gas pressure
DESCRIPTION
Gas Pressure. Air Pressure. Pressure Units. Units of pressure: atmosphere (atm) Pa (N/m 2 , 101,325 Pa = 1 atm)Torr (760 Torr = 1 atm) bar (1.01325 bar = 1 atm) mm Hg (760 mm Hg = 1 atm) lb/in 2 (14.696 lb/in 2 = 1 atm) in Hg (29.921 in Hg = 1 atm). - PowerPoint PPT PresentationTRANSCRIPT
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Gas Pressure
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Air Pressure
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Pressure Units
• Units of pressure: atmosphere (atm)
Pa (N/m2, 101,325 Pa = 1 atm)Torr (760 Torr = 1 atm)
bar (1.01325 bar = 1 atm)
mm Hg (760 mm Hg = 1 atm)
lb/in2 (14.696 lb/in2 = 1 atm)
in Hg (29.921 in Hg = 1 atm)
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Universal Gas Behavior
• Unlike solids and liquids, gas behavior is generally independent of chemical identity.
• Depends on four things only:– Absolute temperature– Pressure– Volume– Amount (moles)
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Kinetic Molecular Theory
• This theory presents physical properties of gases in terms of the motion of individual molecules.
• Kinetic Theory (in this class) will be based upon six assumptions:
• Average Kinetic Energy Kelvin Temperature
• Gas molecules are points separated by a great distance
• Particle volume is negligible compared to gas volume
• Gas molecules are in rapid random motion
• Gas collisions are perfectly elastic
• Gas molecules experience no attraction or repulsion
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Gas Behavior:Gases in a Box
• Insert 1 mole of gas into a fixed volume container. Then:
1. Gas expands to fill the container. Why?
2. The pressure becomes whatever value the gas laws dictate for that volume, mole, and temperature combination.
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Gas Behavior:Gases in a Piston
• Insert 1 mole of gas into a piston. Then:
1.Gas fills the piston. Why?
2.The piston changes volume until the pressure inside is equal to the pressure outside. Why?
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Understanding the Gas Laws
• Two keys to understanding the gas laws:– Understand which parameters are changing– Understand which are NOT changing
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Boyle’s Law• Pressure–Volume Law (Boyle’s Law):
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Boyle’s Law• Pressure–Volume Law (Boyle’s Law):
• The volume of a fixed amount of gas maintained at constant temperature is inversely proportional to the gas pressure.
Pressure1
Volume
XPV 11
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Charles’ Law
• Temperature–Volume Law (Charles’ Law):
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Charles’ Law• Temperature–Volume Law (Charles’ Law):
• The volume of a fixed amount of gas at constant pressure is directly proportional to the Kelvin temperature of the gas.
V T
XT
V
1
1
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Avogadro’s Law
• The Volume–Amount Law (Avogadro’s Law):
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Avogadro’s Law• The Volume–Amount Law (Avogadro’s Law):
• At constant pressure and temperature, the volume of a gas is directly
proportional to the number of moles of the gas present.
nV
Xn
V
1
1
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Collecting the Gas Laws
• Mathematically one can combine all of the statements we’ve made about gases.
• Two equivalent equations come from this:– Combined gas law– Ideal gas law
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Combined Gas Law• Combining the law gives:
• But if it equals a constant, then after any change it will still be equal to the constant:
• We write it this way:
• Nothing needs to be held constant now• Remember that anything that does stay constant can be
cancelled.
XTn
VP
1
1
11
2
22
1
11 Tn
VP
Tn
VP
21
4
44
3
33
2
22
1
11 X Tn
VP
Tn
VP
Tn
VP
Tn
VP
4321
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Ideal Gas Law
• This constant “X” is just a number.
• Units of (pressure * volume) / (moles * temp)
• That is, L·atm·K–1·mol–1
• Numerically, this constant has a value of R = 0.08206 L·atm·K–1·mol–1
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Ideal Gas Law
• The equation then becomes
We usually write it this way instead:
PV = nRT
RTn
VP
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STP
• Standard temperature: 273.15 K
• Standard pressure: 1 atm
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Ideal gas law vs. combined gas law
• Ideal gas law– Under unchanging conditions
• Combined gas law– Under changing conditions
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What is the volume of one mole of helium gas at STP?
22.4 L
What is the volume of one mole of argon gas at STP?
22.4 L
What is the volume of one mole of radon gas at STP?
22.4 L
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What is the density of one mole of helium gas at STP?
4.003 g / 22.4 L = 0.179 g/L
What is the volume of one mole of argon gas at STP?
39.948 g / 22.4 L = 1.78 g/L
What is the volume of one mole of radon gas at STP?
222 g / 22.4 L = 9.91 g/L
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What information would you need to calculate the molar mass of a gas?
• Mass / moles (m / n)• Enough information to get mass• P,V,T to use ideal gas law to get n
• What is the molar mass of a gas with a density of
1.342 g/L–1 at STP?
mole
g
mole
STPatL
L
g06.30
1
4.22
1
342.1
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Funky questions
• At what temperature do you have 0.1 moles/atm of helium in a 1 L pure helium sample?
• In one mole of chlorine gas at STP, how many Kelvins are there per liter?
