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Prentice-Hall © 2008 General Chemistry: Chapter 6 Slide 1 of 41
Chapter 6: Gases
Philip DuttonUniversity of Windsor, Canada
Prentice-Hall © 2008
General ChemistryPrinciples and Modern Applications
Petrucci • Harwood • Herring
8th Edition
Prentice-Hall © 2008 General Chemistry: Chapter 6 Slide 2 of 41
Contents
6-1 Properties of Gases: Gas Pressure
6-2 The Simple Gas Laws
6-3 Combining the Gas Laws:
The Ideal Gas Equation and
The General Gas Equation
6-4 Applications of the Ideal Gas Equation
6-5 Gases in Chemical Reactions
6-6 Mixtures of Gases
Prentice-Hall © 2008 General Chemistry: Chapter 6 Slide 3 of 41
Contents
6-7 Kinetic—Molecular Theory of Gases
6-8 Gas Properties Relating to the Kinetic—Molecular Theory
6-9 Non-ideal (real) Gases
Focus on The Chemistry of Air-Bag Systems
Prentice-Hall © 2008 General Chemistry: Chapter 6 Slide 4 of 41
6-1 Properties of Gases: Gas Pressure
• Gas Pressure
• Liquid Pressure
P (Pa) =
Area (m2)
Force (N)
P (Pa) = g ·h ·d
d(Hg) = 13.5951 g/cm3 (0°C)
g = 9.807 m/s2 - acceleration due to gravity
h - height of the liquid column
d - density of the liquid
Prentice-Hall © 2008 General Chemistry: Chapter 6 Slide 5 of 41
Barometric Pressure
Standard Atmospheric Pressure
1.00 atm
760 mm Hg, 760 torr
101.325 kPa
1.01325 bar
1013.25 mbar
Atmospheric Pressure: isobars in hPa
General Chemistry: Chapter 6 Slide 6 of 41
Prentice-Hall © 2008 General Chemistry: Chapter 6 Slide 7 of 41
Manometers
Prentice-Hall © 2008 General Chemistry: Chapter 6 Slide 8 of 41
6-2 Simple Gas Laws, Isotherm: T=const
• Boyle 1662 P ~ 1V PV = constant
T=const
Prentice-Hall © 2008 General Chemistry: Chapter 6 Slide 9 of 41
Example 5-6
Relating Gas Volume and Pressure – Boyle’s Law.
P1V1 = P2V2 V2 = P1V1
P2
= 694 L Vtank = 644 L
Prentice-Hall © 2008 General Chemistry: Chapter 6 Slide 10 of 41
Charles’s Law, Isobar, P=const
Charles 1787
Gay-Lussac 1802
V ~ T V = b T
Prentice-Hall © 2002 General Chemistry: Chapter 6 Slide 11 of 41
STP
• Gas properties depend on conditions.• Define standard temperature and pressure
(STP).• International Union of Pure and Applied Chemistry
(IUPAC):
Temperature Absolute pressure Publishing or establishing entity
°C kPa 0 100 IUPAC (present definition)
0 101.325 IUPAC (former definition), NIST, ISO 10780
20 101.325 EPA, NIST25 101.325 EPA
Prentice-Hall © 2008 General Chemistry: Chapter 6 Slide 12 of 41
Avogadro’s Law
• Gay-Lussac 1808– Small volumes of gases react in the ratio of
small whole numbers.
• Avogadro 1811– Equal volumes of gases have equal numbers of
molecules and– Gas molecules may break up when they react.
Prentice-Hall © 2008 General Chemistry: Chapter 6 Slide 13 of 41
Formation of Water
Prentice-Hall © 2008 General Chemistry: Chapter 6 Slide 14 of 41
Avogadro’s Law
V ~ n or V = c n
At STP
1 mol gas = 22.41 L gas
At an a fixed temperature and pressure:
Prentice-Hall © 2008 General Chemistry: Chapter 6 Slide 15 of 41
6-3 Combining the Gas Laws: The Ideal Gas Equation and the General Gas
Equation
• Boyle’s law V ~ 1/P
• Charles’s law V ~ T• Avogadro’s law V ~ n
PV = nRT
V ~ nTP
Prentice-Hall © 2008 General Chemistry: Chapter 6 Slide 16 of 41
The Gas Constant
R = PVnT
= 0.082057 L atm mol-1 K-1
= 8.3145 m3 Pa mol-1 K-1
PV = nRT
= 8.3145 J mol-1 K-1
= 8.3145 m3 Pa mol-1 K-1
P-V-T Surface
General Chemistry: Chapter 6 Slide 17 of 41
Prentice-Hall © 2008 General Chemistry: Chapter 6 Slide 18 of 41
The General Gas Equation
R = = P2V1
n1T2
P1V1
n1T1
= P2
T2
P1
T1
If we hold the amount and volume constant:
Prentice-Hall © 2008 General Chemistry: Chapter 6 Slide 19 of 41
6-4 Applications of the Ideal Gas Equation
Prentice-Hall © 2008 General Chemistry: Chapter 6 Slide 20 of 41
Molar Mass Determination
PV = nRT and n = mM
PV = mM
RT
M = m
PVRT
Prentice-Hall © 2008 General Chemistry: Chapter 6 Slide 21 of 41
Example 6-4
Determining a Molar Mass with the Ideal Gas Equation.
