Physical chemistry homework help

CHM 360: Exam 2 (100 Points)
(Dated: October 14, 2020)
Abstract
This is a take home exam. You can use any notes, books, or any information you find on the internet. You
cannot post this exam for people to answer for you, work with others, or ask others for help.. This is to be
done by you and you alone. Partial credit will be given, so please include all of your work. Good luck!
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Question 1 (30 points). Please plot out (quantitatively) the phase diagram of a substance A
of molecular weight 127 g/mol that can exist in solid, liquid, and gas phases using the following
information: standard boiling temperature 553.2 K, critical temperature of 660.1 K, standard
melting temperature 328.708
o
C, Cp;solid = 87:4
J
molK
, Cp;liquid = 92:44
J
molK
, Cp;gas = 82:44
J
molK
,
f H
(A(g)) = 57 kJ/mol,
f H
(A(l)) = 50 kJ/mol, and
f H
(A(s)) = 46 kJ/mol,
A(s) = 1:7 g/ml and A(l) = 1:8 g/ml. You may assume coexistence curves are given by the
Clausius Equation (solid-liquid) and the Clausius-Clapeyron equations for an ideal gas (solid-gas,
liquid-gas). (Hint: you’ll need to determine the triple point and triple pressure likely by graphical
means).
Question 2: (20 Points) (a) Please draw the phase diagram for a mixture of substances A and
B, and label the corresponding phases. You’ll need the following information: T
A
boil
= 400K,
T
B
boil
= 350K, T
A
melt
= 140K, T
B
melt
= 100K. For the solid phases, A and B form the compound
A2B that melts congruently at Tmelt = 160K. There exist two eutectics at xA = 0:4 at temperature
of T = 80K and at xA = 0:8 at T = 120K. Finally, there is an azeotrope that boils at T = 250K
at xA = 0:3.
(b) If you start with a liquid solution of 3 moles of A and 5 moles of B, can you fractionally distill
A, or will you end up with the azeotrope? Please explain using your phase diagram above.
Question 3: (10 Points) Consider the T vs. composition phase diagram for two substances,
A and B, that behave ideally. Please explain why in the T vs. composition phase diagrams you
do not observe boiling point elevation for both components A and B when they mix (and that
only one of them experiences boiling point elevation (which one?)). Hint: since these are ideal
solutions, it cannot be due to interactions. Equations are welcome but not necessarily required.
Quesiton 4: (20 points) Consider a sealed container filled with 0.7 moles of H2(g), 0.9 moles of
trans-2 butene C4H8(g) and 0.4 moles of butane (C4H10(g)) at 400K. The initial total pressure in
the container is 2 bar. Calculate the amounts of each component in the mixture at equilibrium for
the reaction H2(g)+C4H8(g) *) C4H10(g). You may not assume that the entropies and enthalpies
are temperature independent (but you can assume Cp’s are temperature independent). You may
treat the gases ideally. Also please calculate
G for going to equilibrium.
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(B) Once the system reached equilibrium, assume you squeezed on the container and reduced
the volume by a factor of 30. Calculate the the new composition of molecules in your container,
and
G for this process of squeezing the equilibrium state in (A) to go to a new equilibrium state.
Problem 5(20 points) Consider the liquid-liquid coexistence curve of two species A and B.
The mole fractions of A in the upper (xu) and lower (xl) phases within the two phase region are
given by:
T=K 309:820 309:432 309:031 308:006 306:686
xl 0:473 0:400 0:371 0:326 0:293
xu 0:529 0:601 0:625 0:657 0:690
(1)
T=K 304:553 301:803 299:097 296:000 294:534
xl 0:255 0:218 0:193 0:168 0:157
xu 0:724 0:758 0:783 0:804 0:814
(A) Plot the phase diagram. (B) Suppose you form a mixture with 2 moles of A and 1 mole of
B at T = 299:1 K. How much of the upper and lower phases do you have? To what temperature
must the mixture be heated to form a single-phase? (C) If A and B can be treated as forming a
regular solution, please determine  as a function of temperature. Plot your results.
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