3. Derivation of the Equilibrium Conditions Based on the Gibbs Energy Please consider a pure substance in which the vapor phase and a liquid phase are in equilibrium. Let dG¹ =

the change in Gibbs Energy when a differential amount of the liquid phase becomes vapor. a. Please use the Fourth Fundamental Property Relation to show that dGlv - SdTv +Vdplv b. Based on our discussion in class, what is the value of dTv and of dplv? c. Based on the result of Part b, please show that dGlv = 0. d. Please integrate the equation in Part c from the liquid phase to the vapor phase to show that G¹ = Gº. e. Please take the derivative of the result in Part d to show that dG¹ = dGº. f. We derived the results in Parts c, d, and e based on Vapor/Liquid equilibrium. Could a similar result be obtained for Solid/Liquid or Solid/Vapor equilibrium? Please use a sentence or two to explain your response. g. Please allo w and a and ß to represent any two distinct phases. Please rewrite the results in Parts c, d, and e in terms of the general phases a and ß. What is the significance of this result? Please use a sentence or two to explain. 2