Question

Suppose a reaction has the equilibrium constant \(K=\) \(1.3 \times 10^{8} .\) What does the magnitude of this constant tell you about the relative concentrations of products and reactants that will be present once equilibrium is reached? Is this reaction likely to be a good source of the products?

Short answer

The given equilibrium constant, K, is \(1.3 \times 10^{8}\). This large value indicates that at the equilibrium state, the concentrations of products are much higher than the concentrations of reactants. The large value of K implies that the reaction predominantly moves towards the products, and when equilibrium is reached, there will be a high concentration of products compared to reactants. Thus, this reaction is likely to be a good source of products since it results in higher concentrations of products at the equilibrium state.

Step-by-step solution

Understanding the equilibrium constant

The equilibrium constant, K, of a reaction gives the measure of the ratio of the concentrations of products to the concentrations of reactants once the reaction has reached equilibrium state. It can be mathematically expressed as: \( K=\frac{[Products]}{[Reactants]} \) where [Products] and [Reactants] are the concentrations of products and reactants at equilibrium state respectively. A larger K value indicates that the equilibrium concentrations of products are higher than the concentrations of reactants. A smaller K value indicates that the concentrations of reactants are higher than the concentrations of products at equilibrium.

Interpreting the given equilibrium constant

The given equilibrium constant, K, is 1.3 * 10^8. Since this value of K is very large, it means that at the equilibrium state, the concentrations of products are much higher than the concentrations of reactants. The larger value of K implies that the reaction is moving predominantly towards the products, and when equilibrium is reached, there will be a high concentration of products compared to reactants.

Assessing if the reaction is a good source of products

As mentioned above, the large value of the equilibrium constant (K) indicates that the reaction has a higher concentration of products than reactants at equilibrium. This means that the reaction will mostly move in the forward direction, leading to a significant formation of products. Therefore, the reaction is likely to be a good source of products since it results in higher concentrations of products at the equilibrium state.

Key concepts

Chemical Equilibrium

Chemical equilibrium occurs in a reaction when the rate of the forward reaction equals the rate of the reverse reaction. At this point, the concentration of reactants and products remains constant because they are being formed at the same rate at which they are being consumed. This balance doesn't necessarily mean equal concentrations of reactants and products; rather, it means the concentrations stabilize over time.

• The system is dynamic, indicating continuous reaction forward and backward.
• Equilibrium can be affected by changes in concentration, temperature, and pressure.

It's important to understand that equilibrium does not imply a stoppage of reaction. The molecules continue to react, but there's no net change in the concentration of reactants and products. This state can be represented and quantified using the equilibrium constant, denoted as \(K\), which shows the ratio of product concentrations to reactant concentrations once equilibrium is achieved.

Reaction Direction

The reaction direction is determined by the equilibrium constant \(K\). By looking at the magnitude of \(K\), one can predict which way the reaction is leaning, whether it favors the formation of reactants or products.

• If \(K >> 1\), it means the reaction strongly favors the products, showing a high propensity towards product formation at equilibrium.
• If \(K << 1\), the reaction favors the reactants, indicating minimal product formation.

In the example of \(K = 1.3 \times 10^8\), the value is considerably large, suggesting that the reaction predominantly forms products, driving the reaction to proceed mostly in the forward direction. This insight into direction helps chemists and industry experts understand how successful a reaction is in yielding the desired products.

Product Formation

Product formation in a chemical reaction is significantly influenced by the equilibrium constant. When \(K\) is large, like in the example provided, it designates a substantial formation of products at equilibrium.

This happens because the high \(K\) implies more products are being formed than reactants, often making the process efficient in manufacturing and laboratory settings where product yield is essential.

Such reactions are highly desirable for producing valuable compounds and materials, as they convert a considerable amount of reactants into the intended products.

Understanding this can help in decisions about scaling up reactions for industrial applications where maximizing product output is the goal. Knowing a reaction's tendency towards product formation assists chemists in process design, ensuring that resources are optimally used in obtaining the desired end products.