Mixture Properties and Phase Equilibria - Thermodynamics - Chemical Engineering Previous Year Questions

1

2007 · Chemical Engineering · Thermodynamics · Mixture Properties and Phase Equilibria

Chemical Engineering (CH) 2007

If \(m_i, \bar{m}_i, m_i^R, m_i^E\) are molar, partial molar, residual and excess properties respectively for a pure species “i”, the mixture property \(M\) of a binary non-ideal mixture of components 1 and 2, is given by

A

\(x_1 \bar{m}_1 + x_2 \bar{m}_2\)

B

\(x_1 m_1^R + x_2 m_2^R\)

C

\(x_1 m_1 + x_2 m_2\)

D

\(x_1 m_1^E + x_2 m_2^E\)

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2

2008 · Chemical Engineering · Thermodynamics · Mixture Properties and Phase Equilibria

Chemical Engineering (CH) 2008

The molar volume (v) of a binary mixture, of species 1 and 2 having mole fractions \( x_1 \) and \( x_2 \) respectively is given by \( v = 220 x_1 + 180 x_2 + x_1 x_2 (90 x_1 + 50 x_2) \)
The partial molar volume of species 2 at \( x_2 = 0.3 \) is

A

183.06

B

212.34

C

229.54

D

256.26

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3

2008 · Chemical Engineering · Thermodynamics · Mixture Properties and Phase Equilibria

Chemical Engineering (CH) 2008

An ideal flash vaporization is carried out with a binary mixture at constant temperature and pressure. A process upset leads to an increase in the mole fraction of the heavy component in the feed. The flash vessel continues to operate at the previous temperature and pressure and still produces liquid and vapor. After steady state is re-established,

A

the amount of vapor produced will increase

B

the amount of liquid produced will decrease

C

the new equilibrium compositions of the vapor and liquid products will be different

D

the new equilibrium compositions of the vapor and liquid products will remain as they were before the upset occurred

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4

2009 · Chemical Engineering · Thermodynamics · Mixture Properties and Phase Equilibria

Chemical Engineering (CH) 2009

For a binary mixture at constant temperature and pressure, which ONE of the following relations between activity coefficient (\(\gamma_i\)) and mole fraction (\(x_i\)) is thermodynamically consistent?

A

\(\ln \gamma_1 = -1 + 2x_1 - x_1^2, \; \ln \gamma_2 = \frac{1}{2} x_1^2\)

B

\(\ln \gamma_1 = -1 + 2x_1 - x_1^2, \; \ln \gamma_2 = x_1^2\)

C

\(\ln \gamma_1 = -1 + 2x_1 - x_1^2, \; \ln \gamma_2 = -\frac{1}{2} x_1^2\)

D

\(\ln \gamma_1 = -1 + 2x_1 - x_1^2, \; \ln \gamma_2 = -x_1^2\)

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5

2010 · Chemical Engineering · Thermodynamics · Mixture Properties and Phase Equilibria

Chemical Engineering (CH) 2010

An equimolar liquid mixture of species 1 and 2 is in equilibrium with its vapour at 400 K. At this temperature, the vapour pressures of the species are \( P_1^{sat} = 180 \) kPa and \( P_2^{sat} = 120 \) kPa. Assuming that Raoult's law is valid, the value of \( y_1 \) is

A

0.30

B

0.41

C

0.50

D

0.60

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6

2010 · Chemical Engineering · Thermodynamics · Mixture Properties and Phase Equilibria

Chemical Engineering (CH) 2010

At constant T and P, the molar density of a binary mixture is given by \( \rho = 1 + x_2 \), where \( x_2 \) is the mole fraction of component 2. The partial molar volume at infinite dilution for component 1, \( \bar{V}_1^\infty \), is

A

0.75

B

1.0

C

2.0

D

4.0

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7

2011 · Chemical Engineering · Thermodynamics · Mixture Properties and Phase Equilibria

Chemical Engineering (CH) 2011

Minimum work (\(W\)) required to separate a binary gas mixture at a temperature \(T_0\) and pressure \(P_0\) is
\[W = -RT_0 \left[ y_1 \ln \left( \frac{\hat{f}_1}{f_{pure,1}} \right) + y_2 \ln \left( \frac{\hat{f}_2}{f_{pure,2}} \right) \right]\]
where \(y_1\) and \(y_2\) are mole fractions, \(f_{pure,1}\) and \(f_{pure,2}\) are fugacities of pure species at \(T_0\) and \(P_0\), and \(\hat{f}_1\) and \(\hat{f}_2\) are fugacities of species in the mixture at \(T_0\), \(P_0\) and \(y_1\). If the mixture is ideal then \(W\) is

