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Gases: Their Properties and Behavior

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Title: Gases: Their Properties and Behavior


1
Chapter 9
  • Gases Their Properties and Behavior

2
Properties of Gases
  • There are 5 important properties of gases
  • Confined gases exerts pressure on the wall of a
    container uniformly
  • Gases have low densities
  • Gases can be compressed
  • Gases can expand to fill their contained
    uniformly
  • Gases mix completely with other gases in the same
    container

3
Kinetic Molecular Theory of Gases
  • The Kinetic Molecular Theory of Gases is the
    model used to explain the behavior of gases in
    nature.
  • This theory presents physical properties of gases
    in terms of the motion of individual molecules
  • Average Kinetic Energy ? Kelvin Temperature
  • Gas molecules are points separated by a great
    distance
  • Particle volume is negligible compared to gas
    volume
  • Gas molecules are in rapid random motion
  • Gas collisions are perfectly elastic
  • Gas molecules experience no attraction or
    repulsion

4
Properties that Describe a Gas
  • These properties are all related to one another.
  • When one variable changes, it causes the other
    three to react in a predictable manner.

5
Gas Pressure (P)
  • Gas pressure (P) is the result of constantly
    moving gas molecules striking the inside surface
    of their container.

6
Atmospheric Pressure
  • Atmospheric pressure is the pressure exerted by
    the air on the earth.
  • Evangelista Torricelli invented the barometer in
    1643 to measure atmospheric pressure.
  • Atmospheric pressure is 760 mm of mercury or 1
    atmosphere (atm) at sea level.

What happens to the atmospheric pressure as you
go up in elevation?
7
Measurement of Gas Pressure
  • Traditionally, the gas pressure inside of a
    container is measured with a manometer

8
Units of Pressure
  • Standard pressure is the atmospheric pressure at
    sea level, 760 mm of mercury.
  • Here is standard pressure expressed in other
    units

9
Gas Pressure Conversions
  • The barometric pressure is 697.2 torr. What is
    the barometric pressure in atmospheres? In mm Hg?
    In Pascals (Pa)?

10
Gas Law Problems
11
Boyles Law (V and P)
  • Boyles Law states that the volume of a gas is
    inversely proportional to the pressure at
    constant temperature.
  • Mathematically, we write
  • For a before and after situation

P1V1 P2V2
12
Boyles Law Problem
  • A 1.50 L sample of methane gas exerts a pressure
    of 1650 mm Hg. What is the final pressure if the
    volume changes to 7.00 L?

(1650 mm Hg )(1.50 L)
354 mm Hg
7.00 L
13
Charles Law (V and T)
  • In 1783, Jacques Charles discovered (while hot
    air ballooning) that the volume of a gas is
    directly proportional to the temperature in
    Kelvin.
  • Mathematically, we write
  • For a before and after situation

T ? V
14
Charles Law Problem
  • A 275 L helium balloon is heated from 20?C to
    40?C. What is the final volume at constant P?

V1 T2
V2
rearranges to

T1
15
Gay-Lussacs Law (P and T)
  • In 1802, Joseph Gay-Lussac discovered that the
    pressure of a gas is directly proportional to the
    temperature in Kelvin.
  • Mathematically, we write
  • For a before and after situation

T ? P
16
Gay-Lussacs Law Problem
  • A steel container of nitrous oxide at 15.0 atm is
    cooled from 25?C to 40?C. What is the final
    volume at constant V?

P1 T2
P2
rearranges to
T1
(15.0 atm)(298 K)
11.7 atm
233 K
17
Avogadros Law (n and V)
  • In the previous laws, the amount of gas was
    always constant.
  • However, the amount of a gas (n) is directly
    proportional to the volume of the gas, meaning
    that as the amount of gas increases, so does the
    volume.
  • Mathematically, we write
  • For a before and after situation

n ? V
18
Avogadros Law Problem
  • A steel container contains 2.6 mol of nitrous
    oxide with a volume 15.0 L. If the amount of
    nitrous oxide is increased to 8.4 mol, what is
    the final volume at constant T and P?

V1 n2
rearranges to
V2
n1
(15.0 L)(8.4 mol)
48.5 L
2.6 mol
19
Combined Gas Law
  • When we introduced Boyles, Charles, and
    Gay-Lussacs Laws, we assumed that one of the
    variables remained constant.
  • Experimentally, all three (temperature, pressure,
    and volume) usually change.
  • By combining all three laws, we obtain the
    combined gas law

20
Combined Gas Law Problem
  • Oxygen gas is normally sold in 49.0 L steel
    containers at a pressure of 150.0 atm. What
    volume would the gas occupy if the pressure was
    reduced to 1.02 atm and the temperature raised
    from 20oC to 35oC?

21
Molar Volume and STP
  • Standard temperature and pressure (STP) are
    defined as 0?C and 1 atm.
  • At standard temperature and pressure, one mole of
    any gas occupies 22.4 L.
  • The volume occupied by one mole of gas (22.4 L)
    is called the molar volume.