Polypropylene is an important commercial chemical. It is used in the synthesis of other organic chemicals and in plastics production. A glass vessel weighs 40.1305 g when clean, dry and evacuated; it weighs 138.2410 g when filled with water at 25°C (δ=0.9970 g cm-3) and 40.2959 g when filled with propylene gas at 740.3 mm Hg and 24.0°C. What is the molar mass of polypropylene?
Strategy:
Determine Vflask. Determine mgas. Use the Gas Equation.
Prentice-Hall © 2008 General Chemistry: Chapter 6 Slide 22 of 41
Example 6-4
Determine Vflask:
Vflask = mH2O / dH2O = (138.2410 g – 40.1305 g) / (0.9970 g cm-3)
Determine mgas:
= 0.1654 g
mgas = mfilled - mempty = (40.2959 g – 40.1305 g)
= 98.41 cm3 = 0.09841 dm3
General Chemistry: Chapter 6 Slide 23 of 41
Example 5-6Example 6-4, Molar Mass with the Ideal Gas Equation
Use the Ideal Gas Equation:
PV = nRT PV = mM
RT M = m
PVRT
M = (P kPa)(0.09841 dm3)
(0.1654 g)(8.3145 J mol-1 K-1)(297.2 K)
M = 42.08 g · mol-1
P = 740.3/760 * 101.325 kPa
[Pa · m3] = [kPa · dm3] = [J]
Prentice-Hall © 2008 General Chemistry: Chapter 6 Slide 24 of 41
Gas Densities
PV = nRT and d = mV
PV = mM
RT
MPRTV
m= d =
, n = mM
Prentice-Hall © 2008 General Chemistry: Chapter 6 Slide 25 of 41
6-5 Gases in Chemical Reactions
• Stoichiometric factors relate gas quantities to quantities of other reactants or products.
• Ideal gas equation used to relate the amount of a gas to volume, temperature and pressure.
• Law of combining volumes can be developed using the gas law.
Prentice-Hall © 2008 General Chemistry: Chapter 6 Slide 26 of 41
Example 6-5
Using the Ideal gas Equation in Reaction Stoichiometry Calculations.
The decomposition of sodium azide, NaN3, at high temperatures produces N2(g). Together with the necessary devices to initiate the reaction and trap the sodium metal formed, this reaction is used in air-bag safety systems. What volume of N2(g), measured at 735 mm Hg and 26°C, is produced when 70.0 g NaN3 is decomposed.
2 NaN3(s) → 2 Na(l) + 3 N2(g)
Prentice-Hall © 2008 General Chemistry: Chapter 6 Slide 27 of 41
Example 6-5
Determine moles of N2:
Determine volume of N2:
nN2 = 70 g ·
1 mol NaN3
65.01 g·
3 mol N2
2 mol NaN3
= 1.62 mol N2
= 41.1 l
P
nRTV = =
(735 mm Hg)
(1.62 mol)(8.3145 J mol-1 K-1)(299 K)
760 mm Hg101.325 kPa
Airbag design
Prentice-Hall © 2008 General Chemistry: Chapter 6 Slide 28 of 41
Prentice-Hall © 2008 General Chemistry: Chapter 6 Slide 29 of 41
6-6 Mixtures of Gases
• Partial pressure– Each component of a gas mixture exerts a
pressure that it would exert if it were in the container alone.
• Gas laws apply to mixtures of gases.• Simplest approach is to use ntotal, but....
Prentice-Hall © 2008 General Chemistry: Chapter 6 Slide 30 of 41
Dalton’s Law of Partial Pressure
General Chemistry: Chapter 6 Slide 31 of 41
Partial pressure and volume
Ptot = Pa + Pb +…
Va = naRT/Ptot and Vtot = Va + Vb+…
Va
Vtot
naRT/Ptot
ntotRT/Ptot= =
na
ntot
Pa
Ptot
naRT/Vtot
ntotRT/Vtot= =
na
ntot
na
ntot
= xaRecall
Average molar mass of ideal gas mixtures
The average molar mass is a sum of the products of the components molar fractions (xi) and masses (Mi).
n
iiinn MxMxMxMxM
12211 ...
The athmosphere
Average
molar mass?
Prentice-Hall © 2008 General Chemistry: Chapter 6 Slide 35 of 41
Pneumatic Trough
Ptot = Pbar = Pgas + PH2O
Equilibrium vapor pressure of H2O vs temperature
Csonka,G. I. © 2008 General Chemistry: Chapter 6 Slide 36 of 41
0 10 20 30 40 50 60 70 80 90 1000
20
40
60
80
100
t (C)
P*
(kP
a)
Prentice-Hall © 2008 General Chemistry: Chapter 8 Slide 37 of 32
Water Vapor
• nH2O PH2O in air.
