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RYERSON UNIVERSITY, TORONTO DEPARTMENT OF CHEMICAL ENGINEERING Final Exam: Thermodynamics CHE214 Time: 2-5pm Question \#1: ( $ \mathbf{2 0} $ Marks) Consider the benzene(1)-ethanol(2) system which exhibits an azeotrope at 760 mmHg and $ 68.24^{\circ} \mathrm{C} $ containing 44.8\% (mole basis) of ethanol. Given the constants in Antoine equations for: Benzene: $ \log \left(\mathrm{P}_{1}^{\text {sat }}\right)=6.87987-1196.76 /(\mathrm{T}+219.161) $ Ethanol: $ \log \left(\mathrm{P}_{2}^{\text {sat }}\right)=8.1122-1592.86 /(\mathrm{T}+226.18), \mathrm{T} $ is in degree Celsius. 1. Determine the constants in Van Laar equation. 2. Determine the composition of the vapor in equilibrium for a liquid solution containing $ 60 \% $ of ethanol at 760 mmHg at an appropriate different temperature. Question \#2: (30 Marks) Using the formulation of Gibbs energy equation and the equilibrium principle, deduce Gibbs-Duhem equation and explain its utility for nonideal theory of liquids. a) Starting from Gibbs-Duhem equilibrium relation for a binary system, deduce Henry's law. Comment on Henry's law limitations. b) Develop expressions of the changes in entropy and enthalpy for the following cases following cases: 1. A nonideal liquid solution 2. An ideal liquid solution 3. A nonideal gas mixture 4. An ideal gas mixture. Question \#3: ( $ \mathbf{2 5} $ Marks) An uninsulated piston/cylinder contains propene (propylene) $ \mathrm{C}_{3} \mathrm{H}_{6} $ at ambient temperature, $ 19^{\circ} \mathrm{C} $, with a quality of $ 50 \% $ and a volume of 10 L . The propene now expands very slowly until the pressure in the cylinder drops to 460 kPa . The process is isothermal and reversible. 1. Draw the process T-s diagram and read the initial pressure (kPa) 2. Calculate the mass of propene, the heat transfer and work for this process. Data: $ \mathrm{Tc}=364.9 \mathrm{~K}, \mathrm{Pc}=4.6 \mathrm{MPa}, \mathrm{R}=8.314 \mathrm{~J} / \mathrm{mol} . \mathrm{K} ., \mathrm{Cp}=1.5 \mathrm{~J} / \mathrm{mol} . \mathrm{K} $. Question \#4: (25 Marks) Acetic acid is esterified in the liquid phase with ethanol at $ 100^{\circ} \mathrm{C} $ and atmospheric pressure to produce ethyl acetate and water according to the reaction: \[ \mathrm{CH}_{3} \mathrm{COOH}(l)+\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(l) \quad \rightarrow \quad \mathrm{CH}_{3} \mathrm{COOC}_{2} \mathrm{H}_{5}(l)+\mathrm{H}_{2} \mathrm{O}(l) \] Initially there is one mole each of acetic acid and ethanol, estimate the equilibrium constant at $ 100^{\circ} \mathrm{C} $, the conversion x and the mole fraction of each component in the reacting mixture at equilibrium. Data for ethyl acetate: $ \Delta \mathrm{H}_{\mathrm{f} 298}^{\mathrm{o}}=-480 \mathrm{~kJ} / \mathrm{mol} $ and $ \Delta \mathrm{G}_{\mathrm{f} 298}^{\mathrm{o}}=-332.2 \mathrm{~kJ} / \mathrm{mol} $.

          RYERSON UNIVERSITY, TORONTO
DEPARTMENT OF CHEMICAL ENGINEERING
Final Exam: Thermodynamics CHE214
Time: 2-5pm

Question \#1: ( \( \mathbf{2 0} \) Marks)
Consider the benzene(1)-ethanol(2) system which exhibits an azeotrope at 760 mmHg and \( 68.24^{\circ} \mathrm{C} \) containing 44.8\% (mole basis) of ethanol. Given the constants in Antoine equations for:
Benzene: \( \log \left(\mathrm{P}_{1}^{\text {sat }}\right)=6.87987-1196.76 /(\mathrm{T}+219.161) \)
Ethanol: \( \log \left(\mathrm{P}_{2}^{\text {sat }}\right)=8.1122-1592.86 /(\mathrm{T}+226.18), \mathrm{T} \) is in degree Celsius.
1. Determine the constants in Van Laar equation.
2. Determine the composition of the vapor in equilibrium for a liquid solution containing \( 60 \% \) of ethanol at 760 mmHg at an appropriate different temperature.
Question \#2: (30 Marks)
Using the formulation of Gibbs energy equation and the equilibrium principle, deduce Gibbs-Duhem equation and explain its utility for nonideal theory of liquids.
a) Starting from Gibbs-Duhem equilibrium relation for a binary system, deduce Henry's law. Comment on Henry's law limitations.
b) Develop expressions of the changes in entropy and enthalpy for the following cases following cases:
1. A nonideal liquid solution
2. An ideal liquid solution
3. A nonideal gas mixture
4. An ideal gas mixture.

