Question

In which of the following reactions, the concentration of product is higher than the concentration of reactant at equilibrium? = equilibrium constant): (a) \(\mathrm{A} \rightleftharpoons \mathrm{B} ; \mathrm{K}=0.001\) (b) \(\mathrm{M} \rightleftharpoons \mathrm{N} ; \mathrm{K}=10\) (c) \(\mathrm{X} \rightleftharpoons \mathrm{Y} ; \mathrm{K}=0.005\) (d) \(\mathrm{R} \rightleftharpoons \mathrm{P} ; \mathrm{K}=0.01\)

Short answer

Reaction (b) has a higher concentration of products at equilibrium.

Step-by-step solution

Understanding the Equilibrium Constant

The equilibrium constant, K, describes the ratio of the concentrations of products to reactants at equilibrium. If K > 1, products are favored. If K < 1, reactants are favored.

Evaluating Each Reaction

For each reaction, compare K to 1. A larger K value indicates a higher product concentration. (a) K = 0.001. This is much less than 1, so reactants are favored. (b) K = 10. This is greater than 1, so products are favored. (c) K = 0.005. This is less than 1, so reactants are favored. (d) K = 0.01. This is less than 1, indicating reactants are favored.

Determining the Reaction with Higher Product Concentration

From the analysis, only reaction (b) has a K > 1. This means that in reaction (b), the concentration of the product, N, is higher than that of the reactant, M, at equilibrium.

Key concepts

Equilibrium Constant

The equilibrium constant, commonly represented by the symbol \( K \), plays an essential role in determining the balance between products and reactants in a chemical reaction when it reaches a state of equilibrium. At equilibrium, the rate of the forward reaction equals the rate of the backward reaction, meaning that the concentrations of products and reactants remain constant over time.

Understanding \( K \) helps us to know whether the products or the reactants are more prevalent at equilibrium:

• If \( K > 1 \), this suggests that at equilibrium, products are present in a higher concentration than reactants. In other words, the forward reaction is favored.
• If \( K < 1 \), it implies that reactants are more concentrated than products, and thus, the backward reaction is favored.
• When \( K = 1 \), neither the forward nor the backward reaction is favored, resulting in an equal tendency toward products and reactants.

This variable \( K \) is dimensionless and is derived from the concentrations of products over reactants, each raised to the power of their stoichiometric coefficients in the balanced chemical equation.

Product Concentration

In a chemical reaction, product concentration refers to the amount of product that is present at equilibrium. This concentration can vary depending on the value of the equilibrium constant \( K \).

If the equilibrium constant \( K \) is greater than 1, this typically means that the concentration of products is higher than that of reactants at equilibrium. The products are "favored," meaning the chemical system favors the formation of products over reactants.

Consider reaction (b) from the original problem, \( \mathrm{M} \rightleftharpoons \mathrm{N} \), with \( K = 10 \). Since \( K > 1 \), the concentration of \( \mathrm{N} \) (product) will be higher compared to \( \mathrm{M} \) (reactant) at equilibrium.

It is important to remember that higher product concentration signifies that the forward reaction dominates to achieve the equilibrium state, leading to a greater conversion of reactants into products. This makes the equilibrium constant a useful tool for predicting the point at which a reaction will stabilize.

Reactant Concentration

Reactant concentration, much like product concentration, is the amount of reactant present in a chemical reaction at equilibrium. The concentration of reactants is determined relative to product concentration by the value of the equilibrium constant \( K \).

When \( K < 1 \), the chemical equilibrium is said to favor reactants. This is because reactants are present in high concentrations compared to products. The backward reaction, which converts products back into reactants, is more prominent in reaching equilibrium.

For example, in the reactions given in parts (a), (c), and (d) of the exercise:

• Reaction (a) \( K = 0.001 \)
• Reaction (c) \( K = 0.005 \)
• Reaction (d) \( K = 0.01 \)

All of these have \( K < 1 \), meaning that in these scenarios, the reactant concentrations are higher than the product concentrations. This indicates an equilibrium position that heavily favors the reactants and only slightly proceeds to form products. The equilibrium constant thus provides a valuable insight into predicting reactant concentrations in various chemical reactions.