A

0

B

\(-RT_0 [ y_1 \ln y_1 + y_2 \ln y_2 ]\)

C

\(RT_0 [ y_1 \ln y_1 + y_2 \ln y_2 ]\)

D

\(RT_0\)

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8

2011 · Chemical Engineering · Thermodynamics · Mixture Properties and Phase Equilibria

Chemical Engineering (CH) 2011

The partial molar enthalpies of mixing (in J/mol) for benzene (component 1) and cyclohexane (component 2) at 300 K and 1 bar are given by \(\Delta \bar{H}_1 = 3600 x_2^2\) and \(\Delta \bar{H}_2 = 3600 x_1^2\), where \(x_1\) and \(x_2\) are the mole fractions. When ONE mole of benzene is added to TWO moles of cyclohexane, the enthalpy change (in J) is

A

3600

B

2400

C

2000

D

800

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9

2011 · Chemical Engineering · Thermodynamics · Mixture Properties and Phase Equilibria

Chemical Engineering (CH) 2011

Consider a binary mixture of methyl ethyl ketone (component 1) and toluene (component 2). At 323 K the activity coefficients \( \gamma_1 \) and \( \gamma_2 \) are given by \( \ln \gamma_1 = x_2^2 (\psi_1 - \psi_2 + 4\psi_2 x_1) \), \( \ln \gamma_2 = x_1^2 (\psi_1 + \psi_2 - 4\psi_2 x_2) \) where \( x_1 \) and \( x_2 \) are the mole fractions in the liquid mixture, and \( \psi_1 \) and \( \psi_2 \) are parameters independent of composition. At the same temperature, the infinite dilution activity coefficients, \( \gamma_1^\infty \) and \( \gamma_2^\infty \) are given by \( \ln \gamma_1^\infty = 0.4 \) and \( \ln \gamma_2^\infty = 0.2 \). The vapour pressures of methyl ethyl ketone and toluene at 323 K are 36.9 and 12.3 kPa respectively. Assuming that the vapour phase is ideal, the equilibrium pressure (in kPa) of a liquid mixture containing 90 mol % toluene is

A

19

B

18

C

16

D

15

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10

2012 · Chemical Engineering · Thermodynamics · Mixture Properties and Phase Equilibria

Chemical Engineering (CH) 2012

Consider a binary liquid mixture at constant temperature \( T \) and pressure \( P \). If the enthalpy change of mixing, \( \Delta H = 5 x_1 x_2 \), where \( x_1 \) and \( x_2 \) are the mole fraction of species 1 and 2 respectively, and the entropy change of mixing \( \Delta S = -R [x_1 \ln x_1 + x_2 \ln x_2] \) (with \( R = 8.314 \) J/mol.K), then the minimum value of the Gibbs free energy change of mixing at 300 K occurs when

A

\(x_1 = 0 \)

B

\(x_1 = 0.2 \)

C

\(x_1 = 0.4 \)

D

\(x_1 = 0.5 \)

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11

2013 · Chemical Engineering · Thermodynamics · Mixture Properties and Phase Equilibria

Chemical Engineering (CH) 2013

A binary liquid mixture is in equilibrium with its vapor at a temperature T = 300 K. The liquid mole fraction \(x_1\) of species 1 is 0.4 and the molar excess Gibbs free energy is 200 J/mol. The value of the universal gas constant is 8.314 J/mol-K, and \(\gamma_i\) denotes the liquid-phase activity coefficient of species i. If \(\ln(\gamma_1) = 0.09\), then the value of \(\ln(\gamma_2)\), up to 2 digits after the decimal point, is ______

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12

2014 · Chemical Engineering · Thermodynamics · Mixture Properties and Phase Equilibria

Chemical Engineering (CH) 2014

Consider a binary liquid mixture at equilibrium with its vapour at 25 °C. Antoine equation for this system is given as \( \log_{10} P_i^{sat} = A - \frac{B}{t + C} \) where t is in °C and P in Torr. The Antoine constants (A, B, and C) for the system are given in the following table:

Component	A	B	C
1	7.0	1210	230
2	6.5	1206	223

The vapour phase is assumed to be ideal and the activity coefficients (\( \gamma_i \)) for the non-ideal liquid phase are given by
\( \ln(\gamma_1) = x_2^2 [2 - 0.6 x_1] \)
\( \ln(\gamma_2) = x_1^2 [1.7 + 0.6 x_2] \)
If the mole fraction of component 1 in liquid phase (\( x_1 \)) is 0.11, then the mole fraction of component 1 in vapour phase (\( y_1 \)) is ______

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13

2017 · Chemical Engineering · Thermodynamics · Mixture Properties and Phase Equilibria

Chemical Engineering (CH) 2017

A sparingly soluble gas (solute) is in equilibrium with a solvent at 10 bar. The mole fraction of the solvent in the gas phase is 0.01. At the operating temperature and pressure, the fugacity coefficient of the solute in the gas phase and the Henry's law constant are 0.92 and 1000 bar, respectively. Assume that the liquid phase obeys Henry's law.

