The excess Gibbs energy of a binary liquid mixture at T and P is given by: GE/RT = (-2.6x1 – 1.8x2)x1x2 (a) Find expressions for ln y1 and ln y2 at T and P. b) Show that when these expressions are combined in accord with Eq.(11.99) the given equation for GE/RT is recovered. c) Show that these equations satisfy Eq.(11.100), the Gibbs/Duhem equation. d) Show that (d ln y1/dx1)x1=1 = (dln y2/dx1)x1=0= 0.

Q3. The following information on the pressure-temperature diagram of nitrogen: P (atm) T(K) 0.123 33.3978 1.0 Triple point Critical point Normal boiling point Density of N₂(s): 1.03g/cm-³ N₂(1): 0.808g/cm-³ 63.15 126.19 77.35 Using this information, sketch a phase-equilibrium diagram of nitrogen and mark each point. Then, describe why the slope of each phase/phase equilibrium is positive or negative.

Two liquids A and B mix to form an ideal solution. Consider A to be the solvent (majority component) and B to be the solute (minority component). What is the relationship between the Gibbs energy and chemical potential for a pure phase? How does the Gibbs energy of A(solution) COmpare to Gibbs energy of Apure liquid)? How does the Gibbs energy of B(solution) compare to Gibbs energy of B(pure liquid)? d. When B is added to pure A, what happens to the Gibbs energy of A? а. b. C. e. Why does the Gibbs energy of the solvent of an ideal solution (in this case, A) decrease upon the addition of a solute (in this case, B)? Provide mathematical and conceptual explanations.

Complete the property table for water below. Use only the Thermodynamic Property Table for Water referring to the Smith, Van Ness and Abbot Thermodynamics textbook. P [kPa] V [m³/kg] H[ kJ/kg] T[°C] Phase Description X 500 Saturated liquid 171 2044.5 300 0.8 Note that x refers to the "quality" or the mass fraction of the water in vapor phase. If the system is composed of pure liquid water, x = 0. If the system is composed of pure gaseous steam, x = 1. The volume of a liquid/vapor system can be determined using the following equation. V = Vj + x(Vg-Vj) V - volume of saturated liquid water Va - volume of saturated gaseous steam Similar calculation can be done for other properties such as internal energy, entropy, and enthalpy. H = HỊ + x(Hg-H) Under phase description, indicate whether the system is composed of saturated liquid, saturated vapor, superheated vapor, or liquid-vapor mixture. Also note that when pressure is given, it is more advisable to use the Superheated Steam Table than…