Which represents the correct equilibrium constant expression for the reaction below?
[tex]Cu(s)+2 Ag^{+}(aq) \longleftrightarrow Cu^{2+}(aq)+2 Ag(s)[/tex]
A. [tex]Keq =\frac{[ Cu ]\left[ Ag ^{+}\right]^2}{\left[ Cu ^{2+}\right][ Ag ]^2}[/tex]
B. [tex]K_{e q}=\frac{\left[ Cu ^{2+}\right]\left[ Ag ^2\right.}{[ Cu ]\left[ Ag ^{+}\right]^2}[/tex]
C. [tex]Keq=\frac{\left[ Ag ^*\right]^2}{\left[ Cu ^{2+}\right]}[/tex]
D. [tex]Keq=\frac{\left[ Cu ^{2+}\right]}{\left[ A g ^{+}\right]^2}[/tex]
Answer (2)
Solids are excluded from the equilibrium constant expression.
The equilibrium constant expression is the ratio of products to reactants, each raised to the power of their stoichiometric coefficients.
For the reaction C u ( s ) + 2 A g + ( a q ) ⟷ C u 2 + ( a q ) + 2 A g ( s ) , the equilibrium constant expression is K e q = [ A g + ] 2 [ C u 2 + ] .
Therefore, the correct answer is K e q = [ A g + ] 2 [ C u 2 + ] .
Explanation
Understanding the Reaction The reaction is: C u ( s ) + 2 A g + ( a q ) ⟷ C u 2 + ( a q ) + 2 A g ( s ) . We need to determine the correct equilibrium constant expression ( K e q ) for this reaction. Remember that in an equilibrium constant expression, we only include aqueous and gaseous species; solids and pure liquids are excluded.
Identifying Relevant Species In the given reaction, C u ( s ) and A g ( s ) are solids, so they will not appear in the K e q expression. The aqueous species are A g + ( a q ) and C u 2 + ( a q ) . The general form of the equilibrium constant expression is the ratio of the concentrations of the products to the reactants, each raised to the power of their stoichiometric coefficients.
Writing the Equilibrium Constant Expression For the given reaction, the equilibrium constant expression is: K e q = [ A g + ] 2 [ C u 2 + ] The concentration of the product C u 2 + is in the numerator, and the concentration of the reactant A g + is in the denominator, raised to the power of 2 because of its stoichiometric coefficient.
Selecting the Correct Option Comparing this expression with the given options, we find that the correct expression is: K e q = [ A g + ] 2 [ C u 2 + ]
Examples
The equilibrium constant is a crucial concept in chemistry. For instance, consider the Haber-Bosch process, which synthesizes ammonia ( N H 3 ) from nitrogen ( N 2 ) and hydrogen ( H 2 ). The equilibrium constant helps determine the optimal conditions (temperature, pressure) to maximize ammonia production. Similarly, in environmental science, understanding equilibrium constants aids in predicting the distribution of pollutants in different environmental compartments (air, water, soil). In pharmacology, it helps in understanding drug-receptor binding and predicting drug efficacy.
The correct equilibrium constant expression for the reaction is K e q = [ A g + ] 2 [ C u 2 + ] because we exclude solids and only include aqueous species. The chosen option is D.
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