While no ideal gases are found innature, real gases can approximateideal gas behavior under certainconditions of temperature and pressure.
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Principle Assumptions of the KMT
1. Gases consist of tiny particles with
mass but negligible volume.
2. The distance between particles is
large compared with the size of the
particles themselves.
3. Gas particles have no attraction for
one another.
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4. Gas particles move in straight linesin all directions, colliding frequentlywith one another and with the wallsof the container.
5. No energy is lost by the collision of agas particle with another gas particleor with the walls of the container.All collisions are perfectly elastic.
Principle Assumptions of the KMT
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6. The average kinetic energy forparticles is the same for all gases atthe same temperature, and its value isdirectly proportional to the Kelvintemperature.
Principle Assumptions of the KMT
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Kinetic Energy
21KE =
2mv
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Standard Temperature
and Pressure
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Standard Temperature and
Pressure
Standard Conditions
Standard Temperature and PressureSTP
273.15 K or 0.00oC
1 atm or 760 torr or 760 mm Hg
Selected common reference points of temperature and
pressure.
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Mole-Mass-Volume
Relationships
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• Volume of one mole of any gas at STP
= 22.4 L.
• 22.4 L at STP is known as the molar
volume of any gas (i.e. 22.4 L/mol.).
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The density of neon at STP is 0.900 g/L. What is the
molar mass of neon?
g = 20.2
mol
0.900 g
1 L
22.4 L
1 mol
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Ideal Gas Equation
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V aP
nTnRTV =
PPV = nRT
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V aP
nTnRTV =
PPV = nRT
atmospheres
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V aP
nTnRTV =
PPV = nRT
liters
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V aP
nTnRTV =
PPV = nRT
moles
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V aP
nTnRTV =
PPV = nRT
Kelvin
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V aP
nTnRTV =
PPV = nRT
Ideal Gas
ConstantL-atm
0.0821mol-K
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A balloon filled with 5.00 moles of helium gas is at a
temperature of 25oC. The atmospheric pressure is 750.
torr. What is the balloon’s volume?
Step 1. Organize the given information.
Convert temperature to kelvins.
K = oC + 273
K = 25oC + 273 = 298K
Convert pressure to atmospheres.
P = 750. torr 1 atm
x 760 torr
= 0.987 atm
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Step 2. Write and solve the ideal gas
equation for the unknown.
Step 3. Substitute the given data into the
equation and calculate.
A balloon filled with 5.00 moles of helium gas is at a
temperature of 25oC. The atmospheric pressure is 750.
torr. What is the balloon’s volume?
nRTV =
PPV = nRT
(0.987 atm)
(5.00 mol)V =
(0.0821 L×atm/mol×K)
(298 K)
= 124 L
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Determination of Molecular Weights
Using the Ideal Gas Equation g
molar mass = mol
gRTM =
PV
gmol =
molar mass
M = molar massg
n = mol = M
PV = nRTg
PV = RTM
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Calculate the molar mass of an unknown gas, if 0.020
g occupies 250 mL at a temperature of 305 K and a
pressure of 0.045 atm.
gRTM =
PV
V = 250 mL = 0.250 L g = 0.020 g
T = 305 K P = 0.045 atm
(0.020 g)M =
(0.082 L × atm/mol × K)
(305 K)
(0.250 L)
(0.045 atm)
g = 44
mol
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Gas Stoichiometry
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Gas Stoichiometry
Primary conversions involved in stoichiometry.
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The problem can be solved in one
continuous calculation.
What volume of oxygen (at STP) can be formed
from 0.500 mol of potassium chlorate?
2 KClO3 2KCl + 3 O2
3(0.500 mol KClO ) 2
3
3 mol O
2 mol KClO
22.4 L
1 mol
2= 16.8 L O
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V aP
nTnRTV =
PPV = nRT
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2 Al(s) + 6 HCl(aq) 2AlCl3(aq) + 3 H2(g)
Step 1 Calculate moles of H2.
grams Al moles Al moles H2
What volume of hydrogen, collected at 30.0oC and
700. torr, will be formed by reacting 50.0 g of
aluminum with hydrochloric acid?
50.0 g Al1 mol Al
26.98 g Al
23 mol H
2 mol Al
2 = 2.78 mol H
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• Convert oC to K: 30.oC + 273 = 303 K
• Convert torr to atm:
2 Al(s) + 6 HCl(aq) 2AlCl3(aq) + 3 H2(g)
Step 2 Calculate liters of H2.
What volume of hydrogen, collected at 30.0oC and
700. torr, will be formed by reacting 50.0 g of
aluminum with hydrochloric acid?
700 torr1 atm
760 torr
= 0.921 atm
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What volume of hydrogen, collected at 30.0oC and
700. torr, will be formed by reacting 50.0 g of
aluminum with hydrochloric acid?
PV = nRT
nRTV =
P
• Solve the ideal gas equation for V
(0.921 atm)2(2.78 mol H )
V =
(0.0821 L-atm)
(303 K)
(mol-K)2 = 75.1 L H
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Real Gases
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Real Gases
• Deviations from the gas laws occur athigh pressures and low temperatures.
–At high pressures the volumes of the realgas molecules are not negligiblecompared to the volume of the gas
–At low temperatures the kinetic energy ofthe gas molecules cannot completelyovercome the intermolecular attractiveforces between the molecules.
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