Gases
What are the four variables
needed to describe a gas?
1
Gases
The simplest state of matter
•K.E. >> molecular attraction
•Random motion
•Predictable behavior
2
Gases at STP
Few Elements:
H2 N2 O2
O3
F2
Cl2
Noble Gases
Few Molecules:
HF
HCl HBr
HI
CO
CO2
NH3 NO NO2
N2O SO2 H2S
No ionic compounds; WHY?
3
KMT of Gases
1. Gas “particles”
(atoms or molecules):
 Hard spheres
 Insignificant volume
 Far apart
4
KMT of Gases
2. Particles motion:
 Straight paths until collision
 Random motion
 Fill container
5
KMT of Gases
3.Gas particles have no
attractions between them.
6
KMT of Gases
4. Collisions are perfectly “elastic”.
 no energy lost
during collision
7
Pressure
What is pressure?
 Collisions of gas particles
with the walls of the container
impart a force (f)
force
P = area
8
Atmospheric Pressure
9
10
Gas Variables
Four “macroscopic” variables
are needed to describe a gas.
P = pressure
V = volume
T = temperature
n = number of moles
Interrelated
11
You Predict
(and Why?)
How to increase P ?
n
add gas
V smaller V
T
f
P=
A
higher T
12
Gas Laws
Boyle’s Law
Charles’ Law
P&V
V&T
Avogadro’s Law
V&n
The other two variables are constant.
13
Boyle’s Law (T,n constant)
Relationship of P & V
14
Boyle’s Law (T,n constant)
P then V 

1
P=k
V
or PV = k
P
1/V
15
Boyle’s Law (T,n constant)
Condition #1:
P1 V1 = k
same
Condition #2:
P2 V2 = k
P1 V1 = P2 V2
before
after
16
P1V1 = P2V2
A balloon is filled with 30. L of He
at 1.0 atm. What is the new
volume of the balloon if it rises to
where P = 0.25 atm?
17
P1V1 = P2V2
Boyle’s law is how
your lungs work !!
18
Charles Law
What happens to the
volume of a balloon if
temperature is increased?
19
Charles Law (P,n constant)

then V
V = k’ T
V/T = k’

