Question

Suppose a reaction has the equilibrium constant \(K=4.5 \times 10^{-6}\) at a particular temperature. If an experiment is set up with this reaction, will there be large relative concentrations of products present at equilibrium? Is this reaction useful as a means of producing the products? How might the reaction be made more useful?

Short answer

Given the equilibrium constant \(K = 4.5 \times 10^{-6}\) (which is much less than 1), this indicates that the equilibrium of the reaction lies towards the side of the reactants, meaning the concentration of the reactants greatly exceeds the concentration of the products. Therefore, there wouldn't be large relative concentrations of products present at equilibrium. As such, this reaction would not be an effective means of producing the products, as the yield would be quite low. To make the reaction more useful, we could employ a catalyst to lower the activation energy and boost the reaction rate. Alternatively, we could use Le Chatelier’s principle and continuously remove one of the products from the system, causing the equilibrium to shift towards the right and increasing the production of products.

Step-by-step solution

Understand the relation between equilibrium constant \( K \) and product concentration

The value of the equilibrium constant \( K \) is the ratio of the concentrations of the products to the concentrations of the reactants, each raised to the power of their stoichiometric coefficients in the balanced chemical equation. If \( K \) is small (less than 1), it means that at equilibrium the concentration of the reactants is greater than the concentration of the products. If \( K \) is large (greater than 1), the concentration of the products is greater than the concentration of the reactants at equilibrium.

Assess product concentration from the given equilibrium constant

For this reaction, \( K \) is given as \( 4.5 \times 10^{-6} \) which is a very small number, much less than 1. Therefore, it is clear that at equilibrium the concentration of the reactants greatly exceeds the concentration of the products. This means that there will not be large relative concentrations of products present at equilibrium.

Evaluate the usefulness of the reaction for product production

If the goal is to use this reaction to produce the products, based on the small value of \( K \), this reaction would not be particularly useful. This is because the majority of the mixture at equilibrium would be reactants, and the yield of products would be quite small.

Propose strategies to make the reaction more useful

If greater product yield is desired from this reaction, a few approaches could be considered. One common strategy is the use of a catalyst to lower the activation energy and increase the reaction rate. Another way might be applying Le Chatelier’s principle: if we continuously remove one of the products from the system, the equilibrium will shift to the right to replace it, hence, increasing the production of products.

Key concepts

Chemical Equilibrium

Chemical equilibrium is a state in a reversible reaction where the rate of the forward reaction equals the rate of the backward reaction.
This balance means that the concentrations of the reactants and products remain constant over time.
The equilibrium constant, represented as \(K\), helps quantify the position of equilibrium:

• If \(K\) is much greater than 1, the reaction favors products.
• If \(K\) is much less than 1, the reaction favors reactants.

For the reaction in the problem, a small \(K\) value (\(4.5 \times 10^{-6}\)) suggests a strong favoring of reactants, meaning very few products present at equilibrium.
Thus, this reaction is not favorable for producing large amounts of product in its current state.

Le Chatelier’s Principle

Le Chatelier’s Principle describes how a chemical equilibrium will respond to changes in concentration, pressure, or temperature.
When a system at equilibrium experiences a change, it will adjust to minimize that change.
For the given reaction with a small \(K\), you can leverage this principle to increase product yield:

• If a product is continuously removed, equilibrium shifts to produce more products.
• Adding reactants can also drive the equilibrium to the right, favoring more product formation.

These approaches are valuable in industrial applications where maximizing product yield is crucial.
By understanding and applying Le Chatelier's principle, more efficient production in reactions that naturally favor the reactants can be achieved.

Reaction Yield

Reaction yield refers to the amount of product obtained from a chemical reaction relative to the theoretical maximum based on the stoichiometry.
In reactions with an equilibrium heavily favoring reactants, like this one, the actual yield is often limited.
Strategies to increase reaction yield include:

• Removing products from the reaction mixture to push the equilibrium towards more product formation.
• Increasing reactant concentrations or adjusting reaction conditions like temperature.
• Utilizing a catalyst to speed up the reaction and potentially alter product formation rates.

A low yield indicates a reaction that is less efficient in producing products from reactants under the given conditions.
Improving reaction conditions is critical to optimizing product gains.

Reaction Kinetics

Reaction kinetics involves the study of the speed at which reactions occur and the factors that affect this speed.
For reactions with low yields due to unfavorable equilibria, kinetics plays a crucial role in improving output.
While a small \(K\) suggests a favoring of reactants at equilibrium, reaction kinetics focuses on:

• Determining the reaction rate and how quickly equilibrium is reached.
• Exploring the effect of factors like temperature and catalysts, which can lower activation energy and speed up reactions.

Even if the equilibrium position is not favorable, optimizing kinetics can help achieve sufficient product formation in a shorter time.
Understanding reaction kinetics allows chemists to control and improve chemical processes, enhancing product efficiency and yield.