Upload
hester-gaines
View
219
Download
0
Tags:
Embed Size (px)
Citation preview
1Problem Set #8, 13, 18, 19, 24, 36, 42, 45, 58, 71, 73;
Recommended #5, 16, 22, 60, 61, 83
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.)
http://chemconnections.org/Java/molecules/index.html
http://zonalandeducation.com/mstm/physics/mechanics/energy/heatAndTemperature/gasMoleculeMotion/gasMoleculeMotion.html
2
A force that acts on a given area
3
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
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
4
Evangelista Torricelli(1608-1647)
1. Closed-end: difference in Hg levels (h) shows P of gas in container compared to a vacuum
http://www.chm.davidson.edu/ChemistryApplets/GasLaws/Pressure.html
5
closed
Difference in Hg levels (h) shows P of gas in container compared to Patm
6
7
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)
Boyle’s law: the volume (V) of a fixed quantity (n) of a gas is inversely proportional to the pressure at constant temperature (T).
8
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 be
halved
reduced to 1/3
V of a fixed quantity of a gas is directly proportional to its absolute T at constant P.
9
T
V
Animation: http://www.grc.nasa.gov/WWW/K-12/airplane/aglussac.html
2
2
1
1
T
V
T
V
TconstantV
Extrapolation to V = 0 is the basis for absolute zero.
V = 11.5 L
2730.1002730.50
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?
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.
10
T
P
2
2
1
1
T
P
T
P
TconstantP
http://www.youtube.com/watch?v=Mytvt0wlZK8&feature=related
Equal volumes of gases at the same T & P contain equal numbers of molecules
11
n
V
nconstantV
› 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?
12
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
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?
13
nRTPV
n = 3.0 x 10-3 mol
)2730.200)(0821.0(1000
0.200
760
450
n
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)
14
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
http://www.chm.davidson.edu/vce/GasLaws/GasConstant.html
15
Gas density (d):
Molar mass (M):
16
RT
PM
V
md
RTPV
mM
nRTPV M
massn
V
md RT
M
mPV
RTM
mPV
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 + …)17
=
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
+
Ratio of moles of one component to the total moles in the mixture (dimensionless, similar to a %)
19
RTVP
RTVP
T
A
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
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
20
See Appendix B for vapor pressures of water at different temperatures.
* 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.
21
Daniel Bernoulli (1700-1782)
4. Two gases at the same T have the same kinetic energy
› KE is proportional to absolute T
22
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/K
http://www.epa.gov/apti/bces/module1/kinetics/kinetics.htm#animate1
Ludwig Boltzmann(1844-1906)
23
James Clerk Maxwell(1831-1879)
http://intro.chem.okstate.edu/1314f00/laboratory/glp.htm
24
kTKEave 2
3
O2 at 273K
O2 at 1000K
H2 at 273K2
2
1 rmsave muKE
Nu
mb
er
at
speed
, u
Speed, u
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.
25
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
Effusion: escape of gas molecules through a tiny hole into an evacuated space
http://www.rkm.com.au/animations/GAS-effusion.html
26
Diffusion: spread of one substance throughout a space or throughout a second substance
http://sci-culture.com/advancedpoll/GCSE/diffusion%20simulator.html
The effusion rate of a gas is inversely proportional to the square root of its molar mass
27
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
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)
28
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)
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.
29