Question \#3: ( \( \mathbf{2 5} \) Marks)
An uninsulated piston/cylinder contains propene (propylene) \( \mathrm{C}_{3} \mathrm{H}_{6} \) at ambient temperature, \( 19^{\circ} \mathrm{C} \), with a quality of \( 50 \% \) and a volume of 10 L . The propene now expands very slowly until the pressure in the cylinder drops to 460 kPa . The process is isothermal and reversible.
1. Draw the process T-s diagram and read the initial pressure (kPa)
2. Calculate the mass of propene, the heat transfer and work for this process.
Data: \( \mathrm{Tc}=364.9 \mathrm{~K}, \mathrm{Pc}=4.6 \mathrm{MPa}, \mathrm{R}=8.314 \mathrm{~J} / \mathrm{mol} . \mathrm{K} ., \mathrm{Cp}=1.5 \mathrm{~J} / \mathrm{mol} . \mathrm{K} \).
Question \#4: (25 Marks)
Acetic acid is esterified in the liquid phase with ethanol at \( 100^{\circ} \mathrm{C} \) and atmospheric pressure to produce ethyl acetate and water according to the reaction:
\[
\mathrm{CH}_{3} \mathrm{COOH}(l)+\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(l) \quad \rightarrow \quad \mathrm{CH}_{3} \mathrm{COOC}_{2} \mathrm{H}_{5}(l)+\mathrm{H}_{2} \mathrm{O}(l)
\]

Initially there is one mole each of acetic acid and ethanol, estimate the equilibrium constant at \( 100^{\circ} \mathrm{C} \), the conversion x and the mole fraction of each component in the reacting mixture at equilibrium.
Data for ethyl acetate: \( \Delta \mathrm{H}_{\mathrm{f} 298}^{\mathrm{o}}=-480 \mathrm{~kJ} / \mathrm{mol} \) and \( \Delta \mathrm{G}_{\mathrm{f} 298}^{\mathrm{o}}=-332.2 \mathrm{~kJ} / \mathrm{mol} \).

$RYERSON UNIVERSITY, TORONTO DEPARTMENT OF CHEMICAL ENGINEERING Final Exam: Thermodynamics CHE214 Time: 2-5pm Question #1: ( 2 0 Marks) Consider the benzene(1)-ethanol(2) system which exhibits an azeotrope at 760 mmHg and 68.24^∘C containing 44.8% (mole basis) of ethanol. Given the constants in Antoine equations for: Benzene: log(P1^sat )=6.87987-1196.76 /(T+219.161) Ethanol: log(P2^sat )=8.1122-1592.86 /(T+226.18), T is in degree Celsius. 1. Determine the constants in Van Laar equation. 2. Determine the composition of the vapor in equilibrium for a liquid solution containing 60 % of ethanol at 760 mmHg at an appropriate different temperature. Question #2: (30 Marks) Using the formulation of Gibbs energy equation and the equilibrium principle, deduce Gibbs-Duhem equation and explain its utility for nonideal theory of liquids. a) Starting from Gibbs-Duhem equilibrium relation for a binary system, deduce Henry's law. Comment on Henry's law limitations. b) Develop expressions of the changes in entropy and enthalpy for the following cases following cases: 1. A nonideal liquid solution 2. An ideal liquid solution 3. A nonideal gas mixture 4. An ideal gas mixture. Question #3: ( 2 5 Marks) An uninsulated piston/cylinder contains propene (propylene) C3H6 at ambient temperature, 19^∘C, with a quality of 50 % and a volume of 10 L . The propene now expands very slowly until the pressure in the cylinder drops to 460 kPa . The process is isothermal and reversible. 1. Draw the process T-s diagram and read the initial pressure (kPa) 2. Calculate the mass of propene, the heat transfer and work for this process. Data: Tc=364.9 K, Pc=4.6 MPa, R=8.314 J / mol . K ., Cp=1.5 J / mol . K. Question #4: (25 Marks) Acetic acid is esterified in the liquid phase with ethanol at 100^∘C and atmospheric pressure to produce ethyl acetate and water according to the reaction: CH3COOH(l)+C2H5OH(l) → CH3COOC2H5(l)+H2O(l) Initially there is one mole each of acetic acid and ethanol, estimate the equilibrium constant at 100^∘C, the conversion x and the mole fraction of each component in the reacting mixture at equilibrium. Data for ethyl acetate: ΔHf 298^o=-480 kJ / mol and ΔGf 298^o=-332.2 kJ / mol.$

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