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1
A Gas
Uniformly fills any container.
Mixes completely with any other gas
Exerts pressure on its surroundings.
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2
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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3
Figure 5.2A Torricellian Barometer
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5
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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6
Figure 5.4A J-Tube Similar to the One Used by Boyle
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7
Figure 5.5Plotting Boyle’s Data from Table 5.1
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8
Figure 5.6 A Plot of PV versus P for Several Gases at Pressures Below 1 ATM
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9
A gas that strictly obeys Boyle’s Law is called an ideal gas.
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10
Figure 5.7 A Plot of PV Versus P for 1 mol of Ammonia
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11
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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12
Figure 5.8 Plots of V Versus T (ºC) for Several Gases
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14
Charles’s Law
VT
VT
P1
1
2
2 ( constant)
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15
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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16
Figure 5.10: Balloons Holding 1.0 L of Gas at 25º C and 1 atm
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17
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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18
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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19
S/E 5.6 – 5.14
• Get thee to the Journal Notes.1
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20
Standard Temperature and Pressure
“STP”P = 1 atmosphere
T = CThe molar volume of an ideal gas is 22.42 liters at STP
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21
Figure 5.11A Mole of Any Gas Occupies a
Volume of Approximately 22.4 L at STP
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22
Gas Stoichiometry (+ Gas Density)
• S/E 5.11 – 5.14: See Journal Notes.2
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23
Dalton’s Law of Partial Pressures
For a mixture of gases in a container,
PTotal = P1 + P2 + P3 + . . .
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Figure 5.12 Partial Pressure of Each Gas in a Mixture
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Dalton’s Law of Partial Pressures (& the Mole Fraction concept)
• See the Journal Notes.3 and S/E 5.15 – 5.17
• Get thee there.
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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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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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Heat and Temperature
• TEMPERATURE is a measure of the AVERAGE K.E. of all the particles present.
• HEAT is the SUM of all the K.E. of all the particles present.
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Root Mean Square Velocity
• (KE)avg = 3/2 RT (this shows the relation between temperature and average K.E.)
• See Journal Note 10/3/a3 /RT M
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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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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:Effusion:
Diffusion:Diffusion:
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32
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 pressurecorrected pressure corrected volumecorrected volume
PPidealideal VVidealideal