CHEMISTRY 161 Chapter 5 www.chem.hawaii.edu/Bil301/welcome.html

REVISION 1. ideal gas equation p × V = n × R × T R = 8.314 J / mol / K 2. molar volume Vm = 22.4 l 3. Dalton’s Law p = p1 + p2 + …

1. Kinetic Molecular Theory of Gases macroscopic (gas cylinder) microscopic (atoms/molecules) Maxwell (1831-1879) Boltzmann (1844-1906)

Kinetic Energy of Gases physical properties of gases can be described by motion of individual gas atoms/molecules each macroscopic and microscopic particle in motion holds an energy (kinetic energy)

kinetic energy = energy of an object in motion SI Units of Energy energy = force × distance W = F × Δs [W] = [F] × [s] [W] = N m = kg m2 s-2 = J Joule (1818-1889) kinetic energy = energy of an object in motion

Assumptions of the Kinetic Theory of Gases gases are composed of atoms/molecules which are separated from each other by a distance l much more than their own diameter d d = 10-10 m l = 10-3 m….. few m molecules are mass points with negligible volume l

2. gases are constantly in motion in random reactions and hold a kinetic energy gases collide and transfer energy (billiard ball model)

F(inter) = 0 p(inter) = 0 3. gases atoms/molecules do not exert forces on each other (absence of intermolecular interactions) F(inter) = 0 p(inter) = 0

Gas Diffusion

Ekin = ½ m u2 Ekin = ½ m u2 T ∞ ½ m u2 const T = ½ m u2 4. the average kinetic energy of a gas molecule/atom is proportional to the temperature Ekin = ½ m u2 Ekin = ½ m u2 u12 + u22 + u32 + … + uN2 u2 = N T ∞ ½ m u2 const T = ½ m u2

1. Compressibility of gases Applications 1. Compressibility of gases p ∞ 1/V

2. Kinetic energy of gases Ekin = ½ m u2 ∞ T p ∞ T

2. Distribution of Molecular Speeds Maxwell-Boltzmann distribution

activation energy

Quantification Ekin = ½ m u2 = const T Ekin = ½ M u2 = const’ T Ekin = ½ M u2 = 3/2 R T root mean square speed urms =√ (3 R T / M)

Calculate the RMS of molecular helium at 25oC 1. apply urms =√ (3 R T / M) 2. calculate numbers and SI units 1360 ms-1

deviation of ideal gas law 3. Real Gases p × V = n × R × T (n = 1) deviation of ideal gas law at high pressures p ≈ 90 atm

North America Nebula p << 10-10 atm

(van der Waals equation) (p + (a n2 / V2) ) (V – n b) = n R T ideal gas law p V = n R T real gas law (van der Waals equation) (p + (a n2 / V2) ) (V – n b) = n R T corrected volume (volume occupied by molecules) corrected pressure (additional pressure/force from attraction)

REVISION 1. Kinetic Molecular Theory of Gases 2. Distribution of Molecular Speeds Ekin = ½ M u2 = 3/2 R T 3. Real Gas Law (p + (a n2 / V2) ) (V – n b) = n R T

Homework Chapter 5, p. 179-193` problems