2NO(g) + 2H₂(g) = 2H₂O(g) + N₂(g) K = 0.110 ΔΗ° = −707 kJ What is the equilibrium constant for the reaction when it is altered as below? H₂O(g) + N₂(g) = NO(g) + H₂(g) K' = [?]
2NO(g) + 2H₂(g) = 2H₂O(g) + N₂(g) K = 0.110 ΔΗ° = −707 kJ What is the equilibrium constant for the reaction when it is altered as below? H₂O(g) + N₂(g) = NO(g) + H₂(g) K' = [?]
Chemistry
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ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Chapter1: Chemical Foundations
Section: Chapter Questions
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![**Chemical Equilibrium and Equilibrium Constant**
In this educational module, we will explore the concept of chemical equilibrium and how to determine the equilibrium constant for a given reaction.
### Original Reaction and Equilibrium Data
Consider the following chemical reaction:
\[ 2 \text{NO}(g) + 2 \text{H}_2(g) \rightleftharpoons 2 \text{H}_2\text{O}(g) + \text{N}_2(g) \]
The equilibrium constant (\( K \)) for this reaction is given as:
\[ K = 0.110 \]
Additionally, the enthalpy change (\( \Delta H^\circ \)) for this reaction is:
\[ \Delta H^\circ = -707 \text{kJ} \]
### Altered Reaction
Now, we need to determine the equilibrium constant for an altered version of the original reaction:
\[ \text{H}_2\text{O}(g) + \frac{1}{2} \text{N}_2(g) \rightleftharpoons \text{NO}(g) + \text{H}_2(g) \]
Let's denote the equilibrium constant for this altered reaction as \( K' \).
### Solution Approach
To find \( K' \), consider the relationship between the original reaction and the altered reaction. Here, the altered reaction can be obtained by reversing and then halving the original reaction.
When a reaction is reversed, the equilibrium constant for the reversed reaction is the reciprocal of the original equilibrium constant. Furthermore, when a reaction is halved, the equilibrium constant for the halved reaction is the square root of the original equilibrium constant.
Therefore, the steps to calculate \( K' \) are as follows:
1. Reverse the original reaction to get the reciprocal of \( K \).
2. Halve the coefficients in the reversed reaction and take the square root of the resulting equilibrium constant.
### Mathematical Calculation
1. Reverse the original reaction:
\[ 2 \text{H}_2\text{O}(g) + \text{N}_2(g) \rightleftharpoons 2 \text{NO}(g) + 2 \text{H}_2(g) \]
\[ K_{\text{reversed}} = \frac{1}{K} = \frac{1}{0.110} \approx 9.09 \]
2. Halve the reversed](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2329c5a6-0449-4dd4-95b7-c97128962f87%2Fd5e4167d-2c5f-4dea-a554-18444a8222a6%2F2ofmduf_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Chemical Equilibrium and Equilibrium Constant**
In this educational module, we will explore the concept of chemical equilibrium and how to determine the equilibrium constant for a given reaction.
### Original Reaction and Equilibrium Data
Consider the following chemical reaction:
\[ 2 \text{NO}(g) + 2 \text{H}_2(g) \rightleftharpoons 2 \text{H}_2\text{O}(g) + \text{N}_2(g) \]
The equilibrium constant (\( K \)) for this reaction is given as:
\[ K = 0.110 \]
Additionally, the enthalpy change (\( \Delta H^\circ \)) for this reaction is:
\[ \Delta H^\circ = -707 \text{kJ} \]
### Altered Reaction
Now, we need to determine the equilibrium constant for an altered version of the original reaction:
\[ \text{H}_2\text{O}(g) + \frac{1}{2} \text{N}_2(g) \rightleftharpoons \text{NO}(g) + \text{H}_2(g) \]
Let's denote the equilibrium constant for this altered reaction as \( K' \).
### Solution Approach
To find \( K' \), consider the relationship between the original reaction and the altered reaction. Here, the altered reaction can be obtained by reversing and then halving the original reaction.
When a reaction is reversed, the equilibrium constant for the reversed reaction is the reciprocal of the original equilibrium constant. Furthermore, when a reaction is halved, the equilibrium constant for the halved reaction is the square root of the original equilibrium constant.
Therefore, the steps to calculate \( K' \) are as follows:
1. Reverse the original reaction to get the reciprocal of \( K \).
2. Halve the coefficients in the reversed reaction and take the square root of the resulting equilibrium constant.
### Mathematical Calculation
1. Reverse the original reaction:
\[ 2 \text{H}_2\text{O}(g) + \text{N}_2(g) \rightleftharpoons 2 \text{NO}(g) + 2 \text{H}_2(g) \]
\[ K_{\text{reversed}} = \frac{1}{K} = \frac{1}{0.110} \approx 9.09 \]
2. Halve the reversed
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