CH4Notes - Chapter
Four
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Unformatted text preview: Chapter
Four
 The
Proper.es
of
Gases
 CHEM
1211K
 Fall
2010
 1
 Objec.ves 
 •  Become
familiar
with
the
concept
of
pressure
and
the
 units
used
to
measure
it.
 •  Use
gas
laws
to
examine
changes
in
pressure,
 temperature,
and
volume
of
gases.
 •  Use
gas
laws
to
determine
gas
density
and
in
 stoichiometric
calculaDons.
 •  Understand
the
principles
governing
effusion
and
 diffusion.
 •  Explain
the
behavior
of
gases
using
kineDc
molecular
 theory.
 •  Understand
how
and
when
gases
deviate
from
ideal
 behavior.
 2
 Key
Ideas 
 •  We
can
predict
the
physical
properDes
of
any
 gas
by
using
the
set
of
equaDons
known
as
the
 “gas
laws.”

 •  These
equaDons
can
be
explained
in
terms
of
 a
model
of
a
gas
in
which
the
molecules
are
in
 ceaseless
random
moDon
and
so
widely
 separated
that
they
do
not
interact
wit
one
 another
except
during
brief
collisions.
 3
 Why
is
it
important? 
 •  Gases
are
the
simplest
state
of
maOer,
and
so
 the
connecDons
between
the
properDes
of
 individual
molecules
and
those
of
the
bulk
 maOer
are
relaDvely
easy
to
idenDfy.
 •  In
later
chapters,
these
concepts
will
be
used
 to
study
thermodynamics,
equilibrium,
and
 the
rates
of
chemical
reacDons.
 4
 Observing
Gases
(3.1) 
 •  SecDon
summary:
 –  The fact that gases are readily compressible and immediately fill the space available to them suggest that molecules of gases are widely separated and in ceaseless chao9c mo9on 5
 Pressure
(4.2) 
 •  Pressure
is
the
force
exerted
per
unit
area
by
 gas
molecules
as
they
strike
the
surfaces
of
 their
containers. Figure 4.3 Figure 4.4 6
 Pressure
(4.2) 
 •  SecDon
summary:
 –  The pressure of a gas is the force that it exerts divided by the area subjected to the force. –  The pressure of a gas arises from the impacts of molecules. 7
 Alterna.ve
Units
of
Pressure
(4.3) 
 •  The
SI
unit
of
pressure
is
the
pascal (Pa).
 kg 1
Pa
=
1 m ⋅ s2 
 



1
bar
=
105
Pa 
 1
atm
=
1.01325
x
105
Pa 
 € 1
atm
=
760
mm
Hg 
 1
mm
Hg
=
1
torr 
 8
 Alterna.ve
Units
of
Pressure
(4.3) 
 •  SecDon
summary:
 –  The principal units for repor9ng pressure are torr, atmosphere, and pascal. –  Pressure units can be interconverted by using the conversion factors in Table 4.1 9
 •  Boyle
 The
Experimental
 
 Observa.ons
(4.4) 
 –  For
a
fixed
amount
of
gas
at
constant
 temperature,
volume
is
inversely
proporDonal
to
 pressure.
 constant V= P 1 Vα P PV = constant Figure 4.9 10
 The
Experimental
 
 Observa.ons
(4.4) 
 •  Charles
and
Guy‐Lussac
 –  For
a
fixed
amount
of
gas
under
constant
pressure,
the
 volume
varies
linearly
with
the
temperature.
 Figure 4.11 11
 The
Experimental
 
 Observa.ons
(4.4) 
 •  Avagadro’s
principle
 –  Under
the
same
condiDons
of
temperature
and
 pressure,
a
given
number
of
gas
molecules
occupy
 the
same
volume
regardless
of
their
chemical
 idenDty.
 volume V Molar volume = → Vm = amount n V = nVm 12
 The
Experimental
 
 Observa.ons
(4.4) 
 •  What
do
we
know
so
far?
 •  Combined,
we
end
up
with:
 PV
=
constant
x
nT
 PV
=
nRT
 13
 The
Experimental
 
 Observa.ons
(4.4) 
 •  SecDon
summary:
 –  The ideal gas law is PV = nRT. –  The ideal gas law summarizes the rela9ons describing the response of an ideal gas to changes in pressure, volume, temperature, and amount of molecules. –  The ideal gas law is a limi9ng law. 14
 Applica.ons
of
the
 
 Ideal
Gas
Law
(4.5) 
 •  Example:
A
sample
of
methane,
CH4,
occupies
 2.60
x
102
mL
at
32oC
under
a
pressure
of
 0.500
atm.

