PRACTICE PROBLEMS—MID EXAM 2 (CHE-604)1. It has been claimed that the equation of state: Z = 1 + (BP/RT) can be

expressed in a V-explicit as well as in a P-explicit form. If so, similar

to the ideal gas equation of state PV = RT, one should be able to compute

residual properties (e.g. GR, HR, SR) using two different types of

integrals and both approaches should lead to the same expression for the

computed residual property. Test whether this claim is true for the given

equation of state by computing GR using V-explicit and P-explicit

integrals.

2. A certain gas is described by the following equation of state:

PV = RT + (b where b is a constant and

𝜽

𝑹𝑻

)P

𝜽 is only a function of T.

For this gas, determine the expressions for quantities

below:

(a) the expression for isothermal compressibility

(b) the expression for a new quantity called the thermal pressure

𝝏𝑷

coefficient, which is defined as: (𝝏𝑻)

𝑽

3. The expression for total solution property of a binary mixture is given

by M = Ax1x2. Compute partial molar properties of individual components in

this mixture and test if the computed partial properties satisfy all

conditions for consistency.

4. Using the van der Waals equation of state given below, find an

𝝏𝑯

expression for the derivative ( 𝝏𝑻 )

𝑺

only in terms of T, V, a, b, R, and Cp,

where a and b are constants independent of temperature. The van der Waals

equation of state is given as:

𝑷=

𝑹𝑻

𝒂

− 𝟐

𝑽−𝒃 𝑽

5. The molar enthalpy of a binary mixture of hydrogen fluoride

component 1) and water (component 2) at 20°C is given by:

H = −1850 – 28240𝒙𝟏 + 26800𝒙𝟐𝟏

[J/mol]

Calculate the partial molar enthalpy of water in this mixture at 𝒙𝟏 = 𝟎. 𝟒.

MIDEXAM-2 (CHE604)

April 16th (Thu.) ONLINE; noon-2:00PM

Exam Format (Open Book/Notes)

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Material: All topics/material covered since the first mid-exam until 4/15/2020

100 points

3 to 5 questions with multiple sub-parts

Submission

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Exam will be released 5 minutes before noon (i.e. 11:55am) and online submission will close 5 minutes

after 2pm (i.e. 2:05pm)

A new online submission for MidExam2 will appear on the exam day. Submission of files is identical to

homework with the following formats allowed: .jpg, .jpeg, .doc, .docx, and .pdf. A single

PDF file is HIGHLY preferred.

Online system will stop accepting submissions after 2:05pm. Please strictly stick to the deadline.

Major concepts

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Closed system fundamental equations, Maxwell-Relations, Gibbs-energy as a generating function

Residual property calculations using equations of state and generalized correlations

Bubble point/Dew point/Flash calculations

Open system fundamental equations

Chemical potential definitions and connections with the Gibbs energy

Partial property definitions and conditions (e.g. Gibbs-Duhem)

Calculations on partial properties in mixtures (binary, ternary, and higher-order)

Fugacity and Fugacity coefficients calculations

Activity coefficient calculations from Excess Gibbs Energy Models

While questions of the type that appeared in the first exam will NOT be on the second exam, the concepts

learned about first law, second law, ideal gases, and very importantly energy balances for Process

Equipment are highly important to revise since they could be used in many ways for problems related to

recent material for the second mid-exam.

Relevant HW and Practice Sets

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HW6 through HW10; HW10 will be assigned on 4/13.

Practice Problem Sets 6 through 10

MID-TERM-EXAM-2

CHE-604

CHEMICAL ENGINEERING THERMODYNAMICS

Time: 12:00-2:00PM

NAME:

1. [40 points]

The molar enthalpy of a ternary mixture/solution of species a, b, and c is

given by the following expression:

H = -500𝒙𝒂 𝒙𝒃 𝒙𝒄 –5000𝒙𝒂 –3000𝒙𝒃 -2200𝒙𝒄 [J/mol]

(i)

(ii)

(iii)

Find the expressions for partial molar enthalpies of species a

and b.

Calculate the value of the partial molar enthalpy of species a

for an equimolar ternary solution of species a, b, and c.

Find the value of the partial molar enthalpy of species b for a

solution with 1 mole of b, but no a or c present.

2. [40 points]

Find the expressions for the residual molar enthalpy (HR) and residual

molar entropy (SR) for a fluid that is described by each of the following

equations of state:

𝑹𝑻

𝒂

(i)

𝑷=

(ii)

𝑹𝑻𝒁 = 𝑹𝑻 + 𝑪𝑷𝟐 ; where C is a constant

𝑽

+ 𝑽𝟐; where a is a constant

3. [20 points]

(i)

(ii)

Determine the value of GR/RT and fugacity for an unknown gas at

327°C and 300bar. It is given that Tc = 430.8K; Pc = 78.84bar;

𝜔 = 0.245.

Determine whether the following statement is true or false:

𝝏𝑷

𝝏𝑻

( ) = −( )

𝝏𝑺 𝑽

𝝏𝑽 𝑺

(iii)

Determine whether the following statement is true or false:

For 𝑯(𝑻, 𝑷): 𝒅𝑯 = 𝑪𝒑𝒅𝑻 + (𝟏 − 𝜷𝑻)𝑽𝒅𝑷.

The exam is now set-up online and you can access it under /exams/ module. The actual exam pdf will appear

at scheduled time.

Submissions works in the same way as homework.

Please follow these best practices as they will facilitate easier grading of your exams:

1. Attempt each question on a new sheet of paper and write solutions in much LARGER font than usual

2. Attempt each question only once and NOT multiple times in different ways

3. If possible, write only with blue/black pen INSTEAD of a pencil. Pencil is acceptable but the work does not

scan well when written with a pencil.

4. Scan and make a single file for upload, preferably a pdf–it is SUPER helpful in grading.

5. Review everything carefully before uploading. Two submissions will NOT be allowed.

Summary: Use Large font, write with pen (not pencil), each question on a new sheet of paper, and scan into

a single PDF for online upload.

The exam is now set-up online and you can access it under /exams/ module. The actual exam pdf will appear

at scheduled time.

Submissions works in the same way as homework.

Please follow these best practices as they will facilitate easier grading of your exams:

1. Attempt each question on a new sheet of paper and write solutions in much LARGER font than usual

2. Attempt each question only once and NOT multiple times in different ways

3. If possible, write only with blue/black pen INSTEAD of a pencil. Pencil is acceptable but the work does not

scan well when written with a pencil.

4. Scan and make a single file for upload, preferably a pdf–it is SUPER helpful in grading.

5. Review everything carefully before uploading. Two submissions will NOT be allowed.

Summary: Use Large font, write with pen (not pencil), each question on a new sheet of paper, and scan into

a single PDF for online upload.

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