1 Ch 10: Gases Brown, LeMay AP Chemistry. 2 10.1: Characteristics of Gases Particles in a gas are...
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Transcript of 1 Ch 10: Gases Brown, LeMay AP Chemistry. 2 10.1: Characteristics of Gases Particles in a gas are...
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Ch 10: Gases
Brown, LeMayAP Chemistry
2
10.1: Characteristics of Gases
Particles in a gas are very far apart, and have almost no interaction. Ex: In a sample of air, only 0.1% of the
total volume actually consists of matter.
Gases expand spontaneously to fill their container (have indefinite volume and shape.)
3
10.2: Pressure (P)
A force that acts on a given area A
FP
Atmospheric pressure: the result of the bombardment of air molecules upon all surfaces 1 atm = 760 mm Hg
= 760 torr= 101.3 kPa= 14.7 PSI
100 km
4
Barometer: measures atmospheric P compared to a vacuum
* Invented by Torricelli in 1643 Liquid Hg is pushed up the closed glass tube by air
pressure
Measuring pressure (using Hg)
Evangelista Torricelli(1608-1647)
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1. Closed-end: difference in Hg levels (h) shows P of gas in container compared to a vacuum
closed
Manometers: measure P of a gas
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Difference in Hg levels (h) shows P of gas in container compared to Patm
2. Open-end:
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10.3: The Gas Laws
Amadeo Avogadro(1776 - 1856)
Robert Boyle(1627-1691)
Jacques Charles(1746-1823)
John Dalton(1766-1844)
Joseph Louis Gay-Lussac(1778-1850)
Thomas Graham(1805-1869)
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10.3: The Gas Laws Boyle’s law: the volume (V) of a fixed quantity (n)
of a gas is inversely proportional to the pressure at constant temperature (T).
2211 VPVP P
1constantV
P
V
1/P
V
Animation: http://www.grc.nasa.gov/WWW/K-12/airplane/aboyle.html
Ex: A sample of gas is sealed in a chamber with a movable piston. If the piston applies twice the pressure on the sample, the volume of the gas will be
. If the volume of the sample is tripled, the pressure of the gas will behalved
reduced to 1/3
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V of a fixed quantity of a gas is directly proportional to its absolute T at constant P.
T
V
Animation: http://www.grc.nasa.gov/WWW/K-12/airplane/aglussac.html
Charles’ law
2
2
1
1
T
V
T
V
TconstantV
Extrapolation to V = 0 is the basis for absolute zero.
V = 11.5 L2730.1002730.50
0.10 2
VL
Ex: A 10.0 L sample of gas is sealed in a chamber with a movable piston. If the temperature of the gas increases from 50.0 ºC to 100.0 ºC, what will be the new volume of the sample?
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* Questionably named, seen as derivative of C’s and B’s laws
P of a fixed quantity of a gas is directly proportional to its absolute T at constant V.
T
P
“Gay-Lussac’s law”
2
2
1
1
T
P
T
P
TconstantP
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Equal volumes of gases at the same T & P contain equal numbers of molecules
n
V
Avogadro’s hypothesis
nconstantV
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Ex: A 10.0 L sample of gas at 100.0ºC and 2.0 atm is sealed in a chamber. If the temperature of the gas increases to 300.0ºC and the pressure decreases to 0.25 atm, what will be the new volume of the sample?
Combined gas law
2
22
1
11
T
VP
T
VPconstant
PV
T
V2 =120 L)2730.300(
)25.0(
)2730.100(
)00.10)(0.2( 2
VatmLatm
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Used for calculations for an ideal (hypothetical) gas whose P, V and T behavior are completely predictable.
R = 0.0821 L•atm/mol•K= 8.31 J/mol•K
Ex: How many moles of an ideal gas have a volume of 200.0 mL at 200.0ºC and 450 mm Hg?
