CHEN 354- HW 3- Due Wednesday, February 6, 2013
Problem 1. Thermodynamics tables and charts for a pure component (for example steam) may be used
to compute G when both H and S are tabulated. Since G = H-TS, at constant temperature, the Gibbs free
energy difference for a system at states 2 and 1 is: G = RT ln (f2/f1) = H –T S. If state 1 is at low
pressure where the gas is ideal, then f1 = P1, and RT ln(f2/P1) = H –T S, where the subscripts indicate
states. Use this method to calculate the fugacity of steam at 400oC and 15 MPa. What value does the
fugacity coefficient ( = f/P) have at this pressure?
Problem 2. This problem reinforces the concepts of phase equilibria for pure substances.
(a) Use steam table data to calculate the Gibbs energy of 1kg saturated steam at 150oC, relative to
steam at 150oC and 50 kPa (the reference state). Perform the calculation by plotting the volume data
and graphically integrating. Express your answer in kJ.
(b) Repeat the calculations using the tabulated enthalpies and entropies. Compare your answer to part
(a).
(c) The saturated vapor from part (a) is compressed at constant T and ½ kg condenses. What is the total
Gibbs free energy of the vapor-liquid mixture relative to the reference state of part (a)? What is the total
free energy relative to the same reference state when the mixture is completely condensed to form
saturated liquid?
(d) What is the Gibbs energy of liquid water at 600 kPa and 150oC relative to the reference state from
part (a)? You may assume that the liquid is incompressible.
Problem 3. The molar volume (in cm3/mol) of a binary liquid mixture at T and P is given by
V  320x1  180x2  (20x1  12x2 ) x1x2
a) Find expressions for the partial molar volumes of species 1 and 2 at T and P.
b) Show that when these expressions are combined in accord to M   M i xi the given equation for V is
i
recovered.
c) Show that these expressions satisfy the Gibbs-Duhem equation.
 dV 
 dV 
d) Show that  1    2   0
 dx1  x11  dx1  x10
e) Plot values of V, V1 ,V2 calculated by the given equation for V and by the equations developed in (a) vs.


x1. Label points V1, V2, V1 ,V2 and show their values.
Problem 4.
The following expressions have been proposed for the partial molar properties of a particular binary
mixture:
M1  M1  Ax2
M 2  M 2  Ax1
Here, parameter A is a constant. Can these expressions be correct?
Hint: Start by writing the Gibbs-Duhem equation at constant T and P and dividing the equation by dx1