At
what
temperature
would
it
 occupy
5.00
x
102
mL
under
a
pressure
of
1.20
 x
103
torr?
 15
 Applica.ons
of
the
 
 Ideal
Gas
Law
(4.5) 
 •  The
ideal
gas
law
can
also
be
used
to
predict
 the
molar
volume
of
an
ideal
gas
under
any
 condiDons
of
T
and
P.
 16
 Applica.ons
of
the
 
 Ideal
Gas
Law
(4.5) 
 •  Standard
temperature
and
pressure
(STP):
 –  Exactly
1
atm
 –  Exactly
0oC
 •  Standard
ambient
temperature
and
pressure
 (SATP):
 –  Exactly
1
bar
 –  Exactly
25oC
 17
 Applica.ons
of
the
 
 Ideal
Gas
Law
(4.5) 
 •  Standard
Molar
Volume
 –  The
volume
occupied
by
one mole of any gas at STP is
22.4
L.
 •  This
is
another
way
to
measure
moles.
 •  For
gases,
the
volume
is
proporDonal
to
the
number
of
 moles.
 •  How
many
moles
of
gas
are
there
in
11.2
L
of
 gas
at
STP?

44.8
L?
 18
 Applica.ons
of
the
 
 Ideal
Gas
Law
(4.5) 
 •  SecDon
summary:
 –  The combined gas law describes how a gas responds to changes in condi9ons. –  STP = 0oC (273.15K) and 1 atm. 19
 Gas
Density
(4.6) 
 amount n Molar concentration = = volume V PV / RT P = = V RT 20
 Gas
Density
(4.6) 
 g mass molar mass (M) = = mol n mass = (M)n m = (M) n PV (M) mass (M)n RT Density = = = V V V MP Density = RT 21
 Gas
Density
(4.6) 
 •  From
the
previous
equaDon,
we
see
that:
 22
 Gas
Density
(4.6) 
 •  Example:

A
1.74
g
sample
of
a
compound
that
 contains
only
carbon
and
hydrogen
contains
1.44
 g
of
carbon
and
0.300
g
of
hydrogen.
At
STP
101
 mL
of
the
gas
has
a
mass
of
0.262
gram.

What
is
 its
molecular
formula?
 23
 Gas
Density
(4.6) 
 •  SecDon
summary:
 –  The molar concentra9ons and densi9es of gases increase as they are compressed but decrease as they are heated. –  The density of a gas depends on its molar mass. 24
 The
Stoichiometry
of
Reac.ng
 Gases
(4.7) 
 •  This
is
reacDon
stoichiometry,
just
as
we’ve
 done
before.
 –  We
know
that
one
mole
of
gas
at
STP
occupies
 22.4
L.
 –  We
can
use
the
ideal
gas
equaDon
to
calculate
the
 volume
occupied
by
a
mole
of
gas
under
any
other
 condiDons.
 –  We
us
the
above
informaDon
to
get
to
moles,
 then
we
proceed
as
normal.
 25
 The
Stoichiometry
of
Reac.ng
 Gases
(4.7) 
 •  Example:

What
volume
of
oxygen
measured
 at
STP,
can
be
produced
by
the
thermal
 decomposiDon
of
120.0
g
of
KClO3?
 2KClO3(s)

2
KCl(s)
+
3O2(g) 
 26
 The
Stoichiometry
of
Reac.ng
 Gases
(4.7) 
 •  There
may
be
more
than
a
1000x
increase
in
 volume
when
liquids
or
solids
react
to
form
a
 gas.
 –  The
explosive
release
of
N2(g)
and
the
resulDng
 increase
in
volume
is
the
basis
of
air
bags.
 
