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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