Chapter 10 - Physical Characteristics of Gases


  1. The Kinetic-Molecular Theory of Matter
    Late 19th century - used study of gases to determine the behavior of atoms/molecules

    Kinetic-molecular theory is based on the idea that particles of matter are always in motion -- solids v liquids v gases

    http://mutuslab.cs.uwindsor.ca/schurko/animations/phasesofmatter/phasesofmatter.html
    Physical states of matter


    Factors to remember are energy of particles and forces acting between particles
    1. The Kinetic-Molecular Theory of Gases
      1. applies to an “ideal” gas
      2. ideal gas - definition
      3. assumptions of the k-m theory
        1. Gases consist of large numbers of tiny particles that are far apart relative to their size

          particles are usually atoms or molecules

          generally a gas occupies 1000 x the volume the same number of particles would occupy if they were in the solid state

          most of the volume occupied by a gas is empty space -- lower density of gas compared to corresponding solid -- also gases can be greatly compressed
        2. collisions between gas particles and between particles and the container walls are elastic collisions

          elastic collisions - definition
          depends on temperature remaining constant
        3. Gas particles are in constant, rapid, random motion.

          Have kinetic energy - definition

          Kinetic energy can overcome attractive forces if the energy is large enough and the attractive forces are small enough.

          Figure 10-1 page 304
        4. There are no forces of attraction or repulsion between gas particles
        5. The average kinetic energy of gas particles depends on the temperature of the gas.

          KE = 1/2 m v2 where m is the mass of the particles, v is the velocity (speed) of the particle.

          Because all the particles of a particular gas have the same mass, the speed depends only on the temperature -- higher speed implies a higher temperature.

          All the particles of a gas at the same temperature have the same average kinetic energy. i.e. lighter particles travel at higher speeds and heavier particles travel at slower speeds.
    2. The Kinetic-Molecular Theory and the Nature of Gases

      This theory applies only to ideal gases.

      Ideal gases do not exist.

      Can simulate ideal behavior at very low pressure and very high temperature.
      1. Expansion

        Gases have no definite shape and no definite volume.

        Fill whatever volume is available.

        http://mutuslab.cs.uwindsor.ca/schurko/animations/idealgas/idealGas.htm
        Ideal gas

        Gas molecules move rapidly in all directions and have no attraction or repulsion between themselves and other molecules.
      2. Fluidity

        Gas particles glide easily past one another since the attractive forces are minimal.

        True also in liquids but to a lesser extent.

        Fluid - definition
      3. Low Density

        A gas has a density about 1/1000 of its liquid or solid form.

        Due to distance between particles.
      4. Compressibility

        Compression pushes the gas particles which start out far apart, closer together.

        Gases can be compressed to occupy 1/100 of its normal volume.
      5. Diffusion and Effusion

        Gases spontaneously spread out and, if another gas is present, they mix on their own.

        Diffusion - definition

        Rate of diffusion depends on a) speed of gas particles, b) diameter of the particles, c) attractive forces between particles.

        Figure 10-2 page 305

        Effusion - definition

        Rates of effusion of different gases is directly proportional to the velocities of their particles.

        Molecules of low mass (higher velocity) effuse faster than molecules of high mass (lower velocity).
    3. Deviation of Real Gases from Ideal Behavior

      Real gases can behave like ideal gases when the particles are far enough apart and are moving fast enough to overcome attractive forces.

      Real gas - definition

      1873 - Johannes van der Waals - deviation from ideal behavior by indicating the particles of a real gas occupy space and do exert attraction for each other.

      Van der Waals forces are most noticeable at very high pressure or very low temperature or both.

      Figure 10-3 page 306

      Kinetic molecular theory holds true for gases that have little or no attractive forces for each other viz. noble gases. These are nonpolar molecules. Diatomic molecules also show similar behavior.

      If a gas molecule is polar (dipole) the attractive forces between the molecules will be greater and the deviation from ideal behavior will be larger. e.g. ammonia and water vapor

      Homework: Web page, 10.1: Chapter 10, Kinetic Molecular Theory of Matter Questions
  2. Pressure

    The volume a gas occupies is meaningless unless you specify the temperature and pressure as well.

    The four important variables about a gas are a) volume, b) temperature, c) number of molecules; d) pressure
    1. Pressure and Force

      Pressure - definition

      Equation for pressure: P = f / A

      SI unit of force is the newton (N)

      Newton - definition

      Figure 10-4 page 308

      Weight of dancer = 51 kg ( 1 kg = 2.2 pounds, therefore about 112 pounds)

      Each kilogram of mass exerts 9.8 N (or 98 N / kg) of force due to gravity so (51 kg x 9.8N / kg) = 500 N. That is the force the dancer’s feet exert on the floor.

