Gases

1
Chapter 10
Gases
2
Overview

• Pressure
• Barometer Atmospheric Pressure
• Standard Conditions
• Gas Laws
• Boyles Law
• Charles Law
• Avogadros Law
• Ideal Gas Law

3

• Gas Laws under Two Conditions
• Gas Densities
• Darltons Law of Partial Pressure
• Kinetic Molecular Theory
• Molecular Effusion/Diffusion
• Grahams Law
• Deviation from Ideality

4
Characteristics

• Solids
• have own shape and volume
• particles close together with strong interaction
• Liquids
• have own volume but assume shape of container
• particles farther apart but have moderate
  interaction
• Gases
• assume shape and volume of container
• particles far apart with little/no interaction
• highly compressible

5
Pressure

• P F/A
• Force in Newtons
• Area in m2
• Barometer
• P in N/m2 Pascal unit
• 1 x 105 N/m2 1 x 105 Pa or 100 kPa
• Standard Pressure
• 1 atm 760 mm Hg 1.01325 x 105 Pa 101.325
  kPa (or torr)

6
force of the atmosphere
force of the column
h
when atmospheric force equals the force of the
column the atmospheric pressure is measured as h
7
Gas Laws

• Boyles Law
• P µ 1/V constant T, n
• volume increases as pressure decreases
• Charles Law
• V µ T constant P, n
• volume increases as temperature increases
• Avogadros Law
• V µ n constant P, T
• volume increases as moles of gas (n) increases

8

• Ideal Gas Law
• combines all gas laws PV nRT
• R 0.0821 L-atm mol-K
• any volumes must be in liters
• any temperatures must be in kelvin
• any pressures must be in atmospheres
• STP or SC -- standard temperature/pressure
• P 1 atm (same as 760 mm Hg)
• T 273 K (same as 0 C)

9

• Problem 10.3 A flashbulb contains 2.4 x 10 -4
  mol of O2 gas at 1.9 atm and 19C . What is the
  volulme?
• PV nRT or V nRT
  P
• V 2.4x10 -4 mol x 0.0821 L-atm x 292
  K
  mol-K 1.9
  atm

V 3.0 x 10 -3 L or 3.0 mL or
3.0 cm3
10
Gas Laws Under Two Conditions

• P1V1 P2V2 T1 T2
• Problem 10.4 Pressure in a tank is kept at
  2.20 atm. When the temp. is -15C the volume is
  28,500 ft3. What is the volume is the temp. is
  31C
• P1 P2 2.20 atm T1 258 K T2 304 K
  V1 28,500 ft3
• V2 P1 V1 T2 P2 T1
• V2 28,500 ft3 x 304 K
  258 K

33,600 ft3
11
Gas Densities

• n P from PV nRT V RT
• n moles x g/mol g d PMM V
  L L RT
• d PMM RT

(atm)g mol L atm ( K)mol K
12
Daltons Law of Partial Pressures

• total pressure of a mixture sum of each
  partial pressure
• PT P1 P2 P3 . . . .
• each partial pressure the pressure each gas
  would have if it were alone
• P1 n1RT P2 n2RT P3 n3RT
  V1 V2 V3
• PT n1RT n2RT n3RT (n1 n2 n3)
  RT V1 V2 V3
  V

volumes are the same
13

• P1 n1 therefore P1 n1 PT PT
  nT nT n1
  X1 mole fractionnT P1 X1 PT

14
Kinetic Molecular Theory

• Gases consist of particles in constant, random
  motion
• Volume of gas particles is negligible
• Attractive and repulsive forces are negligible
• Average kinetic energy is proportional to
  temperature
• Collisions are elastic

15

• molecular speed
• u root mean square speed or speed of molecule
  with average kinetic energy
• R is the gas constant (8.314 J/mol-K), T is temp.
  in K MM is molar mass
• What is the rms speed of an He atom at 25C?
• u (3 x 8.314 kg-m2/s2-mol-K x 298 K)1/2
  ( 4.00 x 10 -3
  kg/mol )
• u

1.36 x 103 m/s
16

• Effusion/Diffusion
• small molecules will effuse/diffuse faster than
  large molecules
• effusiondiffusion

17

• Grahams Law
• where r is rate of
  speed MM is the molar mass
• Problem 10.14 Calculate the ratio of the
  effusion rates of N2 and O2.

rN2 1.07 rO2
18
Deviation from Ideality

• Occurs at very high pressure or very low
  temperature
• Correction due to volume
• ideal law assumes molecules have no volume
• for molecules which are far apart, this is a good
  assumption
• must correct for the volume of the molecules
  themselves

19

• Correction due to attraction of molecules
• ideal law assumes the molecules have no
  attraction to each other
• for molecules which are far apart, this is a good
  assumption
• must correct for actual attraction of molecules

correction for molecular volume
correction for molecular attraction