1 Gases What are the four variables needed to describe a gas?
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Gases
What are the four variables
needed to describe a gas?
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Gases
The simplest state of matter
•K.E. >> molecular attraction
•Random motion
•Predictable behavior
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Gases at STP
Few Elements:
H2 N2 O2
O3
F2 Cl2Noble Gases
Few Molecules:
HF HCl HBr
HI CO CO2
NH3 NO NO2
N2O SO2 H2S
No ionic compounds; WHY?
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KMT of Gases
Hard spheres
Insignificant volume
Far apart
1. Gas “particles”
(atoms or molecules):
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Straight paths until collision
Random motion
Fill container
KMT of Gases
2. Particles motion:
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KMT of Gases
3.Gas particles have no
attractions between them.
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4. Collisions are perfectly “elastic”.
no energy lost
during collision
KMT of Gases
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Pressure
What is pressure?
Collisions of gas particles
with the walls of the container
impart a force (f)
P =force
area
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Atmospheric Pressure
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Gas VariablesFour “macroscopic” variables
are needed to describe a gas.
P = pressure
V = volume
T = temperature
n = number of moles
Inter-
related
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You Predict
How to increase P ?
n
V
T
add gas
smaller V
higher T
(and Why?)
P =f
A
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Gas Laws
Charles’ Law V & T
Avogadro’s Law V & n
Boyle’s Law P & V
The other two variables are constant.
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Boyle’s Law (T,n constant)
Relationship of P & V
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Boyle’s Law (T,n constant)
P = k 1
Vor PV = k
P then V
P
1/V
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Boyle’s Law (T,n constant)
P1V1 = P2V2
before after
same
Condition #1: = kP1V1
Condition #2: = kP2V2
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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?
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P1V1 = P2V2
Boyle’s law is how
your lungs work !!
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Charles Law
What happens to the
volume of a balloon if
temperature is increased?
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Charles Law (P,n constant)
(T in Kelvin)
V = k’ T
V/T = k’
V1
T1
=V2
T2
before after
T then V
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V
T (oC)
-200 0 200 4000
Charles Law
-273.15oC
V/T = k’
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Charles Law
A sample of CO occupies
3.20 L at 125oC. Calculate
the temperature at which it
will occupy 1.54 L.
V1 /T1 = V2/T2
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Avogadro’s Law:
Thus any two gas samples with
the same P, V, & T will have the
same number of particles!
At constant P & T,
V a n
independent of gas type!
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Kinetic Molecular Theory
Explain:
Boyle’s Law
Charles’ Law
Avogadro’s Law
In terms of KMT
(what are the particles doing?)
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Help !!!
How are you suppose to
remember all these equations?
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Ideal Gas Law:
V a 1/P
V a T
V a n
V = RnTP
PV = nRT
R = universal gas constant
constant
Independent of type of gas !!
“pivnert”
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PV = nRT
Knowing 1 mole of “ideal” gas
occupies 22.4 L at STP, what is
the value of R? (units?)
R = 0.0821L atm
mol K
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PV = nRT
•How many moles of N2
are in a 2.00 L tank at
25oC and 20. atm?
•How many grams?
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PV = nRT
Units must be consistent with ‘R’
P in atm.
V in liters
n in moles
T in K
First convert from
kPa, mmHg
mL, cm3
g, kg, #particles
oC
R = 0.0821L atm
mol K
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PV = nRTWhat 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?
R =P1V1
n1T1
before change after change
R =P2V2
n2T2
=P2V2
n2T2
P1V1
n1T1
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=P2V2
n2T2
P1V1
n1T1
This can replace Boyle’s,
Charles, etc. laws.
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=P2V2
T2
P1V1
T1
Show that the combined gas
law reduces to Boyle’s law if
T and n are constant.
= P2V2P1V1
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=P2V2
T2
P1V1
T1
The volume of a balloon is 30. L
at 40 oC and 150 kPa.
What is its volume at STP ?
Let’s step through a problem.
P1 = 150 kPa
V1 = 30. L
T1 = 40oC = 313 K
P2 = 101.3 kPa
V2 = ?
T2 = 273 K
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=P2V2
T2
P1V1
T1
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
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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 ?
Try a Problem!!!
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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.
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Which Equation to Use ?Use: PV = nRT
If conditions don’t change.
Not on Regents Chart.
R = 0.0821 L atm/mol K
Units
=P2V2
T2
P1V1
T1
If conditions do change. Table ‘T’
Units: T
must be K
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What is an “Ideal” Gas ?
Ideal gases obey all the
assumptions of KMT.
Most gases under “normal” T & P
behave like ideal gases.
Ideal gases obey PV = nRT
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“Real” GasesParticles 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)
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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!
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Dalton’s Law
PA =nART
V
Mixture of gases A, B, C…
confined in a volume V.
and Ptotal = PA + PB + PC…
Partial pressure of gas ‘A’
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Air: a Mixture of GasesWhat 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
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Graham’s Law of Diffusion
Perfume spreads throughout a
room by diffusion, a mixing
process controlled molecular
collisions.
(start demo)
How fast a gas diffuses
is related to its velocity.
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Graham’s Law of Diffusion
Compare the kinetic energy (KE)
of 2 gases at the same T.
KEA = mAvA21
2KEB = mBvB
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2
Since T’s are the same:
mAvA21
2 mBvB21
2=
mass velocity
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Graham’s Law of Diffusion
mAvA21
2mBvB
21
2=
vA2
vB2
mB
mA=
vA
vB
mB
mA=
=molar massB
molar massA
Diff.RateA
Diff.RateB
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Graham’s Law of Diffusion
NH3
HCl
NH3(g) + HCl(g)
What is equation for this
combination reaction ?
Which gas diffuses faster ?
By how much?
Carry answer to 3 sig figs.
NH4Cl(s)
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Graham’s Law of Diffusion
Which gas “effuses” out of a balloon
faster, N2 or He? By how much?
(Hint: let gas ‘A’ have the
smaller molar mass.)
=molar massB
molar massA
Diff.RateA
Diff.RateB
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Warm-up
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What are the four
“macroscopic” variables
that describe a gas?
Warm-up
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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?
Warm-up
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•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?
Warm-up
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Explain using KMT why the gas
pressure in a container increases
if the temperature is raised.
Warm-up
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How many grams of O2 gas
are in a 42 L container at
370kPa at 58oC?
Warm-up
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Show that the combined gas law
on Table T reduces to Charles’ law.
=P2V2
T2
P1V1
T1
Warm-up
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How many grams of
dintrogen pentoxide are in
a 3.7 L balloon at STP?
Warm-up
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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?