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Lecture 06 (Chapter 6)

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Lecture 06 (Chapter 6) The Gaseous State An important point is that k3 is the same for all gases at the same temperature and pressure. 142 g/mol 142 g/mol 0.605 L O2 ... – PowerPoint PPT presentation

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Title: Lecture 06 (Chapter 6)


1
  • Lecture 06 (Chapter 6)
  • The Gaseous State

2
Physical States of Matter
  • Matter can exist as
  • Solid
  • Liquid
  • Gas

Temperature Dependent States
http//www.uni.edu/iowawet/H2OProperties.html
http//en.wikipedia.org/
3
Solid Phase
  • A solid has fixed shape and volume.

Solid Br2 at low temperature
4
Liquid Phase
  • A liquid has fixed volume but no definite shape.
  • The density of a solid or a liquid is given in
    g/mL.

Liquid Br2
5
Gas Phase
  • A gas has no fixed volume or definite shape.
  • The density of a gas is given in g/L whereas
    liquids and solids are in g/mL.

Gaseous Br2
6
Summary of Gas Phase Characteristics
  • Characteristics of gases
  • Particles in constant random motion
  • Particles far apart, travel in straight lines,
    collide frequently
  • Low Density (particles widely separated)
  • Indefinite Shape (little cohesion, particles
    expand to shape of container)
  • Large Compressibility (gas is mostly empty space)
  • Moderate Thermal Expansion (increase in
    temperature causes particles to collide with more
    energy, increases volume)

Seager SL, Slabaugh MR, Chemistry for Today
General, Organic and Biochemistry, 7th Edition,
2011 http//www.chemistry.wustl.edu/edudev/LabTu
torials/Airbags/airbags.html
7
Pressure of a Gas
  • Pressure is the force per unit area exerted on a
    surface.
  • The pressure of the atmosphere is measured with a
    barometer.

8
Manometers
  • Both open and closed end manometers measure
    pressure differences.
  • In Figs. A and B (open manometers), h represents
    difference in P between a gas and the atmosphere.
  • In Fig. C (closed manometer), h represents P of
    the gas.

A
B
C
9
Units of Pressure
  • One atmosphere of pressure (1 atm) is the normal
    pressure at sea level. The SI unit of pressure
    is the pascal (Pa), but is a very small unit and
    is not used frequently by chemists.

1 atm 760 mm Hg 1 atm 101.3 kPa 1 atm 760
torr 1 atm 1.01 bar 1 torr 133.3 Pa
1 atm 29.9 in Hg 1 atm 14.7 psi
10
Gas Laws
  • Describe behavior of gases when mixed, subjected
    to pressure or temperature changes, or allowed to
    diffuse
  • Laws describes relationships between temperature
    (T), volume (V), pressure (P) and moles (n)
  • The physical properties of all gases behave in
    the same manner, regardless of the identity of
    the gas
  • Boyles law
  • Charless law
  • Combined gas law
  • Avogadros law
  • Ideal gas law

11
Boyles Law
  • A constant relationship exists between pressure
    (P) and volume (V) at constant temperature (T)
  • If pressure increases, volume occupied by the gas
    decreases
  • If volume increases, pressure created by the gas
    decreases

 
 
 
12
Boyles Law
  • A plot of volume versus 1/P is a straight line.

 
 
 
Formula for straight line
13
Example Boyles Law
  • A sample of a gas occupies 5.00 L at 0.974 atm.
    Calculate the volume of the gas at 1.00 atm, when
    the temperature held is constant.

How do you solve this problem? What do you
know? If P1V1 k1, and k1 is constant (at
constant T), then P1V1 P2V2 Check P1V1
(5.00L)(0.974 atm) 4.87 Latm k1 V (k1 /P)
(4.87 Latm)/(1.00 atm) 4.87 L Or P1V1
P2V2 rearranges to V2 (P1V1)/P2 (0.974 atm
5.00 L)/1.00 atm 4.87 L
14
Charless Law
  • At constant pressure, the volume of a gas sample
    is directly proportional to the temperature
    (expressed in kelvins)
  • If temperature increases, volume increases at
    constant pressure

 
 
 
Seager SL, Slabaugh MR, Chemistry for Today
General, Organic and Biochemistry, 7th Edition,
2011
15
Charless Law
  • A plot of volume versus temperature is a straight
    line.
  • Extrapolation to zero volume yields absolute zero
    in temperature (which isnt going to happen!!)
  • -273o C.
  • V k2 x T, where T is given in units of kelvin.

16
Example Charless Law
  • A balloon filled with oxygen gas at 25C occupies
    2.1 L. At constant pressure, what is the volume
    at 100C?