Relative Humidity =PH2O (actual)
PH2O (max)· 100%
Relative humidity map
General Chemistry: Chapter 6 Slide 38 of 41 Csonka,G. I. © 2013
Prentice-Hall © 2008 General Chemistry: Chapter 8 Slide 39 of 32
Chemicals from the Atmosphere
Prentice-Hall © 2008 General Chemistry: Chapter 6 Slide 40 of 41
6-7 Kinetic Molecular Theory
• Particles are point masses in constant,
random, straight line motion.
• Particles are separated by great
distances.
• Collisions are rapid and elastic.
• No force between particles.
• Total energy remains constant.
Prentice-Hall © 2008 General Chemistry: Chapter 6 Slide 41 of 41
Pressure – Assessing Collision Forces
• Translational kinetic energy,
• Frequency of collisions,
• Impulse or momentum transfer,
• Pressure proportional to impulse times frequency
2
2
1muek
V
Nuv
muI
2muV
NP~
Prentice-Hall © 2008 General Chemistry: Chapter 6 Slide 42 of 41
Pressure and Molecular Speed
• Three dimensional systems lead to: 2
3
1um
V
NP
2u
um is the modal speed
uav is the simple average
urms
Prentice-Hall © 2008 General Chemistry: Chapter 6 Slide 43 of 41
Pressure
M
RTu
uMRT
umNRT
umNPV
rms
A
A
3
3
3
3
1
2
2
2
Assume one mole:
PV=RT so:
NAm = M:
Rearrange:
Prentice-Hall © 2008 General Chemistry: Chapter 6 Slide 44 of 41
Distribution of Molecular Speeds
M
RTurms
3
Prentice-Hall © 2008 General Chemistry: Chapter 6 Slide 45 of 41
Determining Molecular Speed
Prentice-Hall © 2008 General Chemistry: Chapter 6 Slide 46 of 41
Temperature
TN
Re
eNRT
)um(NumNPV
Ak
kA
AA
2
33
22
1
3
2
3
1 22
Modify:
PV=RT so:
Solve for ek:
Average kinetic energy is directly proportional to temperature!
Prentice-Hall © 2008 General Chemistry: Chapter 6 Slide 47 of 41
6-8 Gas Properties Relating to the Kinetic-Molecular Theory
• Diffusion– Net rate is proportional to
molecular speed.
• Effusion– A related phenomenon.
Prentice-Hall © 2008 General Chemistry: Chapter 6 Slide 48 of 41
Graham’s Law
• Only for gases at low pressure (natural escape, not a jet).• Tiny orifice (no collisions)• Does not apply to diffusion.
A
BA
Brms
Arms
M
M
RT/MB
RT/M
)(u
)(u
Bofeffusionofrate
Aofeffusionofrate
3
3
• Ratio used can be:– Rate of effusion (as above)– Molecular speeds– Effusion times
– Distances traveled by molecules– Amounts of gas effused.
Prentice-Hall © 2008 General Chemistry: Chapter 6 Slide 49 of 41
6-9 Real Gases
• Compressibility factor PV/nRT = 1 – Ideal gas• Deviations occur for real gases.
– PV/nRT > 1 - molecular volume is significant.– PV/nRT < 1 – intermolecular forces of attraction.
The green molecule is attracted by the red molecules.
Csonka, G. I. © 2008 General Chemistry: Chapter 6 Slide 50 of 41
Real Gases, Isotherms
Compression factor, Z
• Product of pressure (P) and molar volume (Vm) divided by the gas constant (R) and thermodynamic temperature (T).
• For an ideal gas it is equal to 1.
• As n = 1
Csonka, G. I. © 2008 General Chemistry: Chapter 6 Slide 51 of 41
TR
VPZ m
Gas Vm (dm3)
He 22.436
Ne 22.421
H2 22.429
CO2 22.295
H2O 22.199
Real gases at STP
P0 and T = 0 C°
Csonka, G. I. © 2008
Csonka, G. I. © 2008 General Chemistry: Chapter 6 Slide 53 of 41
van der Waals Equation
TRnbnVVn
aP
2
2
Vn
abnV
TRnP
van der Waals Coefficients
Gas a (Pa m6/mol2) b(m3/mol)
Helium 0.0036 24.1 · 10-6
Neon 0.0212 17.1 · 10-6
Hydrogen 0.0245 26.6 · 10-6
Carbon dioxide 0.366 42.8 · 10-6
Water vapor 0.552 30.4 · 10-6
CH4 0.228 42.8· 10-6
2mm V
a
bV
TRP
van der Waals vs ideal curves
Csonka, G. I. © 2008 General Chemistry: Chapter 6 Slide 54 of 41
Prentice-Hall © 2008 General Chemistry: Chapter 6 Slide 55 of 41
Chapter 6 Questions
9, 13, 18, 31, 45, 49, 61, 63, 71, 82, 85, 97, 104.