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Chapter 1. Introduction – Thermodynamics for Process and Product
Design
Problem 1. What fits best?
Match each sentence (system or condition) of column A in table 1.7 with the correct/expected
answer indicated in column B, as shown for example in the case of n-pentane/n-hexane.
Table 1.7. What fits best?
A
n-pentane/n-hexane
B
  1 (ideal solution)
CHCl3/acetone
Water/n-hexane
Methanol/n-pentane
n-pentanol/n-hexanol
Polyethylene/n-hexane
y1  x1
Compound A is “similar to” compound B
 i 1
ˆi  1
Almost ideal solution
Strong negative deviations from Raoult’s law
Ideal gas
Azeotrope
Negative deviations from Raoult’s law
  of order of several thousands
 1
Ideal liquid solution
  of order of 20-50
Problem 2. Ideal solutions
Figure 1.7. (Left): Pxy diagram of the methanol – ethanol mixture at 50 oC. Experimental data
are taken from G.C. Schmidt, Z. Phys. Chem. (Leipzig), 1926, 121, 221. (Right): Txy diagram for
the same mixture at 1 bar. Experimental data are taken from Amer et al., Ind. Eng. Chem., 1956,
48, 142. The lines are guide to the eye.
Figure 1.7 shows the phase diagram of an ideal solution.
i. Show that for ideal binary solutions, the pressure is given by the equation:
P  x1 ( P1sat  P2sat )  P2sat
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ii. What is the vapour pressure of methanol and of ethanol at 50 oC?
iii. What is the normal boiling temperature of methanol and of ethanol?
iv. Are the P-xy or the T-xy diagrams most useful in distillation studies and why?
Problem 3. Relative volatilities
The relative volatility is defined as the ratio of the equilibrium factors as:
aij 
Ki
Kj
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y
Ki  i
xi
Show that the relative volatility of a binary mixture is given by the following expressions:
P1sat
i. a12  sat if all components obey the Dalton-Raoult law
P2
 1 P1sat
ii. a12 
if all components obey the modified Raoult’s law
 2 P2sat
iii. Prove that for any binary mixture, the mole fractions in the vapour and liquid phase are
related to the relative volatility via the equation:
y1 
a12 x1
1  (a12  1) x1
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iv. Distillations are often preferred at low pressures. Why?
Problem 4. Multiple choice questions
Fill in table 1.8. Only one answer is correct for each question.
Table 1.8. Multiple choice questions.
1. Negative deviations from Raoult’s law exist when…
a.
The activity coefficients are negative
b.
The activity coefficients have values between 1 and 2
c.
Azeotropes are present
d.
The pressure of the solution is below the value given by Raoult’s law
2. An ideal liquid solution …
a.
Implies that forces between “like” and “unlike” molecules and size/shape of molecules
are similar
b.
Exists for all mixtures with hydrocarbons
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c.
d.
Exists for polymer solutions if the repeating unit of the polymer is functionally similar to
the solvent
Is always the case when we have aqueous solutions
3. Raoult’s law is valid for...
a.
Ideal gases
b.
Ideal liquid solutions at low pressures
c.
Mixtures of hydrocarbons
d.
Mixtures of alcohols
4. Cubic equations of state are …
a.
Cubic with respect to volume
b.
Cubic with respect to pressure
c.
Cubic with respect to temperature
d.
Called “cubic” for no special reason
5. Only ONE of the following laws/equations does NOT indicate some form of “ideality” in
thermodynamics. Which one?
a.
PV  nRT
b.
Raoult’s law
c.
Lewis-Randall law
d.
Soave-Redlich-Kwong equation of state
6. ˆi designates (in thermodynamics) …
a.
The activity coefficient of compound i
b.
The fugacity coefficient of pure compound i
c.
The fugacity of compound i in a mixture
d.
The fugacity coefficient of compound i in a mixture
7. Polymers in mixtures with low molecular weight chemicals typically form in the liquid
state…
a.
Non-ideal solutions if the molecular weight of the polymer is above 50000 g/mole
b.
Non-ideal solutions due to the large size (molecular weight) difference
c.
Ideal solutions if the repeating unit of the polymer and the chemical have similar
structures
d.
Non-ideal solutions due to pronounced energy differences
8. The concept of activity coefficients is introduced in thermodynamics basically because…
a.
The framework of Gibbs using the chemical potential is not general enough
b.
Fugacity coefficients cannot be used for liquids
c.
It is easier to use than the fugacity coefficients
d.
Many traditional models like cubic equations of state do not represent satisfactorily both
the vapour and liquid phases
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