chapter 10 gases. a gas -uniformly fills any container. -mixes completely with any other gas -exerts...
TRANSCRIPT
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Chapter 10
Gases
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A Gas
- Uniformly fills any container.
- Mixes completely with any other gas
- Exerts pressure on its surroundings.
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Pressure
- is equal to force/unit area
- SI units = Newton/meter2 = 1 Pascal (Pa)
- 1 standard atmosphere = 101,325 Pa
- 1 standard atmosphere = 1 atm =
760 mm Hg = 760 torr
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05_48
h h
Atmosphericpressure (Patm)
Atmosphericpressure (Patm)
Gaspressure (Pgas)less thanatmospheric pressure
Gaspressure (Pgas)greater thanatmospheric pressure
(Pgas) = (Patm) - h (Pgas) = (Patm) + h
(a) (b)
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Gas Laws
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Boyle’s Law*
Pressure Volume = Constant (T = constant)
P1V1 = P2V2 (T = constant)
V 1/P (T = constant)
(*Holds precisely only at very low pressures.)
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05_50P
(in
Hg)
0
V(in3)
20 40 60
50
100
PP2
V
2V
(a)
00
1/P (in Hg)
0.01 0.02 0.03
20
40slope = k
(b)
V(in
3 )
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A gas that strictly obeys Boyle’s Law is called an
ideal gas.
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05_51
PV
(L
• at
m)
022.25
P (atm)
1.000.750.500.25
22.30
22.35
22.40
22.45Ne
O2
CO2
Ideal
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Charles’s Law
The volume of a gas is directly proportional to temperature, and extrapolates to zero at zero Kelvin.
V = bT (P = constant)
b = a proportionality constant
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Charles’s Law
VT
VT
P1
1
2
2 ( constant)
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05_53
V(L
)
-300
T(ºC)
-200 -100 0 100 200
1
2
3
6
4
5
300
-273.2 ºC
N2O
H2
H2O
CH4
He
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Avogadro’s Law
For a gas at constant temperature and pressure, the volume is directly proportional to the number of moles of gas (at low pressures).
V = an
a = proportionality constant
V = volume of the gas
n = number of moles of gas
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Ideal Gas Law
- An equation of state for a gas.
- “state” is the condition of the gas at a given time.
PV = nRT
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Standard Temperature and Pressure
“STP”
P = 1 atmosphere
T = C
The molar volume of an ideal gas is 22.42 liters at STP
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Ideal Gas Law
PV = nRT
R = proportionality constant
= 0.08206 L atm mol
P = pressure in atm
V = volume in liters
n = moles
T = temperature in Kelvins
Holds closely at P < 1 atm
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Dalton’s Law of Partial Pressures
For a mixture of gases in a container,
PTotal = P1 + P2 + P3 + . . .
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Partial Pressure
The partial pressure of a gas equals the mole fraction of the gas time the total pressure.
PA = χAPTotal
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Kinetic Molecular Theory
1. Volume of individual particles is zero.
2. Collisions of particles with container walls cause pressure exerted by gas.
3. Particles exert no forces on each other.
4. Average kinetic energy Kelvin temperature of a gas.
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05_1541
Pext
Pext
Volume is decreased
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05_1542
Pext
Pext
Temperature is increased
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05_1543
Pext
Pext
Energy (heat) added
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05_1544
Increase volume to return to originalpressure
Gas cylinder
Moles of gasincreases
Pext Pext
Pext
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05_58
Rel
ativ
e nu
mbe
r of
O2
mol
ecul
esw
ith g
iven
vel
ocity
0
Molecular velocity (m/s)
4 x 102 8 x102
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05_59
Rel
ativ
e nu
mbe
r of
N2
mol
ecul
esw
ith g
iven
vel
ocity
0Velocity (m/s)1000 2000 3000
273 K
1273 K
2273 K
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The Meaning of Temperature
Kelvin temperature is an index of the random motions of gas particles (higher T means greater motion.)
(KE)32avg RT
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Effusion: describes the passage of gas into an evacuated chamber.
Diffusion: describes the mixing of gases. The rate of diffusion is the rate of gas mixing.
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05_60
Gas
Vacuum
Pinhole
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Rate of effusion for gas 1Rate of effusion for gas 2
2
1
MM
Distance traveled by gas 1Distance traveled by gas 2
2
1
MM
Effusion:
Diffusion:
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Real Gases
Must correct ideal gas behavior when at high pressure (smaller volume) and low temperature (attractive forces become important).
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Real Gases
[ ]P a V nb nRTobs2( / ) n V
corrected pressure corrected volume
Pideal Videal
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END