1. principles and modern applications
Chemistry 140 Fall 2002
ELEVENTH EDITION
GENERAL CHEMISTRY
principles and modern applications
PETRUCCI HERRING MADURA BISSONNETTE 6
Gases
PHILIP DUTTON
UNIVERSITY OF WINDSOR
DEPARTMENT OF CHEMISTRY AND BIOCHEMISTRY
General Chemistry: Chapter 6
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2. General Chemistry: Chapter 6
Chemistry 140 Fall 2002
Gases
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
6-7
Kinetic—Molecular Theory of Gases
6-8
Gas Properties Relating to the Kinetic—Molecular Theory
6-9
Nonideal (Real) Gases
General Chemistry: Chapter 6
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3. The gaseous state of three halogens (group 17)
Chemistry 140 Fall 2002
FIGURE 6-1
The gaseous state of three halogens (group 17)
General Chemistry: Chapter 6
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4. Illustrating the pressure exerted by a solid
Chemistry 140 Fall 2002
6-1 Properties of Gases: Gas Pressure
The Concept of Pressure
Force
Force (N) = g (m/s2) x m (kg)
Pressure
P (Pa) =
Area (m2)
Force (N)
FIGURE 6-2
Illustrating the pressure exerted by a solid
General Chemistry: Chapter 6
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5. The concept of liquid pressure
Chemistry 140 Fall 2002
FIGURE 6-3
The concept of liquid pressure
General Chemistry: Chapter 6
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6. General Chemistry: Chapter 6
Liquid Pressure F W
g x m
g x V x d
g x h x A x d
P (Pa) = = = = =
= g x h x d A A A A A
liquid pressure is directly proportional to the liquid density and the height of the liquid column
General Chemistry: Chapter 6
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7. Measurement of atmospheric pressure with a mercury barometer
Chemistry 140 Fall 2002
Barometric Pressure
FIGURE 6-4
Measurement of atmospheric pressure with a mercury barometer
General Chemistry: Chapter 6
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8. Measurement of gas pressure with an open-end manometer
Chemistry 140 Fall 2002
Manometers
FIGURE 6-5
Measurement of gas pressure with an open-end manometer
General Chemistry: Chapter 6
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9. Units of Pressure: A Summary
General Chemistry: Chapter 6
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10. Relationship between gas volume and pressure – Boyle’s Law
Chemistry 140 Fall 2002
6-2 Simple Gas Laws
FIGURE 6-6
Relationship between gas volume and pressure – Boyle’s Law
General Chemistry: Chapter 6
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11. General Chemistry: Chapter 6
Boyles Law
P a 1 V
PV = a (constant)
For a fixed amount of gas at a constant temperature, the gas volume is inversely proportional to the gas pressure.
General Chemistry: Chapter 6
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12. Gas volume as a function of temperature
Chemistry 140 Fall 2002
FIGURE 6-7
Gas volume as a function of temperature
General Chemistry: Chapter 6
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13. General Chemistry: Chapter 6
Charles’s Law
V a T
V = b T
The volume of a fixed amount of gas at constant pressure is directly proportional to the Kelvin (absolute) temperature.
General Chemistry: Chapter 6
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14. Standard Conditions of Temperature and Pressure
Chemistry 140 Fall 2002
Standard Conditions of Temperature and Pressure
Gas properties depend on conditions. We use the definition of STP recommended by the International Union of Pure and Applied Chemistry (IUPAC).
Standard Temperature and
Pressure (STP) 0ºC and 1 Bar = 105 Pa
General Chemistry: Chapter 6
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15. General Chemistry: Chapter 6
Avogadro’s Law
Gay-Lussac 1808
gases react by volumes in the ratio of small whole numbers.
Avogadro 1811
At fixed T and P
V ∝ n or V = c n
At a fixed temperature and pressure, the volume of a gas is directly proportional to the amount of gas.
