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Gases 
Chemistry, The Central Science, 10th edition 
Theodore L. Brown; H. Eugene LeMay, Jr.; 
and Bruce E. Bursten 
Chapter 10 
Gases 
John Bookstaver 
St. Charles Community College 
St. Peters, MO 
 2006, Prentice Hall, Inc.
Gases 
Characteristics of Gases 
• Unlike liquids and solids, they 
 Expand to fill their containers. 
 Are highly compressible. 
 Have extremely low densities.
Gases 
Pressure 
• Pressure is the 
amount of force 
applied to an area. 
P = 
F 
A 
• Atmospheric 
pressure is the 
weight of air per 
unit of area.
Gases 
Units of Pressure 
• Pascals 
 1 Pa = 1 N/m2 
• Bar 
 1 bar = 105 Pa = 100 kPa
Gases 
Units of Pressure 
• mm Hg or torr 
These units are literally 
the difference in the 
heights measured in mm 
(h) of two connected 
columns of mercury. 
• Atmosphere 
1.00 atm = 760 torr
Gases 
Manometer 
Used to measure the 
difference in pressure 
between atmospheric 
pressure and that of a 
gas in a vessel.
Gases 
Standard Pressure 
• Normal atmospheric pressure at sea 
level. 
• It is equal to 
1.00 atm 
760 torr (760 mm Hg) 
101.325 kPa
Gases 
Boyle’s Law 
The volume of a fixed quantity of gas at 
constant temperature is inversely proportional 
to the pressure.
Gases 
Boyle’s Law
Gases 
As P and V are 
inversely proportional 
A plot of V versus P 
results in a curve. 
Since 
PV = k 
V = k (1/P) 
This means a plot of 
V versus 1/P will be 
a straight line.
Gases 
Charles’s Law 
• The volume of a fixed 
amount of gas at 
constant pressure is 
directly proportional to its 
absolute temperature. 
• i.e., 
V 
T 
= k 
A plot of V versus T will be a straight line.
Gases 
Avogadro’s Law 
• The volume of a gas at constant temperature 
and pressure is directly proportional to the 
number of moles of the gas. 
• Mathematically, this means V = kn
Gases 
Ideal-Gas Equation 
• So far we’ve seen that 
V  1/P (Boyle’s law) 
V  T (Charles’s law) 
V  n (Avogadro’s law) 
• Combining these, we get 
V  
nT 
P
Gases 
Ideal-Gas Equation 
The constant of 
proportionality is 
known as R, the 
gas constant.
Gases 
Ideal-Gas Equation 
The relationship 
then becomes 
nT 
P 
V  
nT 
P 
V = R 
or 
PV = nRT
Gases 
Ideal-Gas Equation
Gases 
Densities of Gases 
If we divide both sides of the ideal-gas 
equation by V and by RT, we get 
n 
V 
P 
RT 
=
Gases 
Densities of Gases 
• We know that 
moles  molecular mass = mass 
n   = m 
• So multiplying both sides by the 
molecular mass ( ) gives 
P 
RT 
m 
V 
=
Gases 
Densities of Gases 
• Mass  volume = density 
• So, 
P 
RT 
m 
V 
d = = 
• Note: One only needs to know the 
molecular mass, the pressure, and the 
temperature to calculate the density of 
a gas.
Gases 
Molecular Mass 
We can manipulate the density equation 
to enable us to find the molecular mass 
of a gas: 
P 
RT 
d = 
Becomes 
dRT 
P 
 =
Gases 
Dalton’s Law of 
Partial Pressures 
• The total pressure of a mixture of gases 
equals the sum of the pressures that 
each would exert if it were present 
alone. 
• In other words, 
Ptotal = P1 + P2 + P3 + …
Gases 
Partial Pressures of Gases
Gases 
Partial Pressures 
• When one collects a gas over water, there is 
water vapor mixed in with the gas. 
• To find only the pressure of the desired gas, 
one must subtract the vapor pressure of 
water from the total pressure.
Gases 
Kinetic-Molecular Theory 
This is a model that 
aids in our 
understanding of what 
happens to gas 
particles as 
environmental 
conditions change.
Gases 
Main Tenets of Kinetic- 
Molecular Theory 
Gases consist of large numbers of 
molecules that are in continuous, 
random motion.
Gases 
Main Tenets of Kinetic- 
Molecular Theory 
• The combined volume of all the 
molecules of the gas is negligible 
relative to the total volume in which the 
gas is contained. 
• Attractive and repulsive forces between 
gas molecules are negligible.
Gases 
Main Tenets of Kinetic- 
Molecular Theory 
Energy can be 
transferred between 
molecules during 
collisions, but the 
average kinetic energy 
of the molecules does 
not change with time, as 
long as the temperature 
of the gas remains 
constant.
Gases 
Main Tenets of Kinetic- 
Molecular Theory 
The average kinetic 
energy of the 
molecules is 
proportional to the 
absolute 
temperature.
Gases 
Effusion 
The escape of 
gas molecules 
through a tiny 
hole into an 
evacuated 
space.
Gases 
Diffusion 
The spread of one 
substance 
throughout a space 
or throughout a 
second substance.
Gases 
Boltzmann Distributions
Effect of Molecular Mass on 
Rate of Effusion and Diffusion 
Gases
Gases 
Real Gases 
In the real world, the 
behavior of gases 
only conforms to the 
ideal-gas equation 
at relatively high 
temperature and low 
pressure.
