Question

In which of the following cases does the reaction go farthest to completion: (a) \(\mathrm{K}=1\) (b) \(\mathrm{K}=10\) (c) \(\mathrm{K}=10^{-2}\) (d) \(\mathrm{K}=10^{2}\)

Short answer

The reaction goes farthest to completion in case (d) \( \mathrm{K}=10^2 \).

Step-by-step solution

Understanding the Equilibrium Constant

The equilibrium constant, denoted as \( K \), indicates the extent to which a chemical reaction proceeds to completion. Larger \( K \) values mean the reaction proceeds further towards the formation of products, whereas smaller \( K \) values mean less product formation. A \( K \) value of 1 suggests a significant amount of both reactants and products are present at equilibrium.

Analyzing Each Option

Review the \( K \) values provided in each option: - (a) \( K=1 \) suggests neither reactants nor products are favored significantly.- (b) \( K=10 \) suggests products are favored slightly.- (c) \( K=10^{-2} \) suggests reactants are favored since it's less than 1.- (d) \( K=10^{2} \) suggests products are strongly favored as \( K \) is much greater than 1.

Finding the Reaction Going Farthest to Completion

From the analysis, the greatest \( K \) value indicates the reaction that goes farthest toward completion. Since \( K=10^{2} \) is greater than the other \( K \) values, option (d) represents the reaction that proceeds farthest toward the products.

Key concepts

Equilibrium Constant

The equilibrium constant, denoted by the symbol \( K \), is a crucial concept in understanding chemical reactions. It represents the ratio of the concentrations of products to reactants at equilibrium. This balance suggests how far a reaction proceeds.
A larger equilibrium constant indicates that a reaction tends to form more products, implying that it proceeds further to completion. On the other hand, a smaller \( K \) value shows that the reactants are preferred, meaning the reaction does not go as far in converting reactants to products. An equilibrium constant value of 1 is unique because it suggests a balance between reactants and products. Both are present in comparable amounts when the system reaches equilibrium.
Key points to remember:

• \( K > 1 \): Products are favored.
• \( K < 1 \): Reactants are favored.
• \( K = 1 \): Neither side is strongly favored.

Understanding \( K \) allows chemists to predict how environmental changes or shifts in concentration might affect the equilibrium position of a given chemical reaction.

Reaction Completion

Knowing how far a reaction goes towards completion is essential in chemistry. The concept of completion signifies the extent to which reactants are converted into products. The equilibrium constant plays a significant role in this assessment.
When a chemical reaction has a high \( K \) value, it suggests that the reaction goes largely towards completion. A substantial amount of product is formed, indicating that the reactants have been almost fully converted. Conversely, a low \( K \) value signals that the reaction does not favor the products as much, and many of the reactants remain unreacted.
For instance:

• In a reaction with \( K = 10^{2} \), most reactants convert to products, suggesting a high degree of completion.
• If \( K = 10^{-2} \), it indicates the reaction has limited completion, with reactants largely remaining unreacted.

Chemists use the concept of reaction completion to determine feasible conditions for reactions and optimize processes to ensure maximum yield of desired products.

Product Formation

Product formation refers to the creation of new substances as a result of a chemical reaction. It depends largely on the equilibrium constant.
The higher the \( K \) value, the more products are formed because the equilibrium lies far to the product side. This means any increase in \( K \) indicates a higher concentration of products at equilibrium compared to reactants. A reaction with a high \( K \) proceeds with significant product formation, assuring a larger yield.
Let's break it down:

• A high \( K \), like \( 10^{2} \), means a substantial product yield.
• Most of the reactants are transformed into products in such cases.
• In comparison, a low \( K \), such as \( 10^{-2} \), results in minimal product formation, with high levels of unconverted reactants.

Having insight into product formation is invaluable in industries and laboratories where maximizing product yield is desired. Understanding this characteristic helps in modifying reaction conditions to improve overall efficiency and outcomes in chemical processes.