Lecture 10 Goals Ch. 8.5c-8.6, p. 399-409 Interpret Enthalpy-Concentration Charts Using Enthalpy-Concentration Charts, solve energy balances for Type 4 changes. Intrepret Multi-phase Enthalpy-Concentration Charts. Using Enthalpy-Concentration Charts, solve energy balances for Type 3 and 4 changes. Understand adiabatic mixing using enthalpy-concentration charts. Use enthalpy concentration charts to solve energy balances with adiabatic mixing. Using Hs Tables (B.11) What is H for 10 mol of HCl in 400 mol H2O at 25 C? Pure solvent and infinitely dilute solution at 25 C Represents energy to dilute a solution of molarity M with an infinite amount of pure water. [ Dilution] Discussion of infinite dilution in your book (p. 396-397) is almost non-sensical. Ignore it. Another common reference state: Infinite Dilution Infinite Dilution The book says that for infinite dilution reference states: What this means is that to convert to an infinite dilution reference state, you must subtract the value listed as Hs() from Hs(r) to convert to H(specific) with reference to infinite dilution. Worksheet #10 Infinite Dilution of HCl Solution (Revisted) Enthalpy Of Mixtures What if Tmix ≠ 25 C? Use cp to bring mixture from 25 C to Tmix. What if we don’t know cp mix? Estimate using Extremely cumbersome… Enthalpy - Concentration charts After trying to calculate enthalpies using heats of solution, we see that this is very cumbersome. Another alternative for data is to use plots and charts. Can use data in Table B.11 to produce a plot of Ĥmixture vs. mole fraction solute. Enthalpy Concentration Charts Enthalpy of mixing, Hs Mass fraction H2SO4 Temperature of Mixing If any two of these are specified the other can be determined from the charts (Degrees of Freedom). Enthalpy Concentration Charts Water, 32 C H2SO4, 77 C Smaller What is the reference state for this figure? What can we say about H2SO4-water bond strength vs. pure components? Stronger, mixing is exothermic. Is the enthalpy of mixing larger or smaller than the pure component enthalpies? Energy Balances using Enthalpy-Conc. Diagrams 1 atm 17 M H2SO4 5 lbm/min, 77 F H2O, x = 1 ?? lbm/min, 77 F 10 M H2SO4 ?? lbm/min, T=120 F Perform Mass Balance: What is Q? Inlet xH2SO4: Energy Balances using Enthalpy-Conc. Diagrams 17 M H2SO4, x = 0.625 5 lbm/min, 77 F H2O, x = 1 ?? lbm/min, 77 F 10 M H2SO4 ?? lbm/min, T=120 F Perform Mass Balance: 1 atm What is Q? Outlet xH2SO4: Energy Balances using Enthalpy-Conc. Diagrams 17 M H2SO4, x = 0.625 5 lbm/min, 77 F H2O, x = 1 ?? lbm/min, 77 F 10 M H2SO4, x = 0.495 ?? lbm/min, T=120 F Perform Mass Balance: 1 atm What is Q? H2SO4 Component Balance: Total Mass Balance: Energy Balances using Enthalpy-Conc. Diagrams 17 M H2SO4, x = 0.625 5 lbm/min, 77 F H2O, x = 1 1.31 lbm/min, 77 F 10 M H2SO4, x = 0.495 6.31 lbm/min, T=120 F Perform Energy Balance: 1 atm Determine H(specific) for each stream: What is Q? Adiabatic Mixing 17 M H2SO4, x = 0.625 5 lbm/min, 77 F -121 Btu/lbm H2O, x = 1 1.31 lbm/min, 77 F 45 Btu/lbm 1 atm 10 M H2SO4, x = 0.495 6.31 lbm/min, T=?? F ?? Btu/lbm Energy Balances using Enthalpy-Conc. Diagrams 17 M H2SO4, x = 0.625 5 lbm/min, 77 F -121 Btu/lbm H2O, x = 1 1.31 lbm/min, 77 F 45 Btu/lbm 10 M H2SO4, x = 0.495 6.31 lbm/min, T=120 F -80 Btu/lbm Solve Energy Balance: 1 atm What is Q? Adiabatic Mixing: H-Conc. Charts Suppose: m1 xa,1 m2 xa,2 m3 xa,3 Why does this matter? H-Conc. Charts are diagrams of H(sp) vs. xa (numerator vs. denominator). This means that the fraction shown here is the slope of a line connecting points 1 and 3 or 2 and 3. Since the slope of 1 and 3 equals 2 and 3, they must lie on the same line. Therefore, for adiabatic changes all points must lie on a connecting line. Your book has a nice proof showing that for an adiabatic system: Adiabatic Mixing 17 M H2SO4, x = 0.625 5 lbm/min, 77 F -121 Btu/lbm H2O, x = 1 1.31 lbm/min, 77 F 45 Btu/lbm 1 atm If this process is now adiabatic: What is final T? What is H(specific)? 10 M H2SO4, x = 0.495 6.31 lbm/min, T=?? F ?? Btu/lbm T ~ 105 F H(specific) = -90 Btu/lbm H-conc. Charts for VLE Systems You will see these again in distillation/separations! Mass fraction H(sp) Liquid phase line Temperature Vapor phase line Reference States H-conc. Charts for VLE Systems Given a T, know xa for V and L phase. Additionally, given mass fraction or V/L can completely define system. H-conc. Charts for VLE Systems Recall the Gibbs Phase Rule (6.2-1): Assuming we have a two component system, with two phases, how many degrees of freedom does this system have? where c = # components, and = # phases 2 H-conc. Charts for VLE Systems What kinds of variables might this system have? P, T, xa, xb On a H-conc. Diagram, one of these is always fixed, which is it? P If we have 2 DF and P is always fixed, we only need to know one other variable to define both phases of the system. H-conc. and the Lever Rule Using the fact that the DF in a VLE sytem are fixed, your book derives the following: This relationship is identical to that of our adiabatic system; therefore, We can connect the phases with a tie line. In this case, corresponding to the system temperature. B C A xf xL xV where L, V are the mass flow of the Liquid and Vapor Using H-conc. for VLE Problems Example 8.5-4 Aq. NH3 in equilibrium with vapor is at 160 F and 1 atm. Liquid phase is 95% of total system mass. What is the wt % of NH3 in each phase and what is the specific enthalpy of the system. xNH3,L = 0.08 xH2O,L = 0.92 H(sp)=110 Btu/lbm xNH3,V = 0.64 xH2O,V = 0.36 H(sp)=855 Btu/lbm 0.05m xNH3,V 0.95m xNH3,L 160 F, 1 atm Using H-conc. for VLE Problems Example 8.5-4 Aq. NH3 in equilibrium with vapor is at 160 F and 1 atm. Liquid phase is 95% of total system mass. What is the wt % of NH3 in each phase and what is the specific enthalpy of the system. 0.05m xNH3,V 0.95m xNH3,L 160 F, 1 atm xNH3,L = 0.08 xH2O,L = 0.92 H(sp)=110 Btu/lbm xNH3,V = 0.64 xH2O,V = 0.36 H(sp)=855 Btu/lbm Worksheet # 11 Using H-conc diagrams Lecture 10 Goals Ch. 8.5c-8.6, p. 399-409 Interpret Enthalpy-Concentration Charts- Figure 8.5-1 Using Enthalpy-Concentration Charts, solve energy balances for Type 4 changes.- Diluted H2SO4 example, Worksheet #11 Use enthalpy concentration charts to solve energy balances with adiabatic mixing.- H2SO4 example, Worksheet #11 Intrepret Multi-phase Enthalpy-Concentration Charts.-Figure 8.5-2 Lecture 10 Goals Ch. 8.5c-8.6, p. 399-409 Using Enthalpy-Concentration Charts, solve energy balances for Type 3 and 4 changes. Example 8.5-4, Worksheet #11