Atkins’ Physical Chemistry Eighth Edition Chapter 1 The Properties of Gases Copyright © 2006 by Peter Atkins and Julio de Paula Peter Atkins Julio de Paula

Consider a case in which two gases, A and B, are in a container of volume V at a total pressure P T P A = n A RT V P B = n B RT V n A is the number of moles of A n B is the number of moles of B P T = P A + P B X A = nAnA n A + n B X B = nBnB n A + n B P A = X A P T P B = X B P T P i = X i P T mole fraction (X i ) = nini nTnT Dalton’s Law of Partial Pressures

An “Ideal Gas” Assumptions: Gas molecules do not exert any force (attractive or repulsive) on each other i.e., collisions are perfectly elastic Volume of molecules themselves is negligible compared to volume of container i.e., the molecules are considered to be points An ideal gas “obeys” PV = nRT i.e., calculated value ≈ experimental value

Real Gases Assumptions made in the kinetic-molecular model:  negligible volume of gas molecules themselves  no attractive forces between gas molecules These breakdown at high pressure and/or low temperature.

Fig 1.13 Variation of the potential energy of two molecules on their separation.  Attractions between electrons and nuclei  Repulsions between electrons  Repulsions between nuclei

Fig 1.14 Variation of the compression factor, Z, with pressure for several gases at 0 o C Compression factor: For a perfect gas Z = 1 under all conditions At high P: Z >1 (large V m ) At lower P: Z < 1 for most gases (attractive forces predominate)

Fig 1.15 Experimental isotherms of CO 2 at several temperatures At high V m and high P real isotherms ≈ perfect isotherms ∴ perfect gas law can be expressed as a virial equation of state: i.e., PV = nRT treated as a power series expansion in V

Fig 1.15 Experimental isotherms of CO 2 at several temperatures T c is the critical temperature ≡ at T ≥ T c gas will not form two phases when compressed The critical point is defined with critical constants ≡ T c, P c, V c Above the critical point a supercritical fluid exists

Supercritical CO 2 The low critical temperature and critical pressure for CO 2 make supercritical CO 2 a good solvent for extracting nonpolar substances (like caffeine)

Diagram of a supercritical fluid extraction process

The van der Waals Equation ) ( V − nb ) = nRT n2an2a ( P + V2V2 Eqn 1.21a

Fig 1.8 A region of a P-V-T surface of a perfect gas surface of a perfect gas Fig 1.17 A region of a P-V-T surface of a vdW gas surface of a vdW gas

When van der Waals equation fails:

Principle of Corresponding States To compare properties of systems choose a fundamental property of the same kind and set up a relative scale Critical constants are characteristic of each gas Introduce dimensionless reduced variables: e.g., gases at the same V r and T r will exert the same P r Called the Principle of Corresponding States (approximation)

Fig 1.19 Compression factors of four gases plotted using reduced variables