Chemistry
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ISBN: 9781305957404
Author: Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher: Cengage Learning
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![**Equilibrium Reaction and Calculation of \( K_p \):**
Gaseous \(\text{NH}_3\) is placed in a closed container at **33 °C**, where it partially decomposes to \(\text{N}_2\) and \(\text{H}_2\), according to the following equilibrium reaction:
\[ 2 \text{NH}_3(g) \rightleftharpoons 1 \text{N}_2(g) + 3 \text{H}_2(g) \]
At equilibrium, the partial pressures are measured as follows:
- \( p(\text{NH}_3) = 0.008450\) atm,
- \( p(\text{N}_2) = 0.007140\) atm,
- \( p(\text{H}_2) = 0.003440\) atm.
**Objective:**
Determine the value of \( K_p \) for this reaction at 33 °C.
**Calculation:**
The equilibrium constant \( K_p \) for the reaction is expressed as:
\[
K_p = \frac{(p(\text{N}_2) \times (p(\text{H}_2))^3)}{(p(\text{NH}_3))^2}
\]
Insert the given partial pressures into the expression to find \( K_p \).
\[ K_p = \frac{(0.007140) \times (0.003440)^3}{(0.008450)^2} \]
**Note to Educators:**
Ensure students are aware that the units for partial pressures must be consistent when calculating \( K_p \). This exercise is useful for reinforcing concepts of chemical equilibrium and the use of equilibrium constants in gaseous reactions.](https://content.bartleby.com/qna-images/question/86624ab7-da2a-4a5b-91b8-0bf4ad8ab366/5c1e2bb8-4d9f-4f47-8fb7-bb25135b1e7c/rwoiq_processed.png)
Transcribed Image Text:**Equilibrium Reaction and Calculation of \( K_p \):**
Gaseous \(\text{NH}_3\) is placed in a closed container at **33 °C**, where it partially decomposes to \(\text{N}_2\) and \(\text{H}_2\), according to the following equilibrium reaction:
\[ 2 \text{NH}_3(g) \rightleftharpoons 1 \text{N}_2(g) + 3 \text{H}_2(g) \]
At equilibrium, the partial pressures are measured as follows:
- \( p(\text{NH}_3) = 0.008450\) atm,
- \( p(\text{N}_2) = 0.007140\) atm,
- \( p(\text{H}_2) = 0.003440\) atm.
**Objective:**
Determine the value of \( K_p \) for this reaction at 33 °C.
**Calculation:**
The equilibrium constant \( K_p \) for the reaction is expressed as:
\[
K_p = \frac{(p(\text{N}_2) \times (p(\text{H}_2))^3)}{(p(\text{NH}_3))^2}
\]
Insert the given partial pressures into the expression to find \( K_p \).
\[ K_p = \frac{(0.007140) \times (0.003440)^3}{(0.008450)^2} \]
**Note to Educators:**
Ensure students are aware that the units for partial pressures must be consistent when calculating \( K_p \). This exercise is useful for reinforcing concepts of chemical equilibrium and the use of equilibrium constants in gaseous reactions.
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