General Chemistry: Chapter 6
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16. General Chemistry: Chapter 6
Chemistry 140 Fall 2002
General Chemistry: Chapter 6
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17. Formation of Water – actual observation and Avogadro’s hypothesis
Chemistry 140 Fall 2002
FIGURE 6-8
Formation of Water – actual observation and Avogadro’s hypothesis
General Chemistry: Chapter 6
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18. Molar volume of a gas visualized
Chemistry 140 Fall 2002
1 mol gas = L gas
(at 0ºC, 1 atm)
1 mol gas = L gas
(at STP)
FIGURE 6-9
Molar volume of a gas visualized
General Chemistry: Chapter 6
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19. General Chemistry: Chapter 6
Chemistry 140 Fall 2002
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 nT
V ∝ P
General Chemistry: Chapter 6
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20. General Chemistry: Chapter 6
The Ideal Gas Equation
PV = nRT
R = PV nT
General Chemistry: Chapter 6
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21. General Chemistry: Chapter 6
Applying the ideal gas equation
General Chemistry: Chapter 6
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22. The General Gas Equation
PiVi
niTi =
PfVf
nfTf =
PfVf Tf
PiVi Ti
If we hold the amount constant (n = constant):
General Chemistry: Chapter 6
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23. 6-4 Applications of the Ideal Gas Equation
Molar Mass Determination
and
n = m M
PV = nRT
PV = m M RT
M = m PV RT
General Chemistry: Chapter 6
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24. General Chemistry: Chapter 6
Gas Density m
d =
KEEP IN MIND
that gas densities are
typically much smaller than
those of liquids and solids.
Gas densities are usually
expressed in grams per liter
rather than grams per
milliliter. V
PV = m M RT MP RT V m
= d =
General Chemistry: Chapter 6
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25. 6-5 Gases in Chemical Reactions
Chemistry 140 Fall 2002
6-5 Gases in Chemical Reactions
Stoichiometric factors relate gas quantities to quantities of other reactants or products. Ideal gas equation relates the amount of a gas to volume, temperature and pressure. Law of Combining Volumes can be developed using the gas law.
General Chemistry: Chapter 6
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26. General Chemistry: Chapter 6
6-6 Mixtures of Gases
Dalton’s law of partial pressures Each component of a gas mixture exerts a pressure that it would exert if it were in the container alone. The total pressure of a mixture of gases is the sum of the partial pressures of the components of the mixture.
Ptot = Pa + Pb +…
General Chemistry: Chapter 6
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27. General Chemistry: Chapter 6
The volume that each gase would individually occupy at a pressure equal to Ptot is
naRT
Ptot
nbRT
Ptot Va =
….. , Vb = ,
and Vtot = Va + Vb +…
Percent by volume can be expressed as: Va
Vtot Vb
Vtot
volume % A =
volume % B =
✕100%
✕100%
General Chemistry: Chapter 6
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28. General Chemistry: Chapter 6Pa
naRT/Vtot na Va
naRT/Ptot na = =
= χa = =
= χa
ntotRT/Vtot
ntot
ntotRT/Ptot
ntot
Ptot
Vtot na Pa Va = = = χa
ntot
Ptot
Vtot
Pa = χaPtot
Va = χaVtot
General Chemistry: Chapter 6
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29. Dalton’s law of partial pressures illustrated
FIGURE 6-12
Dalton’s law of partial pressures illustrated
General Chemistry: Chapter 6
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30. Collecting a gas over water
Chemistry 140 Fall 2002
FIGURE 6-13
Collecting a gas over water
General Chemistry: Chapter 6
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31. General Chemistry: Chapter 6
Ptot = Pbar = Pgas + PH2O
Pgas = Pbar − PH2O
General Chemistry: Chapter 6
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32. Visualizing Molecular Motion
Chemistry 140 Fall 2002
6-7 Kinetic Molecular Theory of Gases
Particles are point masses in constant, random, straight line motion.
