1. John Bookstaver St. Charles Community College Cottleville, MO
Chemistry, The Central Science, 11th edition
Theodore L. Brown; H. Eugene LeMay, Jr.; and Bruce E. Bursten
Chapter 10 Gases
John Bookstaver
St. Charles Community College
Cottleville, MO
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2. Characteristics of Gases
Unlike liquids and solids, gases
expand to fill their containers;
are highly compressible;
have extremely low densities;
Indefinite shape & volume
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3. Pressure F P = A Pressure is the amount of force applied to an area.
Atmospheric pressure is the weight of air per unit of area.
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4. Units of Pressure Pascal 1 Pa = 1 N/m2 kPa 1 kN/m2
(a realtively small unit ≈ 1.45 x 10-4 psi)
kPa 1 kN/m2
Bar 1 bar = 105 Pa = 100 kPa
Atmosphere
mmHg (torr)
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5. Pressure Equivalences
1 atm = x 105 Pa = kPa = 760 mm Hg = 760 torr = 14.7 psi
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6. Barometer
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
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7. Manometer
This device is used to measure the difference in pressure between atmospheric pressure and that of a gas in a vessel.
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8. Standard Pressure
Normal atmospheric pressure at sea level is referred to as standard pressure.
It is equal to
1.00 atm
760 torr (760 mm Hg)
kPa
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9. Boyle’s Law
The volume of a fixed quantity of gas at constant temperature is inversely proportional to the pressure.
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10. As P and V are inversely proportional
A plot of V versus P results in a curve.
Since
V = k (1/P)
This means a plot of V versus 1/P will be a straight line.
PV = k
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11. 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.
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12. Gay-Lussac’s Law of Combining Volumes
At a given temperature and pressure, the volume of gases that react with each other is in small whole numbers.
Example: two volumes of hydrogen gas and one volume of oxygen gas will make two volumes of water vapor.
Stoichiometry based!
Led to …

13. Avogadro’s Law
The volume of a gas at constant temperature and pressure is directly proportional to the number of moles of the gas.
So, at S T P, one mole of ANY gas occupies 22.4 L.
Mathematically:

14. 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
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15. Gay-Lussac Law
Pressure of a confined gas is directly proportional to the absolute temperature of the gas….
Given volume and moles are constant
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16. Ideal-Gas Equation V  nT P 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
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17. Ideal-Gas Equation PV = nRT nT P V  nT P V = R or The relationship
then becomes or
PV = nRT
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18. Ideal-Gas Equation
The constant of proportionality is known as R, the gas constant.
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19. Densities of Gases PV = nRT n P V = RT
If we divide both sides of the ideal-gas equation
by V and by RT, we get
PV = nRT n V P RT =
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20. Densities of Gases n   = m P RT m V = We know that
moles  molecular mass = mass
n   = m
So multiplying both sides by the molecular mass ( ) gives P RT m V =
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21. Densities of Gases P RT m V = d =
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.
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22. Molecular Mass P d = RT dRT P  =
We can manipulate the density equation to enable us to find the molecular mass of a gas: P RT
d =
Becomes
dRT P
 =
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23. 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 + …
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24. Mole Fraction & Dalton’s Law (DS)
PV = nRT
Pressure is directly proportional to moles,
Therefore partial pressure of a gas is the product of the total pressure times the mole fraction of the gas
Px = PTotal x MFx
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25. 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.
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26. Kinetic-Molecular Theory
This is a model that aids in our understanding of what happens to gas particles as environmental conditions change.
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27. Main Tenets of Kinetic-Molecular Theory
Gases consist of large numbers of molecules that are in continuous, random motion.
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28. 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.
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29. Main Tenets of Kinetic-Molecular Theory
Attractive and repulsive forces between gas molecules are negligible.
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30. 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.
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31. Main Tenets of Kinetic-Molecular Theory
The average kinetic energy of molecules is proportional to the absolute temperature.
urms is proportional to T
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32. Kinetic Energy of Molecules: Root Mean Square Speed
Compare mean and rms for velocities of 4.0, 6.0, 10.0, and 12.0 m/s (p. 415).
u ≈ vavg
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33. Calculating u, RMS Speed
R = J/mol K
M = mol mass in kg
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34. Effusion
Effusion is the escape of gas molecules through a tiny hole into an evacuated space.
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35. Effusion
The difference in the rates of effusion for helium and nitrogen, for example, explains a helium balloon would deflate faster.
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36. Diffusion
Diffusion is the spread of one substance throughout a space or throughout a second substance.
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37. Graham's Law
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38. Real Gases
In the real world, the behavior of gases only conforms to the ideal-gas equation at relatively high temperature and low pressure.
Scientists & Engineers often work with gases at P and T in which gases display non-ideal behavior
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39. Real Gases
Even the same gas will show wildly different behavior under high pressure at different temperatures.
This is an example of N2.
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40. Deviations from Ideal Behavior
The assumptions made in the kinetic-molecular model (negligible volume of gas molecules themselves, no attractive forces between gas molecules, etc.) are invalid at high pressure and/or low temperature.
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41. Real Gases Deviate from the Ideal Gas Law with…
High pressures
Low temperatures
Increasing molar mass
Increasing molecular complexity
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42. 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.
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43. The van der Waals Equation
) (V − nb) = nRT
n2a V2
(P +
a & b are constants accounting for:
a: intermolecular attraction
b: molecular volume
due to↓distance and ↓ urms (ds)
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