      Situation A: both feet flat on floor: area of contact with floor is 325 cm2 and pressure = force / area or 500 N / 325 cm2 = 1.5 N / cm2

      Situation B: Dances up on both toes: area of contact with floor is 13 cm2 and pressure = force / area or 500 N / 13 cm2 = 38.5 N / cm2

      Situation C: Dancer up on one toe: area of contact with floor is 6.5 cm2 and pressure = force / area or 500 N / 6.5 cm2 = 77 N / cm2

      Same force is applied to a smaller area in going from situation a to situation c.

      Gas molecules exert a pressure on any surface with which they collide. The pressure depends on a) volume, b) temperature; c) number of molecules.

      The atmosphere exerts pressure on us -- called atmospheric pressure. Serves as a blanket of air surrounding the earth.

      Difference between atmospheric pressure at sea level and atmospheric pressure 30 000 feet above sea level. Why?

      Figure 10-6a page 310

      Figure 10-6b page 310

      http://mutuslab.cs.uwindsor.ca/schurko/animations/collisions/collision_particle.htm
      Pressure due to collisons with container sides.

    2. Measuring Force

      barometer - definition

      Torricelli in early 1600's - why water pumps could only raise water to 34 feet; depends on weight of water compared to weight of air; mercury is 14 times more dense than water should only go up 1/14 the height of water or 1/14 x 34 feet; tested using apparatus in

      figure 10-7 page 311

      torricellian vacuum

      at sea level, at 0o, the average height of mercury is 760 mm

      barometric (atmospheric) pressure varies depending a)elevation, b) weather conditions

      manometer - used to measure pressure of an enclosed gas sample; shaped like a U
    3. http://www.chm.davidson.edu/chemistryapplets/gaslaws/pressure.html
    4. Manometer
      figure 10-8 page 311
    5. Units of Pressure

      a) millimeters of mercury (mm Hg); average atmospheric pressure at zero degrees Celsius and at sea level is 760 mm Hg -- also known as standard pressure.

      b) atmosphere of pressure (atm); one atmosphere - definition

      c) Pascal (Pa); an SI unit; expressed in derived units
      Pascal - definition
      also have kilopascals (kPa); 1 ATM = 1.013 x 105 Pa or 101.325 kPa.
      Unit
      Symbol
      Conversion
      pascal Pa see below
      millimeters of mercury mm Hg

      760 mm Hg = 1 atm

      1 mm Hg = 1 torr
      torr torr

      1 torr = 1 mm Hg

      760 torr = 1 atm
      atmosphere atm

      1 atm = 760 mm Hg

      1 atm = 760 torr

      1 atm = 1.013 x 105 Pa

      1 atm = 101.3 kPa

      table 10-1 page 311
    6. Standard Temperature and Pressure

      When comparing volumes of gases you need to know temperature and pressure.

      We use standard temperature and pressure (STP).

      Standard temperature is defined as zero degrees Celsius.

      Standard pressure is defined as one atmosphere pressure.

      Sample problem 10-1 page 312

      Homework: Web page, 10.2: Chapter 10, Pressure Questions/Problems
    7. The Gas Laws

      the gas laws - definition
    8. Boyle's Law: Pressure-Volume Relationship

      Boyle found doubling the pressure on a gas caused its volume to decrease by 1/2; tripling the pressure caused its volume to decrease by 1/3.

      Figure 10-9 page 313

      pressure due to molecules colliding with walls of container

      smaller container means more collisions and, thus, greater pressure -- temperature must be the same since temperature is a measure of the average KE of the molecules.

      Table 10-2 page 314

      Boyle's Law - statement

      PV = k where the volume of k depends only on the mass of gas and the temperature.

      P1 V1 = P2 V2

      http://www.grc.nasa.gov/WWW/K-12/airplane/aboyle.html
      Boyle's Law

      http://www.chm.davidson.edu/ChemistryApplets/GasLaws/BoylesLaw.html

      http://www.hargrave.edu/academics/science/cpchem2/labnotes/boyle.html

      http://www.upscale/utoronto.ca/IYearLab/Intros/BoylesLaw/BoylesLaw.html

      Sample Problem 10-2 page 315 -- units must be consistent i.e. if pressure is in mm Hg for one then the other pressure must also be in mm Hg

      Homework: Web page 10.3: Chapter 10, Worksheet on Boyle's Law
    9. Charles' Law: Volume-Temperature Relationship

      When pressure is held constant and you heat a gas, the volume increases. E.g. hot air balloon.

      Jacques Charles in 1787.

      All gases expand to the same extent when heated through the same temperature interval.

