Chapter 7: Problem 43
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
Expert verified
The reaction goes farthest to completion in case (d) \( \mathrm{K}=10^2 \).
Step by step solution
01
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.
02
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.
03
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.
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
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:
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.
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:
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.
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:
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.