K
KmolatmL
moles
Latm
nR
PVT 9.121
08206.01.0
11
L
K
KmolatmL
mol
atm
nR
P
V
T2.12
08206.01
1
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Gas-phase stoichiometry
• We have a new route to moles PV=nRT
• But we need to know first how two different gases behave when in the same space
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Gas Mixtures
• Two gases in the same container have the same volume—whatever the volume of the container is.
• Two gases in the same container have the same temperature—whatever the temperature is inside the container.
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Gas Mixtures
• Two gases in the same container do NOT have the same pressure.
• They have whatever pressure they would have if they were in the container alone.
• That is, solve PV=nRT for each gas in the mixture separately.
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Gas Mixtures
• The total pressure inside the container is the sum of the pressures of the individual gases.
• Dalton’s Law of Partial Pressures
i
itotal PP
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New Density Unit: Mole Fraction
• For a two-component system, the moles of components A and B can be represented by the mole fractions (XA and XB).
1 BABA
BB
BA
AA
XX
nn
nX
nn
nX
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Gas Stoichiometry
• In gas stoichiometry, for a constant temperature and pressure, volume is proportional to moles.
• Assuming no change in temperature and pressure, calculate the volume of O2 (in liters) required for the complete
combustion of 14.9 L of butane (C4H10):
2 C4H10(g) + 13 O2(g) 8 CO2(g) + 10 H2O(l)
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Molecular Speed
• It can be shown that:
• So then for neon:
M
RTvrms
3
Molar mass
hr
milesm
molg
KmolKJ
M
RTvrms 3000sec136000
00.4
298314.833
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Mean Molecular Speeds
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Collisions
• It can be shown that:
• A room temp gas collides billions of times per second
• The mean free path is less than 100 nm.
kT
Pvz mean
P
kT
2
Collision frequency Mean free path
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Maxwell speed distribution curves.
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Same Behavior vs. Different Behavior
• Most gas behaviors are based upon comparisons of their relative energies (temperatures)– Same temperature = same behavior
• Some gas behaviors are based upon comparisons of their relative speeds– Same speed = same behavior
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• Diffusion is the mixing of different gases by random molecular motion and collision.
Graham’s Law
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Graham’s Law
• Effusion is when gas molecules escape without collision, through a tiny hole into a vacuum.
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Graham’s Law
• Graham’s Law: Rate of effusion is proportional to its rms speed, vrms.
• For two gases at same temperature and pressure:
M
RTRate rms
3 v
Rate1
Rate2
M2
M1
M2
M1
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Behavior of Real Gases
• Test of ideal gasbehavior.
• Z = PV/RT
Compressibility factor
This plot assumes room temperature.
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Real Gases
• All the assumptions of kinetic molecular theory break down when explored in sufficient detail.
• Two assumptions break down first:– The volume of gas molecules is negligible– There are no attractive or repulsive forces
between molecules
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Non-negligible volumes
• The volume of molecules affects pressure-volume behavior more than temperature-pressure behavior.
• For a given small volume, the pressure will be higher than the ideal gas suggests..
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Behavior of Real Gases
• Test of ideal gasbehavior.
Volume non-idealities seen here!
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Non-negligible interactions
• The long-range interactions of particles are attractions, not repulsions.
• Thus a real gas sample takes up less space than the ideal gas law suggests, when the molecules are not crowded together.
• This effect fades as molecules move faster.
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Behavior of Real Gases
• Test of ideal gasbehavior.
Attractive force non-idealities seen here!
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Behavior of Real Gases• Corrections for non-ideality require a non-ideal gas
law. The van der Waals equation is one of them:
nRTbnVV
naP –
2
2
IntermolecularAttractions
ExcludedVolume
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Van der Waals Constants
Gas a
(L2 atm / mole2)
b
(L / mole)
Helium (He) 0.03412 0.02370
Ammonia (NH3)
4.170 0.03707
Hydrogen (H2) 0.2444 0.02661
n-octane 37.32 0.2368
Water 5.464 0.03049
Carbon dioxide 3.592 0.04267
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Other gas laws
• van der Waals:
• Peng-Robinson:
• Redlich-Kwong:
B
nV
nV
T
A
BnVRT
P
nV
nV
nV
nVRT
P
nV
RT
a
bnVRT
P
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Unifying the Gas Laws
• Under normal temperatures you can liquefy a gas simply by raising the pressure
• Above a certain critical temperature (Tc) you cannot liquefy a gas under any pressure. The pressure and volume of that “last” liquid are Pc and Vc
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Critical Constants
Species Tc (K) Pc (atm) Vc (L)
Helium 5.195 2.2452 0.0578
Ammonia 405.3 109.84 0.0725
Water 647.126 217.66 0.05595
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“Critical” adjustments
• Now we stop using temperature (and pressure and volume) in the gas laws.
• Instead we write the reduced temperature (TR) as a fraction of the critical temperature (Tc).
• That is TR = T / Tc
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Compressibility factor plots redone
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Atmosphere
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Smog (Inversions)
32
2
OOO
ONOhNO
Brownish haze
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Acid Rain
4223
322
22
22
SOHOHSO
SOOSO
SOOS
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Global Warming