10.4: The ideal gas law
nRTPV
n = 3.0 x 10-3 mol
)2730.200)(0821.0(1000
0.200
760
450
n
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What is the V of 1.000 mol of an ideal gas at standard temperature and pressure (STP, 0.00°C and 1.000 atm)
nRTPV
V = 22.4 L (called the molar volume)
22.4 L of an ideal gas at STP contains 6.022 x 1023 particles (Avogadro’s number)
)273)(0821.0)(000.1()000.1( KmolVatm
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10.5: More of the ideal gas law
Gas density (d):
Molar mass (M):
RT
PM
V
md
RTPV
mM
nRTPV M
massn
V
md RT
M
mPV
RTM
mPV
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10.6: Gas Mixtures & Partial Pressures
Partial pressure: P exerted by a particular component in a mixture of gases
Dalton’s law of partial pressures: the total P of a mixture of gases is the sum of the partial pressures of each gas
PTOTAL = PA + PB + PC + …
(also, nTOTAL = nA + nB + nC + …)
Ex: What are the partial pressures of a mixture of 0.60 mol H2 and 1.50 mol He in a 5.0 L container at 20ºC, and what is the total P?
=
nRTPV PH2 =(0.60)(0.0821)(293) / 5.0 = 2.9 atm
PHe =(1.50)(0.0821)(293) / 5.0 = 7.2 atm
PT = 2.9 + 7.2 = 10.1 atm
+
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Ratio of moles of one component to the total moles in the mixture (dimensionless, similar to a %)
RTVP
RTVP
T
A
Mole fraction (X):
Ex: What are the mole fractions of H2 and He in the previous example?
TOTAL
AA n
nX TA PP
T
A
n
n
T
A
P
P ∴
TAA PP X
29.02.10
0.60X
2H 714.02.10
1.50XHe
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Collecting Gases “over Water” When a gas is bubbled through water, the
vapor pressure of the water (partial pressure of the water) must be subtracted from the pressure of the collected gas:
PT = Pgas + PH2O
∴ Pgas = PT – PH2O
See Appendix B for vapor pressures of water at different temperatures.
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10.7: Kinetic-Molecular Theory* Formulated by Bernoulli in 1738
Assumptions:1. Gases consist of particles (atoms
or molecules) that are point masses. No volume - just a mass.
2. Gas particles travel linearly until colliding ‘elastically’ (do not stick together).
3. Gas particles do not experience intermolecular forces.
Daniel Bernoulli (1700-1782)
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10.7: Kinetic-Molecular Theory
4. Two gases at the same T have the same kinetic energy
KE is proportional to absolute T
2
2
1 rmsave muKE kTKEave 2
3
urms = root-mean-square speedm = mass of gas particle
(NOTE: in kg)k = Boltzmann’s constant,
1.38 x 10-23 J/KLudwig Boltzmann
(1844-1906)
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Maxwell-Boltzmann distribution graph
James Clerk Maxwell(1831-1879)
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kTKEave 2
3
O2 at 273K
O2 at 1000K
H2 at 273K2
2
1 rmsave muKE
Nu
mb
er
at
sp
eed
, u
Speed, u
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10.8: Molecular Effusion & Diffusion Since the average KE of a gas has a specific
value at a given absolute T, then a gas composed of lighter particles will have a higher urms.
m
kTurms
3
m = mass (kg)M = molar mass (kg/mol)R = ideal gas law constant, 8.31 J/mol·K
kTmuKE rmsave 2
3
2
1 2
kTmurms 32
M
RT3
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Effusion: escape of gas molecules through a tiny hole into an evacuated space
Diffusion: spread of one substance throughout a space or throughout a second substance
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Graham’s law
The effusion rate of a gas is inversely proportional to the square root of its molar mass
B
A
B
A
u
u
r
r
r = u = rate (speed) of effusiont = time of effusion
B
B
A
A
MRT
MRT
3
3
A
B
t
t
A
B
M
M
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10.9: Deviations from Ideal Behavior
a = correction for dec in P from intermolecular attractions (significant at high P, low T)
b = correction for available free space from V of atoms (significant at high concentrations)
nRTnbVV
anP
2
2
Particles of a real gas:1. Have measurable volumes2. Interact with each other
(experience intermolecular forces)
Van der Waal’s equation:
2
2
V
an
nbV
nRTP
or
Johannes van der Waals(1837-1923)
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10.9: Deviations from Ideal Behavior
A gas deviates from ideal: As the particles get larger (van der Waal’s “b”) As the e- become more widely spread out (van
der Waal’s “a”)
The most nearly ideal gas is He.