Atkins’ Physical Chemistry Eighth Edition Chapter 21 – Lecture 1 Molecules in Motion Copyright © 2006 by Peter Atkins and Julio de Paula Peter Atkins Julio de Paula

Objectives: Describe the motion of all types of particles in all types of fluids Concentrate of transportation properties: Diffusion ≡ migration of matter down a concentration gradient Thermal conduction ≡ migration of energy down a temperature gradient Electrical conduction ≡ migration of charge along a potential gradient Viscosity ≡ migration of linear momentum down a velocity gradient

Kinetic Molecular Theory of Gases 1.A gas is composed of widely-separated molecules. The molecules can be considered to be points; that is, they possess mass but have negligible volume. 2.Gas molecules are in constant random motion. 3.Collisions among molecules are perfectly elastic. 4.The average kinetic energy of the molecules is proportional to the temperature of the gas in kelvins. KE ∝ T

Fig 21.1 The pressure of a gas arises from the impact of its molecules on the wall

Effect of Temperature on Molecular Speeds Effect of Temperature on Molecular Speeds u rms ≡ root-mean-square speed Hot molecules are fast, cold molecules are slow u rms = 3RT (MM)  R = J/(mol K)

The distribution of speeds of three different gases at the same temperature u rms = 3RT (MM)  Fig Effect of Molecular Mass on Molecular Speeds Heavy molecules are slow, light molecules are fast

Fig 21.3 Distribution of speeds with temperature and molar mass Maxwell distribution for fraction (f) of molecules with speeds from v to v + d v

Maxwell Distribution of Speeds Decaying exponential – very few high speed molecules M/2RT forces exp to zero for high molar mass molecules M/2RT keeps exp high for high temperatures v 2 exp goes to zero as v goes to zero: few slow molecules Remaining factors ensure that all speeds are normalized

Fig 21.4 To obtain probability, integrate f(v) between v 1 and v 2

Fig 21.4 Summary of conclusions for Maxwell distribution Most probable speed Mean speed Relative mean speed

Fig 21.8 Schematic of a velocity selector Fast rotation will select fast molecules Slow rotation will select slow molecules

The collision frequency: where σ = πd 2 ≡ collision cross-section N = N/V ≡ number molecules / volume N In terms of pressure :

Fig 21.9 Volume swept by a moving molecule

The mean free path: Substituting in terms of pressure : The mean free path: e.g., doubling the pressure decreases mean free path by half Typically λ ≈ 70 nm for nitrogen at 1 atm c ≈ 500 m s -1 at 298 K

Effusion - escape of gas molecules/atoms through a tiny hole

The rate of effusion Graham’s law of effusion ≡ rate of effusion is inversely proportional to the square root of the molar mass Rate of effusion =

Diffusion - the gradual mixing of molecules of one gas with molecules of another by virtue of their kinetic properties NH 3 17 g/mol HCl 36 g/mol NH 4 Cl Brownian motion

Fig The flux of particles down a concentration gradient Fick’s first law of diffusion: If the concentration gradient varies steeply with position, then diffusion will be fast