The MOLE PERCENTAGE of the solute in the liquid phase, rounded to 2 decimal places, is __________.

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14

2017 · Chemical Engineering · Thermodynamics · Mixture Properties and Phase Equilibria

Chemical Engineering (CH) 2017

The vapour pressure of a pure substance at a temperature \( T \) is 30 bar. The actual and ideal gas values of \( g/RT \) for the saturated vapour at this temperature \( T \) and 30 bar are 7.0 and 7.7, respectively. Here, \( g \) is the molar Gibbs free energy and \( R \) is the universal gas constant.

The fugacity of the saturated liquid at these conditions, rounded to 1 decimal place, is __________ bar.

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15

2018 · Chemical Engineering · Thermodynamics · Mixture Properties and Phase Equilibria

Chemical Engineering (CH) 2018

G denotes the Gibbs free energy of a binary mixture, n_T denotes the total number of moles present in the system, \mu_i is the chemical potential of the i^{th} component (\mu_1 \neq 0 and \mu_1 > \mu_2 ) and x_i is the mole fraction of the i^{th} component. The correct variation of G/n_T (in J/mol) at constant temperature and pressure is given by

A

B

C

D

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16

2019 · Chemical Engineering · Thermodynamics · Mixture Properties and Phase Equilibria

Chemical Engineering (CH) 2019

Consider a sealed rigid bottle containing CO₂ and H₂O at 10 bar and ambient temperature. Assume that the gas phase in the bottle is pure CO₂ and follows the ideal gas law. The liquid phase in the bottle contains CO₂ dissolved in H₂O and is an ideal solution. The Henry’s constant at the system pressure and temperature is H_CO2 = 1000 bar. The equilibrium mole fraction of CO₂ dissolved in H₂O is ______ (rounded off to three decimal places).

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17

2019 · Chemical Engineering · Thermodynamics · Mixture Properties and Phase Equilibria

Chemical Engineering (CH) 2019

For a given binary system at constant temperature and pressure, the molar volume (in m³/mol) is given by: \(v = 30x_A + 20x_B + x_Ax_B (15x_A - 7x_B)\), where \(x_A\) and \(x_B\) are the mole fractions of components A and B, respectively. The volume change of mixing \(\Delta v_{mix}\) (in m³/mol) at \(x_A = 0.5\) is __________ (rounded off to one decimal place).

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18

2019 · Chemical Engineering · Thermodynamics · Mixture Properties and Phase Equilibria

Chemical Engineering (CH) 2019

For a binary nonideal A-B mixture exhibiting a minimum boiling azeotrope, the activity coefficients, \( \gamma_i \) (i = A, B), must satisfy

A

\(\gamma_A > 1, \gamma_B > 1 \)

B

\(\gamma_A < 1, \gamma_B > 1 \)

C

\(\gamma_A = 1, \gamma_B = 1 \)

D

\(\gamma_A < 1, \gamma_B < 1 \)

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19

2020 · Chemical Engineering · Thermodynamics · Mixture Properties and Phase Equilibria

Chemical Engineering (CH) 2020

Mole fraction and activity coefficient of component 1 in a binary liquid mixture are \(x_1\) and \(\gamma_1\), respectively. \(G^E\) is excess molar Gibbs energy of the mixture, \(R\) is universal gas constant and \(T\) is absolute temperature of the mixture. Which one of the following is always true?

A

\(\lim_{x_1 \to 1} \frac{G^E}{RT} = 0\)

B

\(\lim_{x_1 \to 1} \frac{G^E}{RT} = 0.5\)

C

\(\lim_{x_1 \to 1} \gamma_1 = 0\)

D

\(\lim_{x_1 \to 1} \gamma_1 = 0.5\)

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20

2021 · Chemical Engineering · Thermodynamics · Mixture Properties and Phase Equilibria

Chemical Engineering (CH) 2021

A gaseous mixture at 1 bar and 300 K consists of 20 mol % CO₂ and 80 mol% inert gas.
Assume the gases to be ideal. Take R = 8.314 J mol^-1 K^-1.
The magnitude of minimum work required to separate 100 mol of this mixture at 1 bar and 300 K into pure CO₂ and inert gas at the same temperature and pressure is __________ kJ (round off to nearest integer).

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