To determine the equilibrium constant, [tex]\( K_{\text{eq}} \)[/tex], of a chemical reaction, we need to understand what it represents. The equilibrium constant is a number that expresses the ratio of the concentrations of products to reactants for a reversible reaction at equilibrium. For a general reaction:
[tex]\[ \text{aA} + \text{bB} \rightleftharpoons \text{cC} + \text{dD} \][/tex]
The equilibrium constant, [tex]\( K_{\text{eq}} \)[/tex], is given by the ratio:
[tex]\[ K_{\text{eq}} = \frac{[\text{C}]^c [\text{D}]^d}{[\text{A}]^a [\text{B}]^b} \][/tex]
Where:
- [tex]\([\text{A}]\)[/tex] and [tex]\([\text{B}]\)[/tex] are the molar concentrations of the reactants,
- [tex]\([\text{C}]\)[/tex] and [tex]\([\text{D}]\)[/tex] are the molar concentrations of the products,
- [tex]\(a\)[/tex], [tex]\(b\)[/tex], [tex]\(c\)[/tex], and [tex]\(d\)[/tex] are the stoichiometric coefficients of the reactants and products, respectively.
Now let’s consider each of the provided choices:
A. [tex]\( K_{\text{eq}} = \frac{[\text{products}]}{[\text{reactants}]} \)[/tex]
- This form is correct according to the general expression for the equilibrium constant.
B. [tex]\( K_{\text{eq}} = [\text{reactants}] + [\text{products}] \)[/tex]
- This form is incorrect. The equilibrium constant is not a sum of the concentrations but rather a ratio.
C. [tex]\( K_{\text{eq}} = \frac{[\text{reactants}]}{[\text{products}]} \)[/tex]
- This form would invert the ratio and is incorrect.
D. [tex]\( K_{\text{eq}} = [\text{products}] [\text{reactants}] \)[/tex]
- This form is also incorrect because it suggests multiplying the concentrations rather than forming a ratio.
Given the detailed explanation, the correct choice for the equilibrium constant of a reaction is:
A. [tex]\( K_{\text{eq}} = \frac{[\text{products}]}{[\text{reactants}]} \)[/tex]
