At low to moderate pressures, the equilibrium state of the water-gas shift reaction CO + H2O = CO2 + H2O is approximately described by the relation YCO,YH2 4020 = Keq(T) = 0.0247 exp | T(K), YCOYH20 where T is the reactor temperature, Keq is the reaction equilibrium constant, and y; is the mole fraction of species i in the reactor contents at equilibrium. The feed to a batch shift reactor contains 20.0 mole% CO, 10.0% CO2, 40.0% water, and the balance an inert gas. The reactor is maintained at T = 1123 K. (a) Assume a basis of 1 mol feed and draw and label a flowchart. Carry out a degree-of- freedom analysis of the reactor based on extents of reaction and use it to prove that you have enough information to calculate the composition of the reaction mixture at equilibrium. Do not perform the calculations at this point. (b) Calculate the total moles of gas in the reactor at equilibrium (if it takes you more than 5 seconds you are missing the point) and then the equilibrium mole fraction of hydrogen in the product. (Suggestion: Begin by writing expressions for the moles of each species in the product gas in terms of the extent of reaction, and then write expressions for the species mole fractions.) (c) Suppose a gas sample is drawn from the reactor and analyzed shortly after startup and the mole fraction of hydrogen is significantly different from the calculated value. Assuming that no calculation mistakes or measurement errors have been made, what is a likely explanation for the discrepancy between the calculated and measured hy- drogen yields?
At low to moderate pressures, the equilibrium state of the water-gas shift reaction CO + H2O = CO2 + H2O is approximately described by the relation YCO,YH2 4020 = Keq(T) = 0.0247 exp | T(K), YCOYH20 where T is the reactor temperature, Keq is the reaction equilibrium constant, and y; is the mole fraction of species i in the reactor contents at equilibrium. The feed to a batch shift reactor contains 20.0 mole% CO, 10.0% CO2, 40.0% water, and the balance an inert gas. The reactor is maintained at T = 1123 K. (a) Assume a basis of 1 mol feed and draw and label a flowchart. Carry out a degree-of- freedom analysis of the reactor based on extents of reaction and use it to prove that you have enough information to calculate the composition of the reaction mixture at equilibrium. Do not perform the calculations at this point. (b) Calculate the total moles of gas in the reactor at equilibrium (if it takes you more than 5 seconds you are missing the point) and then the equilibrium mole fraction of hydrogen in the product. (Suggestion: Begin by writing expressions for the moles of each species in the product gas in terms of the extent of reaction, and then write expressions for the species mole fractions.) (c) Suppose a gas sample is drawn from the reactor and analyzed shortly after startup and the mole fraction of hydrogen is significantly different from the calculated value. Assuming that no calculation mistakes or measurement errors have been made, what is a likely explanation for the discrepancy between the calculated and measured hy- drogen yields?
Introduction to Chemical Engineering Thermodynamics
8th Edition
ISBN:9781259696527
Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Chapter1: Introduction
Section: Chapter Questions
Problem 1.1P
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![### Equilibrium State of the Water-Gas Shift Reaction
At low to moderate pressures, the equilibrium state of the water-gas shift reaction:
\[ \text{CO} + \text{H}_2\text{O} \rightleftharpoons \text{CO}_2 + \text{H}_2 \]
is approximately described by the relation:
\[
\frac{y_{\text{CO}_2}y_{\text{H}_2}}{y_{\text{CO}}y_{\text{H}_2\text{O}}} = K_{\text{eq}}(T) = 0.0247 \exp \left[\frac{4020}{T(\text{K})}\right],
\]
where \( T \) is the reactor temperature, \( K_{\text{eq}} \) is the reaction equilibrium constant, and \( y_i \) is the mole fraction of species i in the reactor contents at equilibrium.
The feed to a batch shift reactor contains 20.0 mole% CO, 10.0% CO2, 40.0% water, and the balance an inert gas. The reactor is maintained at \( T = 1123 \, \text{K} \).
#### Problem Statement
(a) **Flowchart and Degree-of-Freedom Analysis**:
- Assume a basis of 1 mol feed and draw a labeled flowchart.
- Conduct a degree-of-freedom analysis of the reactor based on extents of reaction.
- Prove that sufficient information exists to calculate the equilibrium composition of the reaction mixture. Avoid performing actual calculations.
(b) **Total Moles and Mole Fraction of Hydrogen**:
- Calculate the total moles of gas in the reactor at equilibrium swiftly.
- Determine the equilibrium mole fraction of hydrogen in the product.
- Start with expressions for moles of each product species in terms of the extent of reaction, and write expressions for the species mole fractions.
(c) **Discrepancy in Hydrogen Yields**:
- If a gas sample is analyzed shortly after startup, and the hydrogen mole fraction differs from the calculated value, propose likely explanations assuming calculations and measurement errors are correct. Discuss possible reasons for discrepancies in hydrogen yields.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8dbff956-e43c-48ff-b648-b98fd3ab1747%2F7e9752f0-a6ea-403d-9544-ee0c1c35270e%2Fs3exqo_processed.png&w=3840&q=75)
Transcribed Image Text:### Equilibrium State of the Water-Gas Shift Reaction
At low to moderate pressures, the equilibrium state of the water-gas shift reaction:
\[ \text{CO} + \text{H}_2\text{O} \rightleftharpoons \text{CO}_2 + \text{H}_2 \]
is approximately described by the relation:
\[
\frac{y_{\text{CO}_2}y_{\text{H}_2}}{y_{\text{CO}}y_{\text{H}_2\text{O}}} = K_{\text{eq}}(T) = 0.0247 \exp \left[\frac{4020}{T(\text{K})}\right],
\]
where \( T \) is the reactor temperature, \( K_{\text{eq}} \) is the reaction equilibrium constant, and \( y_i \) is the mole fraction of species i in the reactor contents at equilibrium.
The feed to a batch shift reactor contains 20.0 mole% CO, 10.0% CO2, 40.0% water, and the balance an inert gas. The reactor is maintained at \( T = 1123 \, \text{K} \).
#### Problem Statement
(a) **Flowchart and Degree-of-Freedom Analysis**:
- Assume a basis of 1 mol feed and draw a labeled flowchart.
- Conduct a degree-of-freedom analysis of the reactor based on extents of reaction.
- Prove that sufficient information exists to calculate the equilibrium composition of the reaction mixture. Avoid performing actual calculations.
(b) **Total Moles and Mole Fraction of Hydrogen**:
- Calculate the total moles of gas in the reactor at equilibrium swiftly.
- Determine the equilibrium mole fraction of hydrogen in the product.
- Start with expressions for moles of each product species in terms of the extent of reaction, and write expressions for the species mole fractions.
(c) **Discrepancy in Hydrogen Yields**:
- If a gas sample is analyzed shortly after startup, and the hydrogen mole fraction differs from the calculated value, propose likely explanations assuming calculations and measurement errors are correct. Discuss possible reasons for discrepancies in hydrogen yields.
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