How do you solve this problem? What do you
know? First, convert T value(s) from C to
K. Ti in K 25 273 298 K Tf in K 100
273 373 K If then
 
 
 
17
P, V, T Relationships Combined Gas Law
  • Boyles law and Charless law can be combined to
    relate P, V and T, when mass of gas remains
    constant.
  • Because k is a constant, we can use this
    equation to evaluate changes in these variables
    over time (between some initial state and a final
    state).
  • Any problem that can be solved with either
    Boyles law or Charless law, can also be solved
    using the Combined Gas Law.

18
Combined Gas Law Examples
  • 2500 liters of oxygen gas is produced at 1.00 atm
    of pressure. It is to be compressed and stored in
    a 20.0 liter cylinder. If temperature is
    constant, calculate the pressure of the oxygen in
    the cylinder.
  • A 3.2 liter sample of gas is at 40C and 1.0
    atmosphere of pressure. If the temperature
    decreases to 20C and the pressure decreases to
    0.60 atmospheres, what is the new volume in
    liters?

19
Combined Gas Law Examples
  • A sample of a gas occupies 4.0 L at 25o C and
    2.0 atm of pressure. Calculate the volume at STP
    (T 0 oC, P 1 atm).
  • A sample of a gas occupies 200 mL at 100oC. If
    the pressure is held constant, calculate the
    volume of the gas at 0oC.

20
Avogadros Hypothesis
  • Two different gases of equal volume measured at
    same T and P contain equal numbers of molecules
  • Mass would not be identical due to different MWs

21
Avogadros Law
  • A plot of the volume of all gas samples, at
    constant T and P, vs. the number of moles (n) of
    gas is a straight line.
  • V k3 x n

 
22
Ideal Gas Law
P Pressure
 
V Volume
n number of moles
 
T Temperature
R Universal Gas Constant
m mass
Also, because
MW molecular weight
 
STP (Standard Temperature and Pressure) T 0
C P 1.0 atm V of 1 mol ideal gas (any gas)
22.4 L at STP
We can also express the ideal gas law as
 
23
Ideal Gas Law Calculation
  • Calculate the number of moles of argon gas in a
    30 L container at a pressure of 10 atm and
    temperature of 298 K.
  • How do we solve this problem?

24
Ideal Gas Law Calculation
  • Calculate the number of moles of argon gas in a
    30 L container at a pressure of 10 atm and
    temperature of 298 K.
  • PV nRT
  • n
  • n 12 mol

25
Molar Mass and Density
  • The ideal gas law can be used to calculate
    density (mass/volume) and molar mass (mass/moles)
    of a gas.
  • At constant pressure and temperature the density
    of a gas is proportional to its molar mass, so
    the higher the molar mass, the greater the
    density of the gas.

26
Example Molar Mass
  • Calculate the molar mass of a gas if a 1.02 g
    sample occupies 220 mL at 95o C and a pressure of
    750 torr.

27
Example Molar Mass
  • Calculate the molar mass of a gas if a 1.02 g
    sample occupies 220 mL at 95o C and a pressure of
    750 torr.

 
 
 
 
 
 
 
 
 
28
Gases and Chemical Equations
  • The ideal gas law can be used to determine the
    number of moles, n, for use in problems involving
    reactions.
  • The ideal gas law relates n to the volume of gas
    just as molar mass is used with masses of solids
    and molarity is used with volumes of solutions.

29
Example Gases with Equations
  • Calculate the volume of O2 gas formed in the
    decomposition of 2.21 g of KClO3 at STP.
    2KClO3(s) 2KCl(s) 3O2(g)

 
 
 
 
30
Gas Volumes in Reactions
  • Equal volumes of gases at same P and T contain
    same number of moles.
  • In chemical rxns under same conditions, gas
    volumes combine in same proportions as
    coefficients of equation.
  • Therefore, 3 L of hydrogen gas, combined with 2 L
    of nitrogen gas, forms 2 L of ammonia.

31
Example Gas Volumes in Reactions
  • Calculate the volume of NH3 gas produced in the
    reaction of 4.23 L of H2 with excess N2 gas.
    Assume the volumes are measured at the same
    temperature and pressure.

 
 
32
Daltons Law of Partial Pressure
  • The pressure exerted by each gas in a mixture is
    called its partial pressure.
  • For a mixture of two gases A and B, the total
    pressure, PT, is
  • PT PA PB

33
Example Partial Pressures
  • Calculate the pressure in a container that
    contains O2 gas at a pressure of 3.22 atm and N2
    gas at a pressure of 1.29 atm.

PT PA PB 3.22 atm 1.29 atm 4.51 atm
34
Example Partial Pressures
  • A gas sample in a 1.2 L container holds 0.22 mol
    N2 and 0.13 mol O2. Calculate the partial
    pressure of each gas, and the total pressure at
    50C.

 
 
We will use Ideal Gas law to calculate P for each
of the 2 gases.
 
