One of the most widely produced chemicals in the world is ammonium to be used as fertilizer. It is synthesized by the Haber process (∆G° = –32.9 kJ/mo

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
icon
Related questions
Question

2. One of the most widely produced chemicals in the world is ammonium to be used as fertilizer. It is synthesized by the Haber process (∆G° = –32.9 kJ/mol):
N2(g) + 3H2(g) → 2NH3(g)
How much does this reaction proceeded if you start with n moles of nitrogen and 3n moles of hydrogen? Also, let’s assume that the reactor maintains a pressure of 1 bar like the reaction is in a balloon, and that the temperature is maintained at 25 °C.

Question to answer:

In question 2, why was the extent of the reaction: N2(g) + 3H2(g) → 2NH3(g) equal to α=0.968 if the pressure is maintained at 1 bar but drops slightly to =0.956 if the pressure drops to 0.5 bar?

### Equilibrium Calculations

#### Hint: 
Use the table below to calculate mole fractions and partial pressures:

|               | N₂               | H₂               | NH₃           |
|---------------|------------------|------------------|---------------|
| **Amount at equilibrium** | n(1 − α)          | 3n(1 − α)        | 2nα         |
| **Mole fractions**        | \(\frac{n(1 - \alpha)}{4n - 2n\alpha}\) | \(\frac{3n(1 - \alpha)}{4n - 2n\alpha}\) | \(\frac{2n\alpha}{4n - 2n\alpha}\) |
| **Partial pressures**     | \(\frac{(1 - \alpha) \cdot P}{4 - 2\alpha}\) | \(\frac{3(1 - \alpha) \cdot P}{4 - 2\alpha}\) | \(\frac{2\alpha \cdot P}{4 - 2\alpha}\) |

Where α represents the extent of the reaction. \( K = \prod \left( \frac{P_i}{P_i^{\circ}} \right)^{\nu_i} \), where \( P_i \) is the partial pressure of species *i*.

i. As usual, \( P^{\circ} \) is just 1 bar. Now we can show:

\[ K = \left(\frac{2\alpha}{4 - 2\alpha} \cdot \frac{P}{P^{\circ}} \right)^2 \bigg/ \left( \left( \frac{(1 - \alpha) \cdot P}{4 - 2\alpha} \right) \left( \frac{3(1 - \alpha) \cdot P}{4 - 2\alpha} \right) \right)^3 \]

**Simplification gives:**

\[ \left(\frac{2\alpha}{4-2\alpha} \cdot \frac{P}{P^{\circ}}\right)^2 \cdot \left(\frac{4-2\alpha}{(1-\alpha) \cdot P}\right)^3 = \frac{16\alpha^2(2-\alpha)^2}{27(1-\
Transcribed Image Text:### Equilibrium Calculations #### Hint: Use the table below to calculate mole fractions and partial pressures: | | N₂ | H₂ | NH₃ | |---------------|------------------|------------------|---------------| | **Amount at equilibrium** | n(1 − α) | 3n(1 − α) | 2nα | | **Mole fractions** | \(\frac{n(1 - \alpha)}{4n - 2n\alpha}\) | \(\frac{3n(1 - \alpha)}{4n - 2n\alpha}\) | \(\frac{2n\alpha}{4n - 2n\alpha}\) | | **Partial pressures** | \(\frac{(1 - \alpha) \cdot P}{4 - 2\alpha}\) | \(\frac{3(1 - \alpha) \cdot P}{4 - 2\alpha}\) | \(\frac{2\alpha \cdot P}{4 - 2\alpha}\) | Where α represents the extent of the reaction. \( K = \prod \left( \frac{P_i}{P_i^{\circ}} \right)^{\nu_i} \), where \( P_i \) is the partial pressure of species *i*. i. As usual, \( P^{\circ} \) is just 1 bar. Now we can show: \[ K = \left(\frac{2\alpha}{4 - 2\alpha} \cdot \frac{P}{P^{\circ}} \right)^2 \bigg/ \left( \left( \frac{(1 - \alpha) \cdot P}{4 - 2\alpha} \right) \left( \frac{3(1 - \alpha) \cdot P}{4 - 2\alpha} \right) \right)^3 \] **Simplification gives:** \[ \left(\frac{2\alpha}{4-2\alpha} \cdot \frac{P}{P^{\circ}}\right)^2 \cdot \left(\frac{4-2\alpha}{(1-\alpha) \cdot P}\right)^3 = \frac{16\alpha^2(2-\alpha)^2}{27(1-\
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 4 steps with 6 images

Blurred answer
Recommended textbooks for you
Introduction to Chemical Engineering Thermodynami…
Introduction to Chemical Engineering Thermodynami…
Chemical Engineering
ISBN:
9781259696527
Author:
J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:
McGraw-Hill Education
Elementary Principles of Chemical Processes, Bind…
Elementary Principles of Chemical Processes, Bind…
Chemical Engineering
ISBN:
9781118431221
Author:
Richard M. Felder, Ronald W. Rousseau, Lisa G. Bullard
Publisher:
WILEY
Elements of Chemical Reaction Engineering (5th Ed…
Elements of Chemical Reaction Engineering (5th Ed…
Chemical Engineering
ISBN:
9780133887518
Author:
H. Scott Fogler
Publisher:
Prentice Hall
Process Dynamics and Control, 4e
Process Dynamics and Control, 4e
Chemical Engineering
ISBN:
9781119285915
Author:
Seborg
Publisher:
WILEY
Industrial Plastics: Theory and Applications
Industrial Plastics: Theory and Applications
Chemical Engineering
ISBN:
9781285061238
Author:
Lokensgard, Erik
Publisher:
Delmar Cengage Learning
Unit Operations of Chemical Engineering
Unit Operations of Chemical Engineering
Chemical Engineering
ISBN:
9780072848236
Author:
Warren McCabe, Julian C. Smith, Peter Harriott
Publisher:
McGraw-Hill Companies, The