Open Systems Gibbs-Duhem Equation for Partial Molal Volumes

OPEN SYSTEMS GIBBS-DUHEM EQUATION FOR PARTIAL MOLAL VOLUMES 

The relationship we are about to describe is due to the work of Pierre Duhem (1861-1916) a French physicist who translated Gibbs work into French and was in his own rights a prolific author of thermodynamic studies. So far the applications of thermodynamic (except for the on-stream ammonia synthesis discussed above) have been for what are closed systems where it is possible to enclose the system with a boundary and separate it from the environment. Many of the synthetic applications in chemical engineering are carried out with on-stream processing rather than in a batch reactor, a system in which a continuous flow of reactants is processed and continuous product flows out of some sort of reaction chamber. While most laboratory synthesis is carried out in batch fashion, there are also static phenomena, which depend on adding an arbitrary amount of one 

FIGURE 6.7 (a) The total volume of an ammonia-water solution, (b) Volume of a solution of MgS04 in 

We know from other courses in chemistry that 

FIGURE 6.8 Partial molal volumes of water and ethanol. (From Lewis, G.N. and Randall, M., Thermodynamics, McGraw-Hill, New York Barrow, G.A., Physical Chemistry, 5th Edn., McGraw-HiU, New York, 1988. With permission.) 

---