 
 
 
 
35
Mole Fraction
  •  

36
Mole Fraction
  • Mole fraction of the yellow gas is 3/12 0.25
    and the mole fraction of the red gas is 9/12
    0.75

37
Example Partial Pressure
  • Calculate the partial pressure of Ar gas in a
    container that contains 2.3 mol of Ar and 1.1 mol
    of Ne and is at a total pressure of 1.4 atm.

 
 
38
Collecting Gases over Water
  • The volume of gas generated in a rxn can be
    determined by water displacement.
  • The collected gas contains both O2 gas from the
    rxn and water vapor, and each contribute to total
    P.

39
Example Collecting Gases
  • Sodium metal is added to excess water, and H2 gas
    produced in the reaction is collected over water
    with the gas volume of 1.2 L. If the pressure is
    745 torr and the temperature 26o C, what was the
    mass of the sodium? The vapor pressure of water
    at 26o C is 25 torr. 2Na(s) 2H2O(l) H2(g)
    2NaOH(aq)

 
 
 
 
40
Kinetic Molecular Theory of Gases
  • Describes the behavior of (ideal) gas particles
    at molecular level, based on 4 postulates.
  • 1. Gases consist of small particles that are in
    constant and random motion.
  • 2. Gas particles are very small compared to the
    average distance that separates them.
  • 3. Collisions of gas particles with each other
    and the walls of the container are elastic (i.e.,
    no loss of kinetic energy).
  • 4. The average kinetic energy of gas particles
    is proportional to the temperature on the Kelvin
    scale.

41
Kinetic Molecular Theory of Gases
  • How does this theory explain the observed
    behavior of gases?
  • Because gases consist of small particles that are
    in constant and random motion and they are
    constantly colliding with each other and with the
    walls of the container, and because these
    collisions involve no loss of average KE, the
    result is increased pressure.
  • 2. Because gas particles are very small compared
    to the average distance that separates them, at
    constant T, they can be compressed into a smaller
    volume (P increases), or they can expand to fill
    a larger volume (P decreases).
  • 3. Because the average kinetic energy of gas
    particles is proportional to the temperature (on
    the Kelvin scale), KE of the molecules increases
    with increasing T resulting in more collisions
    over time involving greater force thus, at
    constant P, V would have to increase (Charless
    law).

 
42
Average Speed of a Gas
Maxwell-Boltzmann distribution curves
  • Although gas particles move at different
    velocities, we can calculate an average velocity
    (see previous slide), which is also called the
    root mean square (rms) speed, urms, and is the
    square root of the average squared speed.
  • This number can be derived mathematically and
    represented by the associated curve.

R 8.314 J/mol.K molar mass in kilograms per
mole
43
Average Speed of a Gas
  • From this plot and the equation, you can see
    that velocity, or root mean square speed, of
    molecules decreases with increasing molar mass
    (at constant T).

44
Effusion (Grahams law) and Diffusion
  • The Kinetic Molecular Theory also correctly
    described both effusion and diffusion
  • Effusion - the passage of a gas through a small
    hole into an evacuated space.
  • Gases with low molar masses effuse more rapidly
    (e.g., heavier gases move more slowly).
  • Diffusion is the mixing of particles due to
    motion.

45
Effusion (Grahams law)
  • Grahams Law is frequently used to compare rates
    of effusion of 2 gases.

 
46
Effusion (Grahams law) Example
Calculate the molar mass of a gas if equal
volumes of nitrogen and the unknown gas take 2.2
and 4.1 minutes, respectively, to effuse through
the same small hole (at constant T and P).
 
 
 
47
Deviations from Ideal Behavior
  • Gases deviate from the ideal gas law at high
    pressures in 2 ways.

48
Deviations from Ideal Behavior
  • The assumption that gas particles are small
    compared to the distances separating them fails
    at high pressures.
  • The observed value of PV/nRT will be greater than
    1 under these conditions.

49
Forces of Attraction in Gases
  • The forces of attraction between closely spaced
    gas molecules reduce the impact of wall
    collisions.
  • These attractive forces cause the observed value
    of PV/nRT to decrease below the expected value of
    1 at moderate pressures.

50
Ideal Gases
  • A gas (O2 below) deviates from ideal gas behavior
    at low temperatures (near the condensation point
    ) and high pressures.
  • In other words, removing heat removes energy
    applied to molecules, so they slow down, and in
    doing so, are more susceptible to effects caused
    by force of attraction.

51
van der Waals Equation
  • The van der Waals equation corrects for
    attractive forces and the volume occupied by the
    gas molecules.
  • a is a constant related to the strength of the
    attractive forces.
  • b is a constant that depends on the size of the
    gas particles.
  • a and b are determined experimentally for each
    gas.
  • (Review Example 6.17 on your own)
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