NaN3(s)




 Na(s)
+
N2(g)
 27
 The
Stoichiometry
of
Reac.ng
 Gases
(4.7) 
 •  SecDon
summary:
   The molar volume (at a specified T and P) is used to convert the amount of a reactant or product in a chemical reac9on into a volume of gas. 28
 Mixtures
of
Gases
(4.8) 
 •  At
low
pressure,
all
gases
respond
in
the
same
 way
to
changes
in
P,
T,
and
V.
 –  In
terms
of
calculaDons,
 it does not maOer whether all the molecules in a sample are the same. –  A mixture of gases that do not react with one another behave like a single pure gas.
 29
 Mixtures
of
Gases
(4.8) 
 •  Dalton’s Law of par9al pressures
 – The
total
pressure
of
a
mixture
of
gases
is
 the
sum
of
the
parDal
pressures
of
its
 components.
 Ptotal
=
PA
+
PB

+
PC

+
..... 
 Figure 4.19 30
 Mixtures
of
Gases
(4.8) 
 •  The
parDal
pressure
of
an
individual
gas
in
a
 mixture
can
also
be
calculated
as:
 PA
=
PtotalXA 
 Where
A
is
some
gas
and
XA
is
the
mole frac9on
 of
gas
A.
 moles of A XA = total moles of all gases present 31
 Mixtures
of
Gases
(4.8) 
 •  Example:

Determine
the
parDal
pressure
of
 each
gas
in
a
mixture
made
up
of
6.0
grams
of
 H2,
32
grams
O2,
and
56
grams
of
N2
if
the
 total
barometric
pressure
is
750
torr.
 32
 Mixtures
of
Gases
(4.8) 
 •  SecDon
summary:
 –  The par9al pressure of a gas is the pressure that it would exert if it were alone in the container. –  The total pressure of a mixture of gases is the sum of the par9al pressure of the components. –  The par9al pressure of a gas is related to the total pressure by the mole frac9on: PA = XAPtotal 33
 Diffusion
and
Effusion
(4.9) 
 •  Diffusion
is
the
mixing
of
gases.
 –  The
rate
of
diffusion
is
the
rate
of
the
mixing
of
 gases.
 •  Effusion
is
the
passage
of
a
gas
through
a
Dny
orifice
 into
an
evacuated
chamber. Figure 4.21 Figure 4.22 34
 Diffusion
and
Effusion
(4.9) 
 •  Graham’s
law
of
effusion
 –  At constant temperature, the rate of effusion of a gas is inversely propor8onal to the square root of its molar mass. Rate of effusion α € 1 molar mass rate of effusion of A molecules = rate of effusion of B molecules 1 MA MB = 1 MA MB 35
 Diffusion
and
Effusion
(4.9) 
 •  The
Dme
it
takes
for
the
same
amount
of
two
 substances
to
effuse
through
a
small
hole
are
 inversely
proporDonal
to
the
rates
at
which
 they
effuse:
 36
 Diffusion
and
Effusion
(4.9) 
 •  Example:
A
sample
of
hydrogen,
H2,
was
found
to
 effuse
through
a
pinhole
5.2
Dmes
as
rapidly
as
 the
same
volume
of
unknown
gas
(at
the
same
 temperature
and
pressure).

