Question

Suppose a reaction has the equilibrium constant \(K=1.3 \times 10^{8} .\) What does the magnitude of this constant tell you about the relative concentrations of products and reactants that will be present once equilibrium is reached? Is this reaction likely to be a good source of the products?

Short answer

The given equilibrium constant, \(K = 1.3 \times 10^8\), is significantly greater than 1, indicating that the reaction is product-favored. At equilibrium, the concentration of products will be much greater than that of reactants. Therefore, this reaction is likely to be a good source of the products.

Step-by-step solution

Understand the meaning of the equilibrium constant

The equilibrium constant (K) is a dimensionless value that helps us determine the extent of a reaction at equilibrium, i.e., the relative concentrations of products and reactants. A reaction can be written in the form: \(aA + bB \rightleftharpoons cC + dD\) At equilibrium, the constant K is defined as: \[K = \frac{[C]^c \cdot [D]^d}{[A]^a \cdot [B]^b}\] Where [A], [B], [C], and [D] are the molar concentrations of the reactants (A and B) and products (C and D) at equilibrium. If K >> 1, the reaction is product-favored, meaning the concentration of products is much greater than that of reactants at equilibrium. If K << 1, the reaction is more reactant-favored.

Interpret the given equilibrium constant

In this exercise, we are given the equilibrium constant as \(K = 1.3 \times 10^8\). This value is significantly greater than 1, meaning the reaction is product-favored. Once equilibrium is reached, the concentration of products will be much greater than that of reactants.

Determine the suitability of the reaction as a product source

Since K >> 1, the reaction is product-favored, and the concentration of products at equilibrium will be much greater than that of reactants. This indicates the system would likely be a good source of the products. The large value of K suggests that the products are largely favored, so if the reactants were introduced into the system, the equilibrium would shift to produce more products.