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General Chemistry I Chapter 10 Gases

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Title: General Chemistry I Chapter 10 Gases


1
General Chemistry I Chapter 10 Gases
2
Gases You Have Encountered
3
Characteristics of Gases
  • Gases always form homogeneous mixtures with other
    gases
  • Gases are highly compressible and occupy the full
    volume of their containers. (Chapter 1)
  • When a gas is subjected to pressure, its volume
    decreases.
  • .

4
Pressure
  • Pressure is the force acting on an object per
    unit area
  • Gravity exerts a force on the earths atmosphere
  • A column of air 1 m2 in cross section exerts a
    force of 105 N.
  • The pressure of a 1 m2 column of air is 100 kPa.
  • SI Units 1 N 1 kg.m/s2 1 Pa 1 N/m2.

5
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7
Atmosphere Pressure and The Barometer
  • If a tube is inserted into a container of mercury
    open to the atmosphere, the mercury will rise 760
    mm up the tube.
  • Atmospheric pressure is measured with a
    barometer.
  • Standard atmospheric pressure is the pressure
    required to support 760 mm of Hg in a column.
  • Units 1 atm 760 mmHg 760 torr 1.01325 ?
    105 Pa 101.325 kPa.

8
Class Guided Practice Problem
  • (a) Convert 0.527 atm to torr
  • (b) Convert 760 torr to kPa

Class Practice Problem
  • (c) Convert 147.2 kPa to (1) atm and (2) torr

9
  • Atmosphere Pressure and The Manometer
  • The pressures of gases not open to the atmosphere
    are measured in manometers.
  • A manometer consists of a bulb of gas attached to
    a U-tube containing Hg
  • If Pgas lt Patm then Pgas Ph2 Patm.
  • If Pgas gt Patm then Pgas Patm Ph2.
  • (See example problem 10.2)

10
Defining States of Gases
  • Gas experiments revealed that four variables will
    affect the state of a gas
  • Temperature, T
  • Volume, V
  • Pressure, P
  • Quantity of gas present, n (moles)
  • These variables are related through equations
    know as the gas laws.

11
The Ideal Gas Equation
  • Consider the three gas laws.
  • We can combine these into a general gas law
  • Boyles Law
  • Charless Law
  • Avogadros Law

12
The Gas Laws Boyles Law
  • The Pressure-Volume Relationship
  • Weather balloons are used as a practical
    consequence to the relationship between pressure
    and volume of a gas.
  • As the weather balloon ascends, the volume
    increases.
  • As the weather balloon gets further from the
    earths surface, the atmospheric pressure
    decreases.
  • Boyles Law the volume of a fixed quantity of
    gas is inversely proportional to its pressure.
  • Boyle used a manometer to carry out the
    experiment.

13
Boyles Law

14
The Pressure-Volume Relationship
  • Mathematically
  • A plot of V versus P is a hyperbola.
  • Similarly, a plot of V versus 1/P must be a
    straight line passing through the origin.
  • The Value of the constant depends on the
    temperature and quantity of gas in the sample.

15
Charless Law
  • The Temperature-Volume Relationship
  • We know that hot air balloons expand when they
    are heated.
  • Charless Law the volume of a fixed quantity of
    gas at constant pressure increases as the
    temperature increases.
  • Mathematically

16
Plotting Charless Law
  • A plot of V versus T is a straight line.
  • When T is measured in ?C, the intercept on the
    temperature axis is -273.15?C.
  • We define absolute zero, 0 K -273.15?C.
  • Note the value of the constant reflects the
    assumptions amount of gas and pressure.

17
All gases will solidify or liquefy before
reaching zero volume.
18
Avogadros Law
  • The Quantity-Volume Relationship
  • Gay-Lussacs Law of combining volumes at a given
    temperature and pressure, the volumes of gases
    which react are ratios of small whole numbers.

19
Avogadros Law
  • Avogadros Hypothesis equal volumes of gas at
    the same temperature and pressure will contain
    the same number of molecules.
  • Avogadros Law the volume of gas at a given
    temperature and pressure is directly proportional
    to the number of moles of gas.

20
Expressing Avogadros Law
  • Mathematically
  • We can show that 22.4 L of any gas at 0?C contain
    6.02 ? 1023 gas molecules.

21
The Ideal Gas Constant
  • If R is the constant of proportionality (called
    the gas constant), then
  • The ideal gas equation is

22
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23
Applying The Ideal Gas Equation
  • We define STP (standard temperature and pressure)
    0?C, 273.15 K, 1 atm.
  • Volume of 1 mol of gas at STP is

24
Class Guided Practice Problem
  • For an ideal gas, calculate the following
    quantities (a) the pressure of the gas if 1.04
    mol occupies 21.8 L at 25 oC (b) the volume
    occupied by 6.72 x 10-3 mol at 265 oC and
    pressure of 23.0 torr

Class Practice Problem
  • (c) the number of moles in 1.50 L at 37 oC and
    725 torr (d) the temperature at which 0.270 mol
    occupies 15.0 L at 2.54 atm.

25
Relating the Ideal-Gas Equation and the Gas Laws
  • If PV nRT and n and T are constant, then PV
    constant and we have Boyles law.
  • Other laws can be generated similarly.
  • In general, if we have a gas under two sets of
    conditions, then

26
Class Guided Practice Problem
  • A sample of argon gas is confined to a 1.00-L
    tank at 27.0 oC and 1 atm. The gas is allowed to
    expand into a larger vessel. Upon expansion, the
    temperature of the gas drops to 15.0 oC, and the
    pressure drops to 655 torr. What is the final
    volume of the gas?
  • Two ways to work this problem.

