What does a value of \(K_{\text {eq }}\) less than \(10^{-3}\) imply? Prove that your answer is correct by using the general expression \(K_{\text {eq }}=\) [Products \(] /[\) Reactants \(]\).

Equilibrium constant (\(K_{eq}\)) is a parameter that is used to quantify the extent of a chemical reaction at equilibrium. It is defined as the ratio of the concentration (or activities) of the products raised to their stoichiometric coefficients to the concentration (or activities) of the reactants raised to their stoichiometric coefficients. Mathematically, it can be represented as: \(K_{eq} = \frac{[Products]}{[Reactants]}\)

A large value of \(K_{eq}\) indicates that the products are favored at equilibrium, while a small value of \(K_{eq}\) indicates that the reactants are favored at equilibrium. When \(K_{eq} < 10^{-3}\), this implies that the equilibrium reaction favors the reactants and the forward reaction does not proceed extensively. In other words, only a small amount of products is formed.

Let's assume a generic chemical equilibrium reaction: \(aA + bB \rightleftharpoons cC + dD\) where, A and B are the reactants, and C and D are the products, with their respective stoichiometric coefficients a, b, c, and d. The \(K_{eq}\) for this reaction will be: \(K_{\text {eq }}=\frac{[C]^{c}[D]^{d}}{[A]^{a}[B]^{b}}\) Now, let's assume that \(K_{eq} < 10^{-3}\). This means: \(K_{\text {eq }}=\frac{[C]^{c}[D]^{d}}{[A]^{a}[B]^{b}} < 10^{-3}\) Since \(10^{-3}\) is a very small value, this inequality indicates that the denominator (i.e., the concentration of reactants) is much greater than the numerator (i.e., the concentration of products). In other words: \([A]^{a}[B]^{b} > [C]^{c}[D]^{d}\) This clearly shows that when \(K_{eq} < 10^{-3}\), the reaction favors the reactants and there's only a small amount of products formed, proving our statement to be correct.