The cell model of liquids is extended to apply to r-mer molecules. The treatment is based on the four main assumptions : (i) that the liquid can be represented by a quasicrystalline lattice, (ii) that the elements of the r-mers are point-centres which interact according to the Lennard-Jones potential law, (iii) that the mean intermolecular field acting on each point-centre is harmonic and has spherical symmetry, (iv) that all displacements are small. The resulting equation of state expresses a principle of corresponding states for r-mer liquids.The extension of the treatment to a monomer 3r-mer solution makes it possible to study the excess properties of the solution which result from the changes in the mean field caused by mixing. Explicit formulae are given for the excess volume, entropy and internal energy; the importance of the new effects is briefly discussed.

The cell method for pure liquids in the form used by Lennard-Jones and Devonshire is extended to solutions. It is assumed that (a) the constituents are spherical in shape, with an isotropic field of force, (b) the distance of the maximum interaction for AA, BB, and AB pairs is about the same, and (c) there is random mixing. For the mean field in the ``cage,'' the complete 6–12 law, the harmonic oscillator, and the smoothed potential model have been studied. The smoothed potential model (potential curve with vertical walls and flat bottom, both depth and width depending on concentration) fits the liquid state best. For this model, one obtains important corrections on both the heat of mixing and the excess entropy to the classical, strictly regular solutions. These corrections are related to the volume changes on mixing resulting from the changes of interactions. According to the value of εAB*, the excess properties such as volume, entropy, heat of mixing, and free energy present a large variety of shapes, including dissymmetry and inversions which correspond rather nicely to experimental evidence. This model permits discussion of the severe limitations of Longuet-Higgins's recent theory of conformal solutions.

An apparatus is described for measuring the following properties of mixtures of condensed gases : (i) the total vapour pressure, (ii) the condensation (i.e. dew-point) pressure, (iii) the volume change on mixing, (iv) the virial coefficients of the gases at the temperature of the other measurements. Such measurements have been made for the system carbon monoxide + methane at 9067" K, the triple-point of methane. This system was chosen View Article Online within a range of 0.2 mm, corresponding to a temperature constant to cf 0*0007".j . The heat of mixing of the system carbon tetrachloride + neopentane has now been measured. The results (to be published in J. Chem. Physics) confirm the predictions of the cell theory.

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In connection with the theory of solutions proposed by Prigogine and Mathot [J. Chem. Phys. 20, 49 (1952)], total vapor pressures and volume changes on mixing have been measured for the systems: CCl4–C(Me)4  IC6H12–C(Me)4  IIC6H6–C(Me)4  III.Volume changes only for the systems: CCl(Me)3–CCl4  IVCCl2(Me)2–CCl4  VCCl3(Me)–CCl4  VIC(Me)3OH–CCl4  VII. For the first three systems I, II, and III, one observes a positive excess free energy (positive deviations to the Raoult law) together with a negative excess volume (contraction on mixing), whereas for the last four IV, V, VI, and VII there is a gradual passage from negative (IV) to positive (VII) excess volume. These results are discussed in terms of the molecular interactions AA, BB, and AB. Reasonable agreement is observed between Prigogine and Mathot's theory and experiment.