Gases

1
Gases

• Chapter 5

2
Kinetic Theory of Gases

• Developed between 1850-1880 by James Maxwell,
  Rudolf Clausius, Ludwig Boltzman, and others.
• Theory is based on the idea that all gases behave
  similarly as far as particle motion is concerned.

3
Kinetic Theory of Gases

• To completely describe the state of a gaseous
  substance the following must be specified
• Volume
• Amount
• Temperature
• Pressure

4
Kinetic Theory of Gases

• Postulates
• All gases consist of particles (atoms, molecules)
  in continuous random motion.
• Collisions between gas molecules are elastic.
  Total energy is constant.
• The volume occupied by the particles is small
  compared to container.
• Attractive forces between particles have a
  negligible effect on their behaviors, act as
  independent particles.
• Et cT, Kinetic energy is directly proportional
  to temperature. At a given T all gases have the
  same KE (Et or translational energy).

5
Ideal Gas Law

• PV nRT
• The Ideal Gas Law can be manipulated depending on
  your conditions.

6
Ideal Gas Law at constant V

• P1V nRT1 P2V nRT2
• P1 nR P2 nR
• T1 V T2 V
• Therefore P1 P2
• T1 T2

7
Ideal Gas Law at constant P

• PV1 nRT1 PV2 nRT2
• V1 nR V2 nR
• T1 P T2 P
• Therefore V1 V2
• T1 T2
• Charles Law

8
Ideal Gas Law at constant T

• P1V1 nRT P2V2 nRT
• Therefore P1V1 P2V2
• Boyles Law

9
Law of Combining Volumes

• Gay-Lussac, 1808
• The volumes of different gases involved in a
  reaction, if measured at the same temperature and
  pressure, are in the same ratio as the
  coefficients in the balanced equation.

10
Partial Pressure and Mole Fraction

• John Dalton 1801 The total pressure of a gas
  mixture is the sum of the partial pressures of
  the components of the mixture.
• PTotal PA PB PC
• Partial pressures may be found by using the ideal
  gas law PV nRT

11
Partial Pressure and Mole Fraction

• PA nA x RT/ V PTotal nTotal x RT/ V
• Dividing PA by PTotal
• PA/PTotal nA/ nTotal or PA nA/nTotal x
  PTotal
• The fraction of nA/ nTotal is called the mole
  fraction of A in the mixture. The symbol used
  for mole fraction is X.
• Therefore PA XA PTotal or the partial pressure
  of a gas in a mixture is equal to its mole
  fraction multiplied by the total pressure.

12

• Grahams Law
• Average Speed of Gas Particles
• Real Gases
• Van Der Waals Equation

13
Average speeds (u) of Gas Particles

• u (3RT/ M)1/2 M Molar mass
• From this we can see average speed is directly
  proportional to the square root of the absolute
  temperature
• u2/ u1 (T2/ T1)1/2
• From this we can see average speed is indirectly
  proportional to the square root of molar mass (M)
• uB/ uA (MA/ MB)1/2

14
Diffusion and Effusion of Gases Grahams Law

• Thomas Graham, 1829
• Diffusion refers to the movement of gas particles
  through space, from a region of high
  concentration to one of low concentration.
• Effusion is the flow of gas particles through
  tiny pores or pinholes.
• Effusion depends on two factors
• The concentration
• The relative velocity of the particle

15
Diffusion and Effusion of Gases Grahams Law

• If two different gases A and B are compared at
  the same pressure, only their speeds are of
  concern, and
• rate of effusion B uB/ uA
• rate of effusion A
• So, at constant pressure and constant
  temperature,
• rate of effusion B (MA/ MB)1/2
• rate of effusion A

16
Real Gases

• All real gases deviate slightly from the ideal
  gas law. This occurs largely at
• high pressures
• low temperatures.
• From a molecular standpoint these deviations are
  due in part to
• Attractive forces between gas particles
• The finite volume of gas particles