Question

Equilibrium constants for some reactions are given. In which of the following case does the reaction go farthest to completion? (a) \(K=10^{2}\) (b) \(K=10^{-2}\) (c) \(K=10\) (d) \(K=1\)

Short answer

The reaction with equilibrium constant (a) K=10^2 goes the farthest to completion.

Step-by-step solution

Understanding Equilibrium Constants

The equilibrium constant (K) tells us the extent to which a reaction proceeds to completion. A larger value of K indicates that the reaction favors the formation of products, while a smaller K value indicates the reaction favors the reactants.

Comparing the Given Constants

Compare the given values of K to determine which is the largest. Since K is based on a 10-logarithm scale, a higher exponent means a larger K value.

Determining the Reaction Completion

In the given options, K=10^2 is the largest equilibrium constant, meaning that the reaction associated with this K goes the farthest to completion.

Key concepts

Chemical Equilibrium

Chemical equilibrium is a state in a chemical reaction where the rate of the forward reaction equals the rate of the reverse reaction. This balance means that the concentrations of the reactants and products remain constant over time, not that they're equal.

During the initial stages of a reaction, reactants are converted into products, causing the forward reaction rate to be high. As products accumulate, the reverse reaction rate increases. Eventually, both rates equalize, leading to an equilibrium state. It's essential to note that reaching this state doesn't mean the reaction has stopped; instead, both reactions occur without net change in concentration. This concept is fundamental because it helps us understand reactions that seem incomplete and why certain conditions can shift the equilibrium, favoring either reactants or products.

Applying this to problem-solving, when given multiple equilibrium constants like in the original problem, we're comparing how 'far' each reaction has proceeded at equilibrium. This comparison doesn't directly tell us the speeds of the reactions or the amount of time needed to reach equilibrium, but rather the ratio of products to reactants when the reaction is in its equilibrium state.

Reaction Completion

The term 'reaction completion' refers to the extent to which reactants are converted to products in a chemical reaction. For a reaction to 'go farthest to completion' means that, at equilibrium, a greater proportion of reactants has been converted into products.

Understanding this concept is crucial when evaluating the equilibrium constant (K). A higher K value typically suggests a reaction which proceeds more towards the products side, indicating that at equilibrium, you will have more products than reactants. Conversely, a low K value means the equilibrium lies more towards the reactant side. It's important to keep in mind that while the position of equilibrium tells us about the relative amounts of reactants and products, it doesn't give information on the reaction's rate.

In our original query, the equilibrium constant values provide insights into reaction completion. The larger the value of K, the more the reaction proceeds towards the product side, indicating a higher degree of completion. Hence, understanding the relationship between K and the degree of reaction completion is pivotal for interpreting chemical reaction behavior.

Logarithmic Scale

A logarithmic scale is a way of displaying numerical data over a very wide range of values in a compact manner. This type of scale is based on orders of magnitude, rather than a standard linear scale. This is beneficial when dealing with values that are exponentially related to each other, such as the equilibrium constants in the given exercise.

In chemistry, the equilibrium constant follows a logarithmic relationship since it is derived from the concentrations of reactants and products raised to their stoichiometric coefficients. This implies that small changes in the numerical value of the equilibrium constant can represent significant changes in the concentration of reactants and products at equilibrium.

The use of a logarithmic scale in determining the size of the equilibrium constant allows us to quickly assess relative reaction completion. When given multiple choices of K, like in the textbook problem, we can conclude that an equilibrium constant with an exponent of 2 (indicating a value of 100 on a base-10 logarithmic scale) suggests a much greater tendency towards the completion of the reaction compared to a constant with a negative exponent, which denotes a much smaller K value. Thus, mastering the concept of logarithmic scales is essential to interpret and compare the significance of equilibrium constants effectively.