What
is
the
 molecular
weight
of
the
unknown
gas?
 37
 Diffusion
and
Effusion
(4.9) 
 •  The
rate
of
effusion
increases
as
the
 temperature
is
raised.
 rate of effusion at T2 = rate of effusion at T1 T2 T1 •  Because
the
rate
of
effusion
is
proporDonal
to
 the
average
speed
of
the
molecules,
we
can
 infer
that
the average speed of molecules in a € gas is propor9onal to the square root of the temperature.
 38
 Diffusion
and
Effusion
(4.9) 
 •  When referring to a gas, the temperature is an indica9on of the average speed of the molecules. 39
 Diffusion
and
Effusion
(4.9) 
 •  SecDon
summary:
 –  The average speed of molecules in a gas is directly propor9onal to thesquare root of the temperature and inversely propor9onal to the square root of the molar mass. 40
 The
Kine.c
Model
of
Gases
(4.10) 
 •  The
kine9c molecular theory
is
based
on
the
 informaDon
we’ve
just
reviewed:
 Figure 4.23 41
 The
Kine.c
Model
of
Gases
(4.10) 
 •  Root mean square speed (vrms)
is
the
square
 root
of
the
average
value
of
the
squares
of
the
 molecular
speeds.
 •  We
can
use
the
ideal
gas
law
to
calculate
the
 root
mean
square
speed
of
the
molecules
of
a
 gas.
 42
 The
Kine.c
Model
of
Gases
(4.10) 
 •  Example:
At
a
certain
speed,
the
root‐mean‐ square‐speed
of
the
molecules
of
hydrogen
in
a
 sample
of
gas
is
1055
ms‐1.
Compute
the
root‐ mean
square
speed
of
molecules
of
oxygen
at
the
 same
temperature.
 43
 The
Kine.c
Model
of
Gases
(4.10) 
 •  SecDon
summary:
 –  The kine9c model of gases is consistent with the ideal gas law and provides an expression for the root mean square speed of the molecules. –  Root mean square speeds of gas molecules are propor9onal to the square root of the temperature. 44
 The
Maxwell
Distribu.on
of
 Speeds
(4.11) 
 •  So
far
we
have
examined
only
the
average
 speed
of
all
molecules
of
gas
in
a
sample. 

 –  The
Maxwell distribu9on equa9on
allows
 calculaDon
of
the
fracDon
of
gas
molecules
having
 a
given
speed
at
any
instant.
 45
 The
Maxwell
Distribu.on
of
 Speeds
(4.11) 
 Figure 4.26 Range of molecular speeds for three gases at the same temperature. 46
 The
Maxwell
Distribu.on
of
 Speeds
(4.11) 
 Figure 4.27 The same gas at three different temperatures. 47
 The
Maxwell
Distribu.on
of
 Speeds
(4.11) 
 •  SecDon
summary:
 –  The molecules of all gases have a wide range of speeds. –  As the temperature increases, the root mean square speed and the range of speeds both increase. –  The range of speeds is described by the Maxwell distribu9on (equa9on 22). 48
 Devia.ons
from
Ideality
(4.12) 
 •  All
actual
gases
are
“real
gases.”

They
don’t
 follow
the
ideal
gas
law
exactly,
especially
as
 pressure
increases.
 –  Gases
can
be
compressed
to
liquids,
and
this
 suggest
that
gas
molecules
DO
aOract
one
 another.
 –  Liquids
are
very
difficult
to
compress,
and
this
 suggests
that
powerful
repulsive
forces
are
 present.
 49
 Devia.ons
from
Ideality
(4.12) 
 •  All
deviaDons
from
ideality
can
be
explained
 by
the
presence
of
intermolecular forces,
or
 aOracDons
and
repulsions
between
molecules.
 –  All
molecules
aOract
one
another
when
they
are
a
 few
molecular
diameters
apart
but
repel
one
 another
as
soon
as
their
electron
clouds
come
into
 contact
(assuming
they
do
not
react).
 50
 Devia.ons
from
Ideality
(4.12) 
 Figure 4.29 51
 Devia.ons
from
Ideality
(4.12) 
 •  SecDon
summary:
 –  Real gases consist of atoms or molecules with intermolecular aOrac9ons and repulsions. –  AOrac9ons have a longer range than repulsions. 52
 Equa.ons
of
State
of
 
 Real
Gases
(4.14) 
 •  The
van der Waals Equa9on accounts
for
the
 behavior
of
real
gases
(i.e.,
gases
at
high
 pressure
and
low
temperature).
 53 53
 Equa.ons
of
State
of
 
 Real
Gases
(4.14) 
 •  The
temperature‐independent
van de Waals parameters,
a
and
b,
are
unique
for
each
gas
 and
determined
experimentally.
 –  Parameter
a
 –  Parameter
b
 54
 Equa.ons
of
State
of
 
 Real
Gases
(4.14) 
 •  SecDon
summary:
 –  The van der Waals equa9on is an approximate equa9on of state for real gases. –  The parameter a represents the role of aOrac9ve forces. –  The parameter b represents the role of repulsive forces. 55
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This note was uploaded on 01/16/2012 for the course CHEM 1211 taught by Professor Ford during the Fall '09 term at Georgia Institute of Technology.

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