      If a substance is at zero degrees Celsius and heated to one degree Celsius, the volume increases by 1/273 of the original volume it had at zero degrees Celsius. The same type of thing happens when cooling a gas except the volume decreases.

      At -273 degrees Celsius (zero Kelvin), the volume theoretically would be zero -- hence the term absolute zero. Generally gases condense to liquids before reaching absolute zero.

      Table 10-3 page 317

      Celsius ---> Kelvin use degrees Celsius + 273

      Charles' Law - statement

      V / T = k

      V1 / T1 = V2 / T2

      http://plabpc.csustan.edu/general/tutorials/temperature/CharlesLaw/CharlesLaw.htm

      http://www.grc.nasa.gov/WWW/K-12/airplane/aglussac.html

      http://www.accad.ohio-state.edu/~midori/GasLaw.html
      Charles' Law

      Table 10-4 page 318

      Figure 10-12 page 318

      Sample Problem 10-3 page 318

      Homework: Web page 10.4: Chapter 10, Worksheet on Charles' Law

    10. Gay-Lussac's Law: Pressure Temperature Relationship

      Pressure is the result of the collisions of molecules with the walls of the container. More collisions, more pressure; hit the wall harder, more pressure.

      Gay-Lussac's law - statement

      P / T = k

      Figure 10-13 page 319

      P1 / T1 = P2 / T2

      Example Problem 10-4 page 320

      Homework: Web page 10.5: Chapter 10, Worksheet on Gay-Lussac's Law
    11. The Combined Gas Law

      Combined gas law - statement

      P V / T = k

      P1 V1 / T1 = P2 V2 / T2

      Sample Problem 10-5 page 321

      Homework: Web page 10.6: Chapter 10, Worksheet on combined gas law
    12. Dalton's Law of Partial Pressures

      John Dalton

      Found if you have two gases that do not react with each other, you place them in the same container, the total pressure would be equal to the pressure each would exert if it occupied the same container by itself.

      Figure 10-14 page 323

      Partial pressure - definition

      Dalton's Law of Partial Pressure - statement

      PT = P1 + P2 + P3 + P4 + .......

      http://www.chm.davidson.edu/chemistryapplets/gaslaws/daltonslaw.html
      Dalton's Law
    13. Gas Collected by Water Displacement

      Figure 10-15 page 324

      As the gas moves through the water some of the water, as vapor, will mix with the gas collected above the liquid water.

      This creates a situation in which you have two gases mixed in the same space.

      The total pressure will be equal to the atmospheric pressure and that pressure will be the same as the partial pressure of the gas collected and the water vapor pressure.

      We can look up the water vapor pressure if we know the temperature of the mixture of gases.

      Patm = PH2O + Pgas

      Sample Problem 10-6 page 324

      Homework: Web page 10.7: Chapter 10, Worksheet on Dalton's Law of Partial Pressure






















      Dalton's Law of Partial Pressure states that the total pressure of a mixture of gases is equal to the sum of the partial pressures of the component gases. back

















      Partial pressure is the pressure of each gas in a mixture. Back
















      The combined gas law expresses the relationship between pressure, volume, and temperature of a fixed amount of gas. Back
















      The pressure of a fixed mass of gas at constant volume varies directly with the Kelvin temperature. Back
















      Charles' law states that the volume of a fixed mass of gas at constant pressure varies directly with the Kelvin temperature. Back















      Absolute zero is -273 degrees Celsius and is the given value of zero in the Kelvin scale. Back

















      Boyle's Law states that the volume of a fixed mass of gas varies inversely with the pressure at constant temperature. Back
















      The gas laws are simple mathematical relationships between the volume, temperature, pressure, and quantity of a gas. Back
















      One pascal is defined as the pressure exerted by a force of one Newton (1 N) acting on an area of one square meter. Back
















      One atmosphere of pressure is defined as being exactly equal to 760 mm Hg. back
















      A barometer is a device used to measure atmospheric pressure. Back
















      A Newton is the force that will increase the speed of one kilogram mass by one meter per second each second it is applied. Back
















      Pressure is the force per unit area on a surface. Back
















      A real gas is a gas that does not behave completely according to the assumptions of the kinetic molecular theory. Back
















      Effusion is the process by which gas particles under pressure pass through a tiny opening. Back
















      Diffusion is the spontaneous mixing of the particles of two substances caused by their random motion. Back
















      A fluid is anything that flows. Includes both liquids and gases. Back
















      An ideal gas is an imaginary gas that perfectly fits all the assumptions of the kinetic-molecular theory. Back
















      Elastic collisions are collisions in which there is no net loss of kinetic energy. Back

      Kinetic energy is energy of motion. Back