CHAPTER 10
Properties of Gases
Evaporating gaseous
globules emerging from
pillars of molecular
hydrogen gas in the Eagle
Nebula (Hubble Space
Telescope, 1995)
http://www.pangeaprogress.com/1/category/cosmos/1.html
1
States of matter

Solid
◦ Fixed shape
◦ Regardless of container shape

Liquid
◦ Fixed volume
◦ Conforms to container shape

Gas
◦ Molecules move freely
◦ Fills container
◦ What else do you know about gases?
2
Pressure

Pressure (P) = Force/Area
Pinternal & Pexternal are caused by
gas molecules pushing on the
walls of the container
 In general, what if . . .

◦ Pinternal = Pexternal
◦ Pinternal < Pexternal
◦ Pinternal > Pexternal
3
Units of pressure
Pa
 atm
 torr
 bar
 psi

SI unit?
= N/m2 = (kg•m/s2)/m2
= average atmospheric pressure at sea level
= 1mm Hg
= 105 Pa
= lb/in2
1 atm = 760 torr = 101325 Pa = 1.013 bar =14.7 psi

Practice: If PO2 = 26.7 kPa, calculate this
pressure in atm, torr, and psi
4
Barometer: measuring atmospheric
gas pressure
∆h
Patm
5
Manometer: measuring
experimental gas pressure
“Closed”
“Open”
6
Gas laws
Variables: P, T,V, n
 Any one can be determined by the other
three

◦ Hold two variables constant
◦ Change one variable
◦ Measure one variable

Three Laws
◦ Boyle’s (P & V)
◦ Charles’ (T & V)
◦ Avogadro’s (n & V)
Ideal gas law (P,T,V,n)
7
Boyle’s Law

Constant: T, n
Change: P
Measure:V
At constant temperature (T), the volume
(V) occupied by a fixed amount of gas (n)
is inversely proportional to the external
pressure (P)
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Boyle’s Law
V  1/P
 PV = constant
 P1V1 = P2V2

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Charles’ Law

At constant: P, n
Change: T
Measure:V
At constant pressure (P), the volume (V)
occupied by a fixed amount of gas (n) is
directly proportional to it absolute
temperature in Kelvin (T)
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Charles’ Law
V T
 V/T = constant
 V1/T1 = V2/T2

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http://www.grc.nasa.gov
Avogadro’s Principle
At constant: T, P
Change: n
Measure:V

At fixed temperature in Kelvin (T), and pressure
(P), equal volumes of any ideal gas contain equal
numbers of moles (n) . . . or the volume of a gas is
directly proportional to its number of moles.
•
•
•
Vn
V/n = constant
V1/n1 = V2/n2
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Ideal Gas Law

Combine
◦ Boyle’s:
◦ Charles’:
◦ Avogadro’s:

PV = nRT
PV = constant
V/T = constant
V/n = constant
Therefore . . . PV/nT = constant
◦ R is the universal gas constant
◦ Solve for R using STP conditions




1 atm
22.4 L
273 K
1 mole
 6.02  1023 gas particles
13
Using the Ideal Gas Law
A weather balloon was measured at a pressure of
0.950 atm at 293 K, and its volume was 35.0 L. How
many moles of an ideal gas are contained in the
balloon?
PV = nRT
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More Ideal Gas Law

If . . .

P1V1
= R
n1T1

Then . . .
P1V1
n1T1
=
P2V2
n2T2
And . . .
P2V2
n2T2
= R
PV = nRT
15
Tips for solving gas law problems
1.
2.
3.
4.
5.
Identify what variables are held constant
Identify what variables are changing
Ensure units are consistent (use Kelvin)
Rearrange ideal gas law to solve for
missing variable
Predict change (/) and solve
16
Solving gas law problems
Air trapped in a J-tube occupies 24.8 cm3 at 1.12 atm.
By adding mercury to the tube, the pressure is
increased to 2.64 atm. Assuming constant
temperature, what is the new volume of air (in L)?
PV = nRT
P1V1
n1T1
P2V2
=
n2T2
1atm = 1.01325x105 Pa
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Density



Mass / Volume
Gases are miscible, when thoroughly mixed
What does it look like if they are not mixed?
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More info on STP, density & molar
volume
n (mol)
1
1
1
P (atm)
1
1
1
T (K)
273
273
273
V (L)
22.4
22.4
22.4
6.02x1023
6.02x1023
6.02x1023
Mass (g)
4.003
28.03
32.00
Density (g/L)
0.179
1.25
1.43
Gas particles
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How are density, molarity, molar
mass & the ideal gas law related?