Molecules are separated by great distances.
Molecules collide only fleetingly, and most of the time are not colliding.
Assumed to be no forces between molecules.
Individual molecules may gain or lose energy but total energy remains constant.
FIGURE 6-14
Visualizing Molecular Motion
General Chemistry: Chapter 6
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33. Pressure and Molecular Speed
Chemistry 140 Fall 2002
Distribution of Molecular Speeds
FIGURE 6-15
Pressure and Molecular Speed
General Chemistry: Chapter 6
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34. General Chemistry: Chapter 6
Maxwell-Boltzmann distribution of speeds
General Chemistry: Chapter 6
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35. Distribution of molecular speeds – an experimental determination
Chemistry 140 Fall 2002
FIGURE 6-17
Distribution of molecular speeds – an experimental determination
General Chemistry: Chapter 6
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36. Distribution of molecular speeds – the effect of mass and temperature
Chemistry 140 Fall 2002
FIGURE 6-16
Distribution of molecular speeds – the effect of mass and temperature
General Chemistry: Chapter 6
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37. Meaning of Temperature
Chemistry 140 Fall 2002
Meaning of Temperature
The Kelvin temperature (T) of a gas is directly proportional to the average
translational kinetic energy (Ek) of its molecules: T ∝ Ek.
General Chemistry: Chapter 6
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38. A model for calculating the pressure exerted by a single molecule
Derivation of Boyles Law
FIGURE 6-18
A model for calculating the pressure exerted by a single molecule
General Chemistry: Chapter 6
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39. Derivation of Boyle’s Law
PV = a
Boyle’s Law stated mathematically
Pressure of a single molecule
Pressure of N molecules
Average speed in each direction
and overall average speed
General Chemistry: Chapter 6
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40. Derivation of Molecular Speeds
Basic equation of KMT
Boyle’s Law from KMT
Since PV=nRT
General Chemistry: Chapter 6
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41. Diffusion and effusion
Chemistry 140 Fall 2002
6-8 Gas Properties Relating to the Kinetic-Molecular Theory
FIGURE 6-20
Diffusion and effusion
General Chemistry: Chapter 6
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42. General Chemistry: Chapter 6
Graham’s Law
The rate of effusion of a gas is inversely proportional to the square root of its
molar mass. 1
Rateeffusion MW
Only for gases at low pressure (natural escape, not a jet). Tiny orifice (no collisions) Does not apply to diffusion.
General Chemistry: Chapter 6
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43. General Chemistry: Chapter 6
Rate of effusion
Molecular speeds
Effusion times
Distances traveled by molecules
Amounts of gas effused.
Ratio of =
ratio of two molar masses
(6.25)
General Chemistry: Chapter 6
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44. Derivation of Graham’s Law
General Chemistry: Chapter 6
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45. General Chemistry: Chapter 6
Chemistry 140 Fall 2002
6.9 Nonideal (Real) Gases ºC
FIGURE 6-21
The behavior of real gases – compressibility factor as a function of pressure at 0ºC
General Chemistry: Chapter 6
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46. The van der Waals Equation
Chemistry 140 Fall 2002
The van der Waals Equation
n2a
P +
V – nb = nRT V2
The van der Waals equation reproduces the observed behavior of gases with moderate accuracy. It is most
accurate for gases comprising approximately spherical molecules that have small dipole moments.
General Chemistry: Chapter 6
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47. General Chemistry: Chapter 6
Chemistry 140 Fall 2002
General Chemistry: Chapter 6
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48. Intermolecular forces of attraction
Chemistry 140 Fall 2002
FIGURE 6-23
Intermolecular forces of attraction
General Chemistry: Chapter 6
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49. The effect of finite molecular size
FIGURE 6-22
The effect of finite molecular size
General Chemistry: Chapter 6
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50. General Chemistry: Chapter 6
End of Chapter
General Chemistry: Chapter 6
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