Deviations from Ideal Behavior 
The assumptions made in the kinetic-molecular 
model break down at high pressure and/or low 
temperature. 
Gases
Gases 
Real Gases
Gases 
Corrections for Nonideal 
Behavior 
• The ideal-gas equation can be adjusted 
to take these deviations from ideal 
behavior into account. 
• The corrected ideal-gas equation is 
known as the van der Waals equation.
Gases 
The van der Waals Equation 
) (V − nb) = nRT 
n2a 
V2 (P +

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Ch. 10 Gases

  • 1. Gases Chemistry, The Central Science, 10th edition Theodore L. Brown; H. Eugene LeMay, Jr.; and Bruce E. Bursten Chapter 10 Gases John Bookstaver St. Charles Community College St. Peters, MO  2006, Prentice Hall, Inc.
  • 2. Gases Characteristics of Gases • Unlike liquids and solids, they  Expand to fill their containers.  Are highly compressible.  Have extremely low densities.
  • 3. Gases Pressure • Pressure is the amount of force applied to an area. P = F A • Atmospheric pressure is the weight of air per unit of area.
  • 4. Gases Units of Pressure • Pascals  1 Pa = 1 N/m2 • Bar  1 bar = 105 Pa = 100 kPa
  • 5. Gases Units of Pressure • mm Hg or torr These units are literally the difference in the heights measured in mm (h) of two connected columns of mercury. • Atmosphere 1.00 atm = 760 torr
  • 6. Gases Manometer Used to measure the difference in pressure between atmospheric pressure and that of a gas in a vessel.
  • 7. Gases Standard Pressure • Normal atmospheric pressure at sea level. • It is equal to 1.00 atm 760 torr (760 mm Hg) 101.325 kPa
  • 8. Gases Boyle’s Law The volume of a fixed quantity of gas at constant temperature is inversely proportional to the pressure.
  • 10. Gases As P and V are inversely proportional A plot of V versus P results in a curve. Since PV = k V = k (1/P) This means a plot of V versus 1/P will be a straight line.
  • 11. Gases Charles’s Law • The volume of a fixed amount of gas at constant pressure is directly proportional to its absolute temperature. • i.e., V T = k A plot of V versus T will be a straight line.
  • 12. Gases Avogadro’s Law • The volume of a gas at constant temperature and pressure is directly proportional to the number of moles of the gas. • Mathematically, this means V = kn
  • 13. Gases Ideal-Gas Equation • So far we’ve seen that V  1/P (Boyle’s law) V  T (Charles’s law) V  n (Avogadro’s law) • Combining these, we get V  nT P
  • 14. Gases Ideal-Gas Equation The constant of proportionality is known as R, the gas constant.
  • 15. Gases Ideal-Gas Equation The relationship then becomes nT P V  nT P V = R or PV = nRT
  • 17. Gases Densities of Gases If we divide both sides of the ideal-gas equation by V and by RT, we get n V P RT =
  • 18. Gases Densities of Gases • We know that moles  molecular mass = mass n   = m • So multiplying both sides by the molecular mass ( ) gives P RT m V =
  • 19. Gases Densities of Gases • Mass  volume = density • So, P RT m V d = = • Note: One only needs to know the molecular mass, the pressure, and the temperature to calculate the density of a gas.
  • 20. Gases Molecular Mass We can manipulate the density equation to enable us to find the molecular mass of a gas: P RT d = Becomes dRT P  =
  • 21. Gases Dalton’s Law of Partial Pressures • The total pressure of a mixture of gases equals the sum of the pressures that each would exert if it were present alone. • In other words, Ptotal = P1 + P2 + P3 + …
  • 23. Gases Partial Pressures • When one collects a gas over water, there is water vapor mixed in with the gas. • To find only the pressure of the desired gas, one must subtract the vapor pressure of water from the total pressure.
  • 24. Gases Kinetic-Molecular Theory This is a model that aids in our understanding of what happens to gas particles as environmental conditions change.
  • 25. Gases Main Tenets of Kinetic- Molecular Theory Gases consist of large numbers of molecules that are in continuous, random motion.
  • 26. Gases Main Tenets of Kinetic- Molecular Theory • The combined volume of all the molecules of the gas is negligible relative to the total volume in which the gas is contained. • Attractive and repulsive forces between gas molecules are negligible.
  • 27. Gases Main Tenets of Kinetic- Molecular Theory Energy can be transferred between molecules during collisions, but the average kinetic energy of the molecules does not change with time, as long as the temperature of the gas remains constant.
  • 28. Gases Main Tenets of Kinetic- Molecular Theory The average kinetic energy of the molecules is proportional to the absolute temperature.
  • 29. Gases Effusion The escape of gas molecules through a tiny hole into an evacuated space.
  • 30. Gases Diffusion The spread of one substance throughout a space or throughout a second substance.
  • 32. Effect of Molecular Mass on Rate of Effusion and Diffusion Gases
  • 33. Gases Real Gases In the real world, the behavior of gases only conforms to the ideal-gas equation at relatively high temperature and low pressure.
  • 34. Deviations from Ideal Behavior The assumptions made in the kinetic-molecular model break down at high pressure and/or low temperature. Gases
  • 36. Gases Corrections for Nonideal Behavior • The ideal-gas equation can be adjusted to take these deviations from ideal behavior into account. • The corrected ideal-gas equation is known as the van der Waals equation.
  • 37. Gases The van der Waals Equation ) (V − nb) = nRT n2a V2 (P +