27
Molar Mass
  • Density has units of mass over volume.
  • Rearranging the ideal-gas equation with M as
    molar mass we get

28
Gas Densities
  • The molar mass of a gas can be determined as
    follows
  • .

29
Class Guided Practice Problem
  • What is the density of carbon tetrachloride vapor
    at 714 torr and 125 oC?

30
Volumes of Gases in Chemical Reactions
  • The ideal-gas equation relates P, V, and T to
    number of moles of gas.
  • The n can then be used in stoichiometric
    calculations

31
Class Guided Practice Problem
  • The safety air bags in automobiles are inflated
    by nitrogen gas generated by the rapid
    decomposition of sodium azide, NaN3
  • 2 NaN3(s) ? 2 Na(s) 3N2(g)
  • If an air bag has a volume of 36 L and is filled
    with nitrogen gas at a pressure of 1.15 atm at a
    temperature of 26 oC, how many grams of NaN3 must
    be decomposed?

32
Gas Mixtures and Partial Pressures
  • Since gas molecules are so far apart, we can
    assume they behave independently.
  • Daltons Law in a gas mixture the total pressure
    is given by the sum of partial pressures of each
    component
  • Each gas obeys the ideal gas equation
  • Combining the equations we get

33
Collecting Gases over Water
34
Collecting Gases over Water
  • It is common to synthesize gases and collect them
    by displacing a volume of water.
  • To calculate the amount of gas produced, we need
    to correct for the partial pressure of the water

35
Class Guided Practice Problem
  • A gaseous mixture made form 6.00g O2 and 9.00g
    CH4 is placed in a 15.0-L vessel at 0 oC. What
    is the total pressure in the vessel?

36
Kinetic Molecular Theory
  • Theory developed to explain gas behavior.
  • Theory of moving molecules.
  • Assumptions
  • Gases consist of a large number of molecules in
    constant random motion.
  • Volume of individual molecules negligible
    compared to volume of container.
  • Intermolecular forces (forces between gas
    molecules) negligible.

37
Kinetic Molecular Theory
  • Assumptions
  • Energy can be transferred between molecules, but
    total kinetic energy is constant at constant
    temperature.
  • Average kinetic energy of molecules is
    proportional to temperature.
  • Kinetic molecular theory gives us an
    understanding of pressure and temperature on the
    molecular level.
  • Pressure of a gas results from the number of
    collisions per unit time on the walls of
    container.

38
Kinetic Molecular Theory
  • Magnitude of pressure given by how often and how
    hard the molecules strike.
  • Gas molecules have an average kinetic energy.
  • Each molecule has a different energy.

39
Kinetic Molecular Theory
  • As kinetic energy increases, the velocity of the
    gas molecules increases.
  • Root mean square speed, u, is the speed of a gas
    molecule having average kinetic energy.
  • Average kinetic energy, ?, is related to root
    mean square speed

40
Application to Gas Laws
  • As volume increases at constant temperature, the
    average kinetic of the gas remains constant.
    Therefore, u is constant. However, volume
    increases so the gas molecules have to travel
    further to hit the walls of the container.
    Therefore, pressure decreases.
  • If temperature increases at constant volume, the
    average kinetic energy of the gas molecules
    increases. Therefore, there are more collisions
    with the container walls and the pressure
    increases.

41
Real Gases Deviations from Ideal Behavior
  • From the ideal gas equation, we have
  • For 1 mol of gas, PV/RT 1 for all pressures.
  • In a real gas, PV/RT varies from 1 significantly.
  • The higher the pressure the more the deviation
    from ideal behavior.

42
Real Gases Deviations from Ideal Behavior
  • From the ideal gas equation, we have
  • For 1 mol of gas, PV/RT 1 for all
    temperatures.
  • As temperature increases, the gases behave more
    ideally.
  • The assumptions in kinetic molecular theory show
    where ideal gas behavior breaks down
  • the molecules of a gas have finite volume
  • molecules of a gas do attract each other
  • .

43
Real Gases Deviations from Ideal Behavior
  • As the pressure on a gas increases, the molecules
    are forced closer together.
  • As the molecules get closer together, the volume
    of the container gets smaller.
  • The smaller the container, the more space the gas
    molecules begin to occupy.
  • Therefore, the higher the pressure, the less the
    gas resembles an ideal gas.

44
Real Gases Deviations from Ideal Behavior
  • As the gas molecules get closer together, the
    smaller the intermolecular distance.

45
Real Gases Deviations from Ideal Behavior
  • The smaller the distance between gas molecules,
    the more likely attractive forces will develop
    between the molecules.
  • Therefore, the less the gas resembles and ideal
    gas.
  • As temperature increases, the gas molecules move
    faster and further apart.
  • Also, higher temperatures mean more energy
    available to break intermolecular forces.

46
Real Gases Deviations from Ideal Behavior
  • Therefore, the higher the temperature, the more
    ideal the gas.

47
The van der Waals Equation
  • We add two terms to the ideal gas equation one to
    correct for volume of molecules and the other to
    correct for intermolecular attractions
  • The correction terms generate the van der Waals
    equation
  • where a and b are empirical constants.

48
The van der Waals Equation
Corrects for molecular volume
Corrects for molecular attraction
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