Chemistry
Chemistry
10th Edition
ISBN: 9781305957404
Author: Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher: Cengage Learning
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Question
### 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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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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