Chemistry
10th Edition
ISBN: 9781305957404
Author: Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher: Cengage Learning
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![### Calculating the Equilibrium Constant
#### Problem Statement:
Calculate the equilibrium constant for the chemical reaction, given the equilibrium concentrations of the reactants and products in the table.
The reaction is:
\[ 2 \text{AB(aq)} + 4 \text{CD(aq)} \rightleftharpoons 2 \text{AD(aq)} + 2 \text{BD(aq)} + 4 \text{C(aq)} \]
#### Equilibrium Concentrations:
| Substance | Equilibrium concentration |
|-----------|-----------------------------|
| AB | 4.99 M |
| CD | 2.54 M |
| AD | 4.02 M |
| BD | 2.28 M |
| C | 1.27 M |
#### Formula for Equilibrium Constant, \( K \):
For the reaction \( aA + bB \rightleftharpoons cC + dD \), the equilibrium constant \( K \) is given by:
\[ K = \frac{[\text{C}]^c [\text{D}]^d}{[\text{A}]^a [\text{B}]^b} \]
#### Applying the Equilibrium Concentrations:
For the given reaction:
\[ 2 \text{AB(aq)} + 4 \text{CD(aq)} \rightleftharpoons 2 \text{AD(aq)} + 2 \text{BD(aq)} + 4 \text{C(aq)} \]
The equilibrium constant \( K \) is:
\[ K = \frac{[\text{AD}]^2 [\text{BD}]^2 [\text{C}]^4}{[\text{AB}]^2 [\text{CD}]^4} \]
Substitute the given equilibrium concentrations:
\[ K = \frac{(4.02)^2 (2.28)^2 (1.27)^4}{(4.99)^2 (2.54)^4} \]
Calculate \( K \):
\[ K = \frac{(16.1604) (5.1984) (2.6013)}{(24.9001) (41.6061)} \]
\[ K = \frac{(16.1604 \times 5.1984 \times 2.6013)}{(](https://content.bartleby.com/qna-images/question/7d591113-c73d-4bf8-a1b7-9966513ce440/780b2336-3233-4f72-92ae-8a0af8ecff99/fr6qtjai_processed.png)
Transcribed Image Text:### Calculating the Equilibrium Constant
#### Problem Statement:
Calculate the equilibrium constant for the chemical reaction, given the equilibrium concentrations of the reactants and products in the table.
The reaction is:
\[ 2 \text{AB(aq)} + 4 \text{CD(aq)} \rightleftharpoons 2 \text{AD(aq)} + 2 \text{BD(aq)} + 4 \text{C(aq)} \]
#### Equilibrium Concentrations:
| Substance | Equilibrium concentration |
|-----------|-----------------------------|
| AB | 4.99 M |
| CD | 2.54 M |
| AD | 4.02 M |
| BD | 2.28 M |
| C | 1.27 M |
#### Formula for Equilibrium Constant, \( K \):
For the reaction \( aA + bB \rightleftharpoons cC + dD \), the equilibrium constant \( K \) is given by:
\[ K = \frac{[\text{C}]^c [\text{D}]^d}{[\text{A}]^a [\text{B}]^b} \]
#### Applying the Equilibrium Concentrations:
For the given reaction:
\[ 2 \text{AB(aq)} + 4 \text{CD(aq)} \rightleftharpoons 2 \text{AD(aq)} + 2 \text{BD(aq)} + 4 \text{C(aq)} \]
The equilibrium constant \( K \) is:
\[ K = \frac{[\text{AD}]^2 [\text{BD}]^2 [\text{C}]^4}{[\text{AB}]^2 [\text{CD}]^4} \]
Substitute the given equilibrium concentrations:
\[ K = \frac{(4.02)^2 (2.28)^2 (1.27)^4}{(4.99)^2 (2.54)^4} \]
Calculate \( K \):
\[ K = \frac{(16.1604) (5.1984) (2.6013)}{(24.9001) (41.6061)} \]
\[ K = \frac{(16.1604 \times 5.1984 \times 2.6013)}{(
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