Density (m/V)
◦ Rearrange PV = nRT

Molarity (n/V)
◦ Rearrange PV = nRT

Molar mass (m/n)
◦ Rearrange PV = nRT
Lab 1:
Molar mass
of CO2
20
Determining molar mass of a gas

As part of a rock analysis, a student added
hydrochloric acid to a rock sample and
observed a fizzing action, indicating a gas
was being evolved. The student collected
the sample of the gas in a 0.220 L bulb
until its pressure reached 0.757 atm at a
temperature of 25.0˚C. The sample
weighed 0.299 g. What is the molar mass
(and the possible identity) of the gas?
21
Stoichiometry and gas law problems
Many chemical reactions consume or give
off gases
 The ideal gas law can be used to relate
the volumes and amounts of substances in
a given reaction
 The next two slides contain pretty tough
questions looking at this

◦ Limiting reactant
◦ Stoichiometry & fun dimensional analysis
practice
22
Reactions with gases
(limiting reactant)

Ammonia and hydrogen chloride gases
react to form solid ammonium chloride.
A 10.0 L reaction flask contains ammonia
at 0.452 atm and 22°C, and 155 mL of
hydrogen chloride gas at 7.50 atm and
271 K is introduced. After the reaction
occurs and the temperature returns to
22°C, what is the pressure inside the
flask?
◦ Note: neglect the volume of solid formed
23
Reactions with gases
(stoichiometry & dimensional analysis practice)
How many liters of molecular oxygen gas
(measured at 740 mm Hg and 24°C) are
consumed when burning 1.5 g of liquid
octane, C8H18 (114.26 g/mol), to form
carbon dioxide and water?
 How many grams of octane (d = 703 g/L)
does your car consume when you drive the
speed limit on the freeway (60 mph) in 1.0 s,
if you get 25 mpg and buy regular 87-grade
gasoline?

◦ Note: Assume 87-grade gasoline = 87 L octane
per 100 L gasoline, 1 gallon = 3.79 L
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Gas mixtures

So far we have only discussed pure gases,
now we are moving the discussion to gas
mixtures?
◦ All components occupy same volume
◦ All components occupy same temperature
◦ What about pressure?
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Dalton’s law of partial pressures

If we assume . . .
◦ Homogenous mixture
◦ Every gas behaves independently (i.e. no chemical
interactions)

. . . then the total pressure of a mixture of gases is
the sum of their individual partial pressures
◦ Ptotal = PA + PB + . . .
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Partial pressure calculation

What is the total pressure of a gas
mixture if PO2 = 159.12 torr, PN2 = 593.44
torr, and PAr = 7.10 torr
27
Mole fraction

“Orange fraction”
◦ The ratio of the number of a given component (oranges)
to the total number of all components (fruit basket)
Xorange 

The ratio of the number of moles of a given
component to the total number of moles of all
components
XA 

oranges 2
  0.3
fruit
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nA
nA

nA  nB  ... ntotal
At constant V & T:
XA 
nA
ntotal
PAV
PA
 RT 
Ptotal V
Ptotal
RT
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Gas movement



Diffusion: spontaneous movement of one gas through another
(mixing)
Effusion: gradual movement of gas escaping through a hole in a
vacuum
Rates are inversely proportional to the square roots of their molar
masses (or densities)

rate of diffusion

1
molar mass
rate of effusion 
molar mass
1
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Kinetic molecular theory

Three postulates (assumptions)
◦ Motion: particles travel in constant random
straight-line motion except for collisions (i.e.
no attraction/repulsion between particles)
◦ Volume: particle size is tiny compared to the
space between them, so their contribution to
volume can be ignored
◦ Collisions: particle collisions are elastic and
are the cause of exerted pressure (no energy
is lost by friction . . . Ek is constant and directly
proportional to T)
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Real gases don’t always behave
Kinetic molecular theory is tends to be useful under
“normal” conditions (i.e. room temperature and
atmospheric pressure)
 At extreme conditions, we may need to rethink our
assumptions (e.g. high external pressure)

◦ Motion: particles travel in constant random straight-line
motion except for collisions (i.e. no attraction/repulsion
between particles)
◦ Volume: particle size is tiny compared to the space
between them, so their contribution to volume can be
ignored
◦ Collisions: particle collisions are elastic and are the cause
of exerted pressure (no energy is lost by friction . . . Ek is
constant and directly proportional to T)
31
Kinetic molecular theory
(at extreme conditions, ↑Pext)

Rethink our assumptions
◦ Motion: particles travel in constant random straight-line motion
except for collisions (i.e. no attraction/repulsion between
particles)
◦ At high external pressure, account for intermolecular forces
 Pcontainer < Ptotal
 Add pressure related to intermolecular attractions
32
Kinetic molecular theory
(at extreme conditions, ↑Pext)

Rethink our assumptions
◦ Volume: particle size is tiny compared to the space
between them
◦ At high external pressure, account for volume of particles
 Vcontainer > Vfree space
 Subtract volume of particles
33
van der Waals equation

Accounts for volume of particles
◦ Vcontainer > Vfree space
◦ Subtract volume of particles
◦ “-nb”

Accounts for intermolecular
forces
◦ Pcontainer < Ptotal
◦ Add pressure related to
intermolecular attractions
◦ “+an2/v2”
Note: a & b are experimentally derived constants
34
The world from N2(g)’s perspective
(at 21˚C & 1 atm)

Average speed:
◦ 0.29mi/s

Mean free path
(distance traveled between collisions):
◦ 6.6x10-8m

Collision frequency
(divide most probable speed by mean free path):
◦ 7.1x109collisions/s
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ANY QUESTIONS?
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