Honors Chemistry, Chapter 10

1
Chapter 10 Physical Characteristics of Gases
2
Kinetic-Molecular Theory

• Kinetic-molecular theory is based on the idea
  that particles of matter are always in motion.
• Ideal Gas an imaginary gas that perfectly fits
  all the assumptions of the kinetic-molecular
  theory.

3
Assumptions of Kinetic-Molecular Theory

• Gases consist of large numbers of tiny particles
  that are far apart relative to their size.
• Collisions between gas particles and between
  particles and container walls are elastic
  collisions. An elastic collision is one in which
  there is no net loss of kinetic energy.
• Gas particles are in continuous, rapid, random
  motion. They therefore posses kinetic energy,
  which is energy of motion.

4
Assumptions of Kinetic-Molecular Theory

• There are no forces of attraction or repulsion
  between gas particles.
• The average kinetic energy of gas particles
  depends on the temperature of the gas.
• KE ½ mv2 where KE is kinetic energy
• m is mass and
• v is velocity

5
Nature of Gases

• Expansion Gases have no definite shape or
  definite volume so they expand to fill the
  container. Gas particles move rapidly in all
  directions (assumption 3) without significant
  attraction or repulsion between them (assumption
  4).
• Fluidity Because the attractive forces between
  gas particles are insignificant (assumption 4),
  gas particles glide easily past one another.

6
Nature of Gases

• Low Density The density of a gas is about
  1/1000 the density of the same substance in the
  liquid or solid state.
• Compressibility During compression, the gas
  particles, which are initially very far apart
  (assumption 1), are crowded closer together.
  Under the influence of pressure, the volume of a
  gas can be greatly decreased.

7
Nature of Gases

• Diffusion Gases spread out and mix with one
  another, even without being stirred. This
  spontaneous mixing of particles of two substances
  caused by their random motion is called
  diffusion.
• Effusion is a process by which gas particles pass
  through a tiny opening. Rates of effusion of
  different gases are directly proportional to the
  velocities of their particles.

8
Real Gases

• A real-gas is a gas that does not behave
  completely according to the assumptions of the
  kinetic-molecular theory.
• Deviations from ideal-gas behavior usually occur
  at high pressures and/or low temperatures where
  the attractive forces between molecules begin to
  play a role.

9
Chapter 10, Section 1 Review

• State the kinetic molecular theory of matter, and
  describe how it explains certain properties of
  matter.
• List the five assumptions of the
  kinetic-molecular theory of gases.
• Define the terms ideal gas and real gas.

10
Chapter 10, Section 1 Review continued

• Describe each of the following characteristic
  properties of gases expansion, density,
  fluidity, compressibility, diffusion, and
  effusion.
• Describe the conditions under which a real gas
  deviates from ideal behavior.

11
Pressure and Force

• Pressure (P) is defined as the force per unit
  area on a surface.
• pressure force/area
• The SI unit for force is the newton, abbreviated
  N. It is the force that will increase the speed
  of a one kilogram mass by 1 meter per second per
  second that it is applied.
• force mass x acceleration

12
Example Pressure on the Feet of a Ballet Dancer

• Acceleration of gravity is 9.8 m/s/s
• What is the force of a 51 Kg dancer on the floor?
  
• F m x a 51 kg x 9.8 m/s/s 500 N
• What is the pressure?
• Flat footed 500 N/325 cm2 1.5 N/cm2
• Two feet tip toes 500 N /13 cm2 38.5
  N/cm2
• One foot tip toes 500 N /6.5 cm2 77 N/cm2

13
Units of Pressure

• A common unit of pressure is millimeters of
  mercury, mm Hg. A pressure of 1 mm of Hg is now
  called 1 torr in honor of Torricelli.
• One atmosphere is defined as being exactly
  equivalent to 760 mm Hg.
• In SI units, pressure is expressed in derived
  units called pascals. One pascal (Pa) is defined
  as the pressure exerted by a force of one newton
  (1 N) acting on an area of 1 square meter. One
  atmosphere is 1.01325 x 105 Pa or 101.325 kPa.

14
Units of Pressure
15
Standard Temperature and Pressure

• For purposes of comparison, scientists have
  agreed on standard conditions of exactly 1 atm
  pressure and 0oC. These conditions are called
  standard temperature and pressure and are
  commonly abbreviated STP.