T
(T in Kelvin)
V1 = V2
before
after
T1
T2
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Charles Law
V/T = k’
-273.15oC
V
0
-200
0
200
T (oC)
400
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Charles Law
V1 /T1 = V2/T2
A sample of CO occupies
3.20 L at 125oC. Calculate
the temperature at which it
will occupy 1.54 L.
22
Avogadro’s Law:
At constant P & T,
Van
independent of gas type!
Thus any two gas samples with
the same P, V, & T will have the
same number of particles!
23
Kinetic Molecular Theory
Explain:
Boyle’s Law
Charles’ Law
Avogadro’s Law
In terms of KMT
(what are the particles doing?)
24
Help !!!
How are you suppose to
remember all these equations?
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Ideal Gas Law:
V a 1/P
Va T
Van
constant
nT
V=R
P
PV = nRT
“pivnert”
R = universal gas constant
Independent of type of gas !!
26
PV = nRT
Knowing 1 mole of “ideal” gas
occupies 22.4 L at STP, what is
the value of R? (units?)
L atm
R = 0.0821
mol K
27
PV = nRT
•How many moles of N2
are in a 2.00 L tank at
25oC and 20. atm?
•How many grams?
28
PV = nRT
L atm
R = 0.0821
mol K
Units must be consistent with ‘R’
First convert from
P in atm.  kPa, mmHg
3
V in liters  mL, cm
n in moles  g, kg, #particles
o
 C
T in K
29
PV = nRT
What is the P in a 4.0 L fire
extinguisher that contains
260 g CO2 at T = 30oC?
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What if conditions of a
gas change?
P1 V1
R=
n1T1
before change
P1 V 1
=
n1T1
P 2 V2
R= n T
2 2
after change
P 2 V2
n2T2
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P1V1
n1T1
=
P2V2
n2T2
This can replace Boyle’s,
Charles, etc. laws.
32
P1V1
T1
=
P2V2
T2
P1V1 = P2V2
Show that the combined gas
law reduces to Boyle’s law if
T and n are constant.
33
P1V1
T1
=
P2V2
T2
Let’s step through a problem.
The volume of a balloon is 30. L
at 40 oC and 150 kPa.
What is its volume at STP ?
P2 = 101.3 kPa
P1 = 150 kPa
V2 = ?
V1 = 30. L
T1 = 40oC = 313 K T2 = 273 K
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P1V1
T1
=
P2V2
T2
1. Cancel n1 & n2 because
n doesn’t change.
2. Substitute values. Use same
units for all pairs; T in K.
(150 kPa)(30.L)
(101.3 kPa)V2
=
313 K
273 K
V2 = 39 L
35
Try a Problem!!!
Before a long road trip, a car tire
has P = 3.1 atm at T = -12oC. After
driving the tire T rises to 45oC.
What is the new P in the tire ?
36
A 2.1 mL bubble rises from the
bottom of a lake where
T = 8oC and P = 6.4 atm to the
lake surface where
T = 25oC and P = 1.0 atm.
What is new V
of the bubble?
Try another.
37
Which Equation to Use ?
Use: PV = nRT
If conditions don’t change.
Not on Regents Chart.
R = 0.0821 L atm/mol K
P 1 V1 P2 V2
=
T1
T2
Units
Units: T
must be K
If conditions do change. Table ‘T’
38
What is an “Ideal” Gas ?
Ideal gases obey all the
assumptions of KMT.
Ideal gases obey
PV = nRT
Most gases under “normal” T & P
behave like ideal gases.
39
“Real” Gases
Particles have volume
Have molecular attractions
Under what conditions of
T & P is a real gas most like
an ideal gas? Why ??
(high T & low P)
40
Dalton’s Law
of Partial Pressures
Every gas in a mixture of
gases (for example, air)
contributes to the total
pressure as if it were the
only gas in the container!
41
Dalton’s Law
Mixture of gases A, B, C…
confined in a volume V.
nART
PA =
V
and Ptotal = PA + PB + PC…
Partial pressure of gas ‘A’
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Air: a Mixture of Gases
What is partial pressure of O2 if
PTotal = 101.3 kPa
PN2
= 79.1 kPa
Pothers = 0.9 kPa
PTotal = PO2 + PN2 + Pothers
101.3 = PO2 + 79.1 + 0.9
PO2 = 21.3 kPa
43
Graham’s Law of Diffusion
Perfume spreads throughout a
room by diffusion, a mixing
process controlled molecular
collisions.
How fast a gas diffuses
is related to its velocity.
(start demo)
44
Graham’s Law of Diffusion
Compare the kinetic energy (KE)
of 2 gases at the same T.
KEA =
1
2
m
v
A
A
2
mass
KEB =
1
2
m
v
B
B
2
velocity
Since T’s are the same:
1
2
m
v
A
A
2
=
1
2
m
v
B
B
2
45
Graham’s Law of Diffusion
1
2
m
v
A
A
2
=
2
vA
vA
mB
=
2
mA
vB
Diff.RateA
Diff.RateB
1
2
m
v
B
B
2
vB
=
mB
=
 mA
molar massB
 molar massA
46
Graham’s Law of Diffusion
NH3(g) + HCl(g)  NH4Cl(s)
What is equation for this
combination reaction ?
HCl Which gas diffuses faster ?
NH3
By how much?
Carry answer to 3 sig figs.
47
Graham’s Law of Diffusion
Diff.RateA
Diff.RateB
=
molar massB
 molar massA
Which gas “effuses” out of a balloon
faster, N2 or He? By how much?
(Hint: let gas ‘A’ have the
smaller molar mass.)
48
49
Warm-up
What are the four
“macroscopic” variables
that describe a gas?
50
Warm-up
A gas at 3.3 atm in a 2.7 L
container is transferred to an
empty 8.6 L container.
What is the new pressure?
51
Warm-up
•What is Charles’ law?
•What assumptions does Charles’
law make?
•Explain, on the molecular level.
•If a gas has a volume of 4.7 L at
120oC, what volume does it
have at 450oC?
52
Warm-up
Explain using KMT why the gas
pressure in a container increases
if the temperature is raised.
53
Warm-up
How many grams of O2 gas
are in a 42 L container at
370kPa at 58oC?
54
Warm-up
P1V1
T1
=
P2V2
T2
Show that the combined gas law
on Table T reduces to Charles’ law.
55
Warm-up
How many grams of
dintrogen pentoxide are in
a 3.7 L balloon at STP?
56
Warm-up
How many grams of CO2 are in a
3700 mL flask at 25oC and 670 kPa?
A 2.7 L balloon on the ground at STP
rises to the upper atmosphere where
T = -12oC and P = 18 kPa.
How big is the balloon?
57