1 mole Gas 22.4 L
22
Molar Volume Calculation Volume to Moles
  • A sample of methane, CH4, occupies 4.50 L at STP.
    How many moles of methane are present?

23
Mole Unit Factors
  • We now have three interpretations for the mole
  • 1 mol 6.02 1023 particles
  • 1 mol molar mass
  • 1 mol 22.4 L (at STP for a gas)
  • This gives us 3 unit factors to use to convert
    between moles, particles, mass, and volume.

24
Mole Calculation - Grams to Volume
  • What is the mass of 3.36 L of ozone gas, O3, at
    STP?

25
Mole Calculation Molecules to Volume
  • How many molecules of hydrogen gas, H2, occupy
    0.500 L at STP?

1.34 1022 molecules H2
26
Gas Density and Molar Mass
  • The density of a gas is much less than that of a
    liquid.
  • We can calculate the density of any gas at STP
    easily.
  • You can rearrange this equation to find the Molar
    mass of an unknown gas too!

molar mass in grams (MM)
density, g/L
molar volume in liters (MV)
27
Calculating Gas Density
  • What is the density of ammonia gas, NH3, at STP?
  • 1.96 g of an unknown gas occupies 1.00 L at STP.
    What is the molar mass?

28
The Ideal Gas Law
  • When working in the lab, you will not always be
    at STP.
  • The four properties used in the measurement of a
    gas (Pressure, Volume, Temperature and moles) can
    be combined into a single gas law
  • Here, R is the ideal gas constant and has a value
    of
  • Note the units of R. When working problems with
    the Ideal Gas Law, your units of P, V, T and n
    must match those in the constant!

PV nRT
0.0821 atm?L/mol?K
29
Ideal Gas Law Problem
  • Sulfur hexafluoride (SF6) is a colorless,
    odorless, very unreactive gas. Calculate the
    pressure (in atm) exerted by 1.82 moles of the
    gas in a steel vessel of volume 5.43 L at 69.5C.

30
Ideal Gas Law and Molar Mass
  • Density and Molar Mass Calculations
  • You can calculate the density or molar mass (M)
    of a gas.
  • The density of a gas is usually very low under
    atmospheric conditions.

31
Ideal Gas Law and Molar Mass
  • What is the molar mass of a gas with a density of
    1.342 g/L1 at STP?
  • What is the density of uranium hexafluoride, UF6,
    (MM 352 g/mol) under conditions of STP?
  • The density of a gaseous compound is 3.38 g/L1
    at 40C and 1.97 atm. What is its molar mass?

32
Gases in Chemical Reactions
  • Gases are involved as reactants and/or products
    in numerous chemical reactions.
  • Typically, the information given for a gas in a
    reaction is its Pressure (P), volume (V) (or
    amount of the gas (n)) and temperature (T).
  • We use this information and the Ideal Gas Law to
    determine the moles of the gas (n) or the volume
    of the gas (V).
  • Once we have this information, we can proceed
    with the problem as we would any other
    stoichiometry problem.

A (g) X (s) ? B (s) Y (l)
33
Reaction with a Gas
  • Hydrogen gas is formed when zinc metal reacts
    with hydrochloric acid. How many liters of
    hydrogen gas at STP are produced when 15.8 g of
    zinc reacts?
  • Zn (s) 2HCl (aq) ? H2 (g) ZnCl2 (aq)

Can use because at STP!
34
Reaction with a Gas
  • Hydrogen gas is formed when zinc metal reacts
    with hydrochloric acid. How many liters of
    hydrogen gas at a pressure of 755 atm and 35C
    are produced when 15.8 g of zinc reacts?
  • Zn (s) 2HCl (aq) ? H2 (g) ZnCl2 (aq)

Use because not at STP!
35
Daltons Law of Partial Pressures
  • In a mixture of gases the total pressure, Ptot,
    is the sum of the partial pressures of the gases
  • Daltons law allows us to work with mixtures of
    gases.

Ptot P1 P2 P3 etc.
36
Daltons Law of Partial Pressures
  • For a two-component system, the moles of
    components A and B can be represented by the mole
    fractions (XA and XB).
  • What is the mole fraction of each component in a
    mixture of 12.45 g of H2, 60.67 g of N2, and 2.38
    g of NH3?

n
n




1









B
A
X
X
X
X
B
A
B
A


n
n
n
n
B
A
B
A
37
Daltons Law of Partial Pressures
  • Mole fraction is related to the total pressure
    by
  • On a humid day in summer, the mole fraction of
    gaseous H2O (water vapor) in the air at 25C can
    be as high as 0.0287. Assuming a total pressure
    of 0.977 atm, what is the partial pressure (in
    atm) of H2O in the air?

