Liquid, fugacity partially miscible

In Chapter 7, we saw that when like a-a and b-b) interactions are significantly stronger than unlike a-b) interactions, liquids can split into two different partially miscible phases, which we labeled a and (3. They form separate phases to lower the total Gibbs energy of the system. In this case, each species i tends to equilibrate between the two phases, leading to liquid-liquid equilibrium (LLE). We can equate the fugacity of component i for each phase to solve for the equilibrium compositions. 

Where R is the gas constant, T the temperature (K), Fthe Faraday constant and H2 is the relative partial pressure (strictly, the fugacity) of hydrogen in solution, which for continued evolution becomes the total external pressure against which hydrogen bubbles must prevail to escape (usually 1 atm). The activity of water a jo is not usually taken into account in elementary treatments, since it is assumed that <7h2 0 = U nd for dilute solutions this causes little error. In some concentrated plating baths Oh2 0 I O nd neither is it in baths which use mixtures of water and miscible organic liquids (e.g. dimethyl formamide). However, by far the most important term is the hydrogen ion activity this may be separated so that equation 12.1 becomes... 

---