16
Pressure Units Conversions

• Convert 0.830 atm to mm of Hg and kPa
• 0.830 atm x 760 mm of Hg/atm 631 mm
  of Hg
• 0.830 atm x 101.325 kPa/atm
• 84.1 kPa

17
Chapter 10, Section 2 Review

• Define pressure and relate it to force.
• Describe how pressure is measured.
• Convert units of pressure.
• State the standard conditions of temperature and
  pressure.

18
Gas Laws

• Gas laws are simple mathematical relationships
  between the volume, temperature, pressure, and
  amount of a gas.
• Boyles Law states that the volume of a fixed
  mass of gas varies inversely with the pressure at
  constant temperature.

19
Illustration of Boyles Law
20
Mathematical Expression of Boyles Law

• V k/P or PV k
• P1V1 k P2V2 k
• P1V1 P2V2
• P1V1 / V2 P2

21
Volume-Pressure Data
22
Boyles Law Example Problem

• V 150. mL of O2 at 0.947 atm.
• What is the volume at 0.987 atm (at constant
  temperature)?
• Formula P1V1 / P2 V2
• 0.947 atm x 150. mL / 0.987 atm 144 mL of O2

23
Absolute Zero

• Absolute zero, -273.15 oC., is the lowest
  temperature possible. This is assigned a value
  of zero on the Kelvin scale.
• To convert from Celsius to Kelvin
• K 273.15 oC.
• To convert from Kelvin to Celsius
• oC. K 273.15

24
Charless Law

• Charless Law states that the volume of a fixed
  mass of gas at constant pressure varies directly
  with the Kelvin temperature.
• V kT or V/T k
• V1 / T1 V2 / T2

25
Plot of Volume vs. Temperature
26
Charless Law Example Problem

• A sample of Ne gas has a volume of 752 mL at 25
  oC. What volume will the gas occupy at 50 oC. if
  the pressure remains constant?
• Convert temperatures to Kelvin
• 25 oC. 273 298 K.
• 50 oC. 273 323 K.

27
Charless Law Sample Problem

• V2 V1 x T2 / T1
• V2 752 mL Ne x 323 K. / 298 K
• 815 mL of Ne

28
Gay-Lussacs Law

• Gay-Lussacs Law The pressure of a fixed mass of
  gas at constant volume varies directly with the
  Kelvin temperature.
• P kT or P/T k
• P1/T1 P2/T2

29
Gay-Lussacs Law Example Problem

• Gas in an aerosol can is 3.00 atm at 25oC.
• What is the pressure at 52oC.?
• P2 P1 x T2/T1
• Convert temperatures to Kelvin
• 25oC. 273 298 K.
• 52oC. 273 325 K.

30
Gay-Lussacs Law Example Problem
P2 3.00 atm x 325 K / 298 K 3.27 atm
31
Combined Gas Law

• The combined gas law expresses the relationship
  between pressure, volume, and temperature of a
  fixed amount of gas.
• PV/T k
• Or
• P1 V1/T1 P2 V2 / T2

32
Combined Gas Law Example Problem

• A helium-filled balloon has a volume of 50.0 L at
  25 oC. and 1.08 atm. What volume will it have at
  0.855 atm and 10 oC.?
• Convert the temperatures to Kelvin
• 25 oC. 273 298 K
• 10 oC. 273 283 K.
• V2 P1 V1 T2 /( P2 T1)

33
Combined Gas Law Example Problem
V2 P1 V1 T2 /( P2 T1) V2 1.08 atm x50 L
Hex283 K/(0.855atm x298 K) 60.0 L
34
Daltons Law of Partial Pressures

• Daltons law of partial pressures states that the
  total pressure of a mixture of gases is equal to
  the sum of the partial pressures of the component
  gases.
• PT P1 P2 P3

35
Partial Pressure Example

• Oxygen gas is collected over water. The
  barometric pressure was 731 torr and the
  temperature was 20.0oC. What was the partial
  pressure of the oxygen collected?
• PT 731 torr
• Pwater 17.5 torr at 20.0oC.

36
Partial Pressure Example
Poxygen PT Pwater Poxygen 731
torr 17.5 torr 713.5 torr
37
Chapter 10, Section 3, Review

• Use the kinetic-molecular theory to explain the
  relationship between gas volume, temperature, and
  pressure.
• Use Boyles law to calculate volume-pressure
  changes at constant temperature.
• Use Gay-Lussacs law to calculate
  pressure-temperature changes at constant volume.

38
Chapter 10, Section 3, Review continued

• Use the combined gas law to calculate
  volume-temperature-pressure changes.
• Use Daltons law of partial pressures to
  calculate the partial pressures and total
  pressures.