38
Daltons Law of Partial Pressures
  • Exactly 2.0 moles of Ne and 3.0 moles of Ar were
    placed in a 40.0 L container at 25C. What are
    the partial pressures of each gas and the total
    pressure?
  • A sample of natural gas contains 6.25 moles of
    methane (CH4), 0.500 moles of ethane (C2H6), and
    0.100 moles of propane (C3H8). If the total
    pressure of the gas is 1.50 atm, what are the
    partial pressures of the gases?

39
Kinetic Molecular Theory of Gases
  • The Kinetic Molecular Theory of Gases is the
    model used to explain the behavior of gases in
    nature.
  • This theory presents physical properties of gases
    in terms of the motion of individual molecules.
  • Average Kinetic Energy ? Kelvin Temperature
  • Gas molecules are points separated by a great
    distance
  • Particle volume is negligible compared to gas
    volume
  • Gas molecules are in rapid random motion
  • Gas collisions are perfectly elastic
  • Gas molecules experience no attraction or
    repulsion

40
Kinetic Molecular Theory of Gases
41
Kinetic Molecular Theory of Gases
  • Average Kinetic Energy (KE) is given by


42
Kinetic Molecular Theory of Gases
  • The RootMeanSquare Speed (uRMS) is a measure
    of the average molecular speed of a particle of
    gas.

Taking square root of both sides gives the
equation
R 8.314 J/mol K
43
Kinetic Molecular Theory of Gases
  • Calculate the rootmeansquare speeds (uRMS) of
    helium atoms and nitrogen molecules in m/s at
    25C.

44
Grahams Law Diffusion and Effusion
  • Diffusion is the mixing of different gases by
    random molecular motion and collision.
  • Effusion is when gas molecules escape without
    collision, through a tiny hole into a vacuum.

45
Grahams Law Diffusion and Effusion
  • Grahams Law The rate of effusion is
    proportional to its RMS speed (uRMS).
  • For two gases at same temperature and pressure

Rate ?
46
Grahams Law Diffusion and Effusion
  • Under the same conditions, an unknown gas
    diffuses 0.644 times as fast as sulfur
    hexafluoride, SF6 (MM 146 g/mol). What is the
    identity of the unknown gas if it is also a
    hexafluoride?
  • What are the relative rates of diffusion of the
    three naturally occurring isotopes of neon 20Ne,
    21Ne, and 22Ne?

47
Behavior of Real Gases
  • Deviations from Ideal behavior result from two
    key assumptions about ideal gases.
  • Molecules in gaseous state do not exert any
    force, either attractive or repulsive, on one
    another.
  • Volume of the molecules is negligibly small
    compared with that of the container.
  • These assumptions breakdown at high pressures,
    low volumes and low temperatures.

48
Behavior of Real Gases
  • At STP, the volume occupied by a single molecule
    is very small relative to its share of the total
    volume
  • For example, a He atom (radius 31 pm) has
    roughly the same space to move about as a pea in
    a basketball
  • Lets say we increase the pressure of the system
    to 1000 atm, this will cause a decrease in the
    volume the gas has to move about in
  • Now our He atom is like a pea in a ping pong ball
  • Therefore, at high pressures, the volume occupied
    by the gaseous molecules is NOT negligible and
    must be considered.
  • So the space the gas has to move around in is
    less than under Ideal conditions!

VReal gt VIdeal
49
Behavior of Real Gases
  • At low volumes, particles are much closer
    together and attractive forces become more
    important than at high volumes.
  • This increase in intermolecular attractions pulls
    the molecules away from the walls of the
    containers, meaning that they do not hit the wall
    with as great a force, so the pressure is lower
    than under ideal conditions.

PReal lt PIdeal
50
Behavior of Real Gases
  • A similar phenomenon is seen at low temperatures
    (aka. The Flirting Effect)
  • As molecules slow down, they have more time to
    interact therefore increasing the effect of
    intermolecular forces.
  • Again, this increase in intermolecular
    attractions pulls the molecules away from the
    walls of the containers, meaning that they do not
    hit the wall with as great a force, so the
    pressure is lower than under ideal conditions.

PReal lt PIdeal
51
Behavior of Real Gases
52
Behavior of Real Gases
  • Corrections for non-ideality require the van der
    Waals equation.

Correction for Intermolecular Attractions
Correction for Molecular Volume
VReal gt VIdeal
PReal lt PIdeal
n moles of gas a and b are constants given in
the problem
53
Behavior of Real Gases
  • Given that 3.50 moles of NH3 occupy 5.20 L at
    47C, calculate the pressure of the gas (in atm)
    using
  • (a) the ideal gas equation
  • (b) the van der Waals equation. (a 4.17, b
    0.0371)
  • Calculate the pressure exerted by 4.37 moles of
    molecular chlorine confined in a volume of 2.45 L
    at 38C. Compare the pressure with that
    calculated using the ideal gas equation. (a
    6.49 and b 0.0562)
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