HW 10—Due Wednesday, Nov. 12—CHEN 354—Fall 08
Problem 1. Suppose that a binary system exhibits liquid-liquid immiscibility, and the system is at a state
where G1/RT = 0.1 and G2/RT =0.3. The change of Gibbs energy of mixing quantifies the energy of the
mixture relative to the Gibbs energies of the pure components. The excess Gibbs energy for this mixture
is given by GE/RT = 2.5 x1 x2.
(a) Calculate the G of mixing across the composition range and plot the results against x1 to illustrate
that this system exhibits liquid-liquid immiscibility.
(b) Draw a tangent to the humps. For what range of z1 compositions (z1 is the overall composition) the
system will be one phase and for what range of compositions the system will split into two phases?
(c) When a mixture splits into two phases, the overall fractions (of total moles) of the two phases are
found by the lever rule along the composition coordinate. Suppose 0.6 mol of component 1 and 0.4 mol
of component 2 are mixed. Use the lever rule to calculate the total number of moles which would be
found in each phase of the actual system. Specify the phases as the (1)-rich phase and the (2)-rich
phase.
(d) What is the value of the hypothetical Gibbs energy (expressed as G/RT) of a mixture of 0.6 mol of (1)
and 0.4 mol of (2) if the mixture were to remain as one phase? Calculate the Gibbs energy of the total
system considering that the phase splits into two phases, and show that the Gibbs energy is less than
the Gibbs energy of the single-phase system.
Problem 2.
a) Estimate the heat and work flows needed to reversibly and isothermally separate an equimolar
mixture of two species into its pure components if the excess Gibbs energy for the mixture is given by
GE = A x1 x2
where A is independent of temperature.
b) How does the temperature at which W =0 compare with the upper consolute temperature of the
mixture?
c) How would the answers to a and b change if A is a function of temperature?
Problem 3.
The binary liquid mixture of nitromethane (1) and n-nonane (2) exhibit LLE. At 70oC one phase has a
nitromethane mole fraction of 0.131 and the other phase has a n-nonane mole fraction of 0.0247. At
90oC the mole fractions are 0.214 and 0.0469 respectively. Use the Van Laar equations.
a) Estimate the excess Gibbs energy of mixing at each of the temperatures over the whole concentration
range
b) Estimate the excess enthalpy of mixing at 80oC over the whole concentration range.
c) Estimate the excess entropy of mixing at 80oC over the whole concentration range.
Problem 4.
At 25oC, a binary liquid mixture contains nonpolar components 1 and 2. Data for the dilute region of this
mixture indicate that 1∞ =9.3 and 2∞ =4.7. At 25oC, are liquids 1 and 2 miscible in all proportions or is
there a miscibility gap?
GE /RT is given by GE/RT=x1x2(A+B(x1-x2))
with ln 1 = (A+3B)x22-4Bx23
ln 2 =(A-3B)x12+4Bx13
Recommended problems: 14.15, 14.18, 14.20