deviations from the ideal-gas law. It is called the fugacity coefficient (). The second, the activity coefficient , is a correction for interactions in the liquid phase between the different molecules. This modified or extended Raoult's law is then written as Real solutions In many pairs of liquids, there is no uniformity of attractive forces, i.e., the adhesive (between dissimilar molecules) and cohesive forces (between similar molecules) are not uniform between the two liquids. Therefore they deviate from Raoult's law, which applies only to ideal solutions. Negative deviation When the adhesion is stronger than the cohesion, fewer liquid particles turn into vapor thereby lowering the vapor pressure and leading to negative deviation in the graph. For example, the system of chloroform (CHCl3) and acetone (CH3COCH3) has a negative deviation from Raoult's law, indicating an attractive interaction between the two components that have been described as a hydrogen bond. The system HCl–water has a large enough negative deviation to form a minimum in the vapor pressure curve known as a (negative) azeotrope, corresponding to a mixture that evaporates without change of composition. When these two components are mixed, the reaction is exothermic as ion-dipole intermolecular forces of attraction are formed between the resulting ions (H3O+ and Cl–) and the polar water molecules so that ΔHmix is negative. Positive deviation When the adhesion is weaker than cohesion, which is quite common, the liquid particles escape the solution more easily that increases the vapor pressure and leads to a positive deviation. If the deviation is large, then the vapor pressure curve shows a maximum at a particular composition and forms a positive azeotrope (low-boiling mixture). Some mixtures in which this happens are (1) ethanol and water, (2) benzene and methanol, (3) carbon disulfide and acetone, (4) chloroform and ethanol, and (5) glycine and water. When these pairs of components are mixed, the process is endothermic as weaker intermolecular interactions are formed so that ΔmixH is positive. See also Antoine equation Atomic theory Azeotrope Dühring's rule Henry's law Köhler theory Solubility References Chapter 24, D. A. McQuarrie, J. D. Simon Physical Chemistry: A Molecular Approach. University Science Books. (1997) E. B. Smith Basic Chemical Thermodynamics. Clarendon Press. Oxford (1993) Physical chemistry Equilibrium chemistry Engineering thermodynamics Solutions