Question

If the equilibrium constant for the reaction \(\mathrm{C} \rightleftharpoons \mathrm{D}\) is \(0.20\), what is the value of the equilibrium constant for the reaction \(\mathrm{D} \rightleftharpoons \mathrm{C}\) ?

Short answer

The equilibrium constant for the reaction D \rightleftharpoons C is 5

Step-by-step solution

Determine the equilibrium constant for the initial reaction

The problem provides the equilibrium constant \( K_1 \) for the reaction \( C \rightleftharpoons D \), which is 0.20.

Use the relationship between the forward and reverse equilibrium constants to find the unknown equilibrium constant

Given that the equilibrium constants for the forward and reverse reactions are inversely related (i.e., \( K_1 = 1/K_2 \)), it is possible to find the equilibrium constant for the reverse reaction. The formula to use here is: \( K_2 = 1/K_1 \)

Compute for \( K_2 \)

Substituting the given \( K_1 \) value into the equation results in \( K_2 = 1/0.20 \)

Key concepts

Chemical Equilibrium

Chemical equilibrium is a fascinating state where the forward and reverse reactions occur at the same rate in a reversible chemical reaction. In this state, the concentrations of the reactants and products remain constant over time, even though the reactions are still happening. This results in no net change in the system.
The idea of chemical equilibrium is critical in understanding how different chemical processes occur in nature and industrial settings. It's important to remember that at equilibrium, it doesn't mean that the reactants and products are equal or that the reaction has stopped. Instead, it means the rate at which the reactants turn into products matches the rate of the reverse, maintaining the balance of concentrations. Understanding this concept helps chemists predict the yield of a reaction under specific conditions, optimizing reactions for desired results.

Reversible Reactions

Reversible reactions are chemical reactions that can proceed in both forward and backward directions. These reactions are symbolized by a double arrow (↔) between the reactants and the products. The characteristic feature of a reversible reaction is that they don't proceed to completion, unlike irreversible reactions which only move in one direction.
In a reversible reaction, the system can shift from producing more products to generating more reactants, depending on certain conditions like temperature, pressure, and concentration. This ability to reverse leads to the establishment of chemical equilibrium, where both forward and backward reactions are balanced. For example, the reaction of CO extsubscript{2} with H extsubscript{2}O to form H extsubscript{2}CO extsubscript{3} is reversible, and altering conditions can shift the equilibrium to produce varying amounts of each component, illustrating the dynamic nature of reversible reactions.

Reaction Quotient

The reaction quotient is a helpful tool in chemistry to determine the direction in which a reaction will proceed to reach equilibrium. Represented by the symbol Q, it is calculated using the concentrations or partial pressures of the reactants and products at any point in time not at equilibrium.
The reaction quotient Q can be compared to the equilibrium constant K to predict the movement of the reaction. If Q < K, the reaction will proceed in the forward direction to produce more products as it moves towards equilibrium. Conversely, if Q > K, the reaction will shift in the reverse direction to form more reactants. When Q = K, the system is already at equilibrium. This concept is instrumental in real-world applications like chemical manufacturing, where predicting the direction of reaction shifts can lead to more efficient processes and better product yields.