Consider the general reversible reaction:
[tex]aA + bB \longleftrightarrow cC +d D[/tex]
What is the equilibrium constant expression for the given system?
A. [tex]K_{e q}=\frac{C^{\prime}[C] d[D]}{a[A] b[B]}[/tex]
B. [tex]K_{e q}=\frac{[C][D]}{[A][B]}[/tex]
C. [tex]K_{e q}=\frac{[A]^a[B]^b}{[C]^c[D]^d}[/tex]
D. [tex]K_{e q}=\frac{[C]^c[D]^d}{[A]^d[B]^b}[/tex]
Answer (2)
The equilibrium constant expression relates the concentrations of products to reactants at equilibrium.
The products, C and D, are in the numerator, raised to the power of their stoichiometric coefficients, c and d, respectively.
The reactants, A and B, are in the denominator, raised to the power of their stoichiometric coefficients, a and b, respectively.
The equilibrium constant expression is K e q = [ A ] a [ B ] b [ C ] c [ D ] d .
Explanation
Understanding the Problem The problem asks for the equilibrium constant expression, K e q , for the reversible reaction a A + b B ⟷ c C + d D . The equilibrium constant expression relates the concentrations of reactants and products at equilibrium.
Defining the Equilibrium Constant The equilibrium constant expression is given by the ratio of the product of the concentrations of the products, each raised to the power of its stoichiometric coefficient, to the product of the concentrations of the reactants, each raised to the power of its stoichiometric coefficient. In this case, the products are C and D, with stoichiometric coefficients c and d, respectively. The reactants are A and B, with stoichiometric coefficients a and b, respectively.
Writing the Expression Therefore, the equilibrium constant expression is: K e q = [ A ] a [ B ] b [ C ] c [ D ] d
Final Answer The correct equilibrium constant expression is therefore K e q = [ A ] a [ B ] b [ C ] c [ D ] d .
Examples
Consider a scenario where you're baking a cake. The ingredients (reactants) combine to form the cake (product). At equilibrium, the rate at which you're mixing ingredients to bake the cake is equal to the rate at which the cake is being 'unbaked' back into its ingredients (although this reverse process isn't something that happens in baking!). The equilibrium constant helps you understand the balance between ingredients and cake at a specific temperature and condition. In chemical reactions, this is crucial for optimizing product yield.
The equilibrium constant expression for the reaction a A + b B ⟷ c C + d D is K e q = [ A ] a [ B ] b [ C ] c [ D ] d . Therefore, the correct answer is option D. This expression summarizes the relationship between the concentrations of products and reactants at equilibrium.
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