Question

In which of the following cases does the reaction go farthest to completion? (a) \(K=10\) (b) \(K=1\) (c) \(K=10^{3}\) (d) \(K=10^{-2}\)

Short answer

The reaction with the constant \(K=10^{3}\) goes the farthest to completion.

Step-by-step solution

Understanding the Reaction Quotient

The reaction quotient, K, is a measure of the ratio of concentrations of products over reactants at equilibrium. It indicates the extent of a reaction - whether it is more product-favored or reactant-faved.

Interpreting the Given Values

In the given exercise, four values of K are provided: \(K=10\), \(K=1\), \(K=10^{3}\), and \(K=10^{-2}\).

Determining the Reaction Extent

A larger K value signifies more products at equilibrium, thus indicating that the reaction has gone farther to completion. Here, \(K=10^{3}\) is the largest value of K among all the provided options, so it represents the reaction having gone the farthest to completion.

Key concepts

Reaction Quotient

When we explore chemical reactions, the reaction quotient, usually denoted as "Q," plays a pivotal role. This concept helps us glimpse into the 'snapshot' of a reaction at any moment before reaching equilibrium. By assessing the ratio of concentrations of products to reactants, Q tells us whether the reaction is likely to proceed towards products or reactants next. The equation is structured similarly to the equilibrium constant (K):

• For gas-phase reactions: \[ Q = \frac{(P_C)^c (P_D)^d}{(P_A)^a (P_B)^b} \] - Where \((P_C)\) and \((P_D)\) are partial pressures of products C and D, and \((P_A)\) and \((P_B)\) are partial pressures of reactants A and B.
• For reactions in solution: \[ Q = \frac{[C]^c [D]^d}{[A]^a [B]^b} \] - Where \([C]\) and \([D]\) are concentrations of products C and D, while \([A]\) and \([B]\) are concentrations of reactants A and B.

If the reaction quotient, Q, is equal to the equilibrium constant, K, the system is at equilibrium. However, if Q differs from K, the reaction will naturally shift to reach equilibrium, moving towards products if Q < K, and towards reactants if Q > K. This helps chemists predict the direction and extent of a reaction under given conditions.

Extent of Reaction

In chemistry, understanding how far a reaction proceeds is vital. This is often referred to as the 'extent of reaction,' which directly ties to the equilibrium constant, K. Essentially, this value quantifies the degree to which reactants transform into products. The bigger the value of K, the more the products are at equilibrium, indicating a greater extent of reaction. The extent of a reaction can be seen on different scales:

• Small K Values (K < 1): The reaction doesn't proceed far, favoring reactants and producing only small amounts of products.
• K Close to 1: At equilibrium, there are comparable amounts of reactants and products.
• Large K Values (K > 1): A large proportion of reactants turn into products, indicating the reaction proceeds extensively towards completion.

The exercise shows that among the given K values, a vast K, such as \(K = 10^3\), signifies a pronounced shift towards products, often denoting that the reaction has reached completion to a more considerable extent compared to smaller values like \(K = 10^{-2}\).

Product-favored Reaction

A product-favored reaction is one in which the equilibrium constant, K, is greater than one. This means, at equilibrium, products are favored over reactants, yielding more product in the reaction mixture. This favorability is crucial for understanding the efficiency and outcome of a chemical process. In product-favored reactions:

• Most reactants have reacted to form high concentrations of products.
• Equilibrium concentration of products surpasses that of reactants.
• Such reactions are often described as moving "far to the right" on reaction diagrams.

Within the context of the exercise, a value like \(K = 10^3\) represents a strongly product-favored equilibrium, underscoring that the reaction shifts significantly towards products compared to lower K values like \(K = 1\) or \(K = 10^{-2}\). Hence, understanding K provides educators and learners a window into how and why reactions behave under given conditions.