Question

The rate of forward reaction is two times that of the backward reaction at a given temperature and identical concentration, \(K_{\text {equilimbrium }}\) is, (a) \(1.5\) (b) \(0.5\) (c) \(2.5\) (d) \(2.0\)

Short answer

The equilibrium constant \(K\) is 2, therefore the correct answer is (d) 2.0.

Step-by-step solution

Understanding the Situation

In a reversible reaction, the rate of the forward reaction is related to the rate of the backward (or reverse) reaction. If it is known that the rate of the forward reaction is double that of the backward reaction, then, in essence, the ratio of the rate of forward reaction to the rate of backward reaction is 2:1.

Relating the Rates to the Equilibrium Constant

The equilibrium constant, denoted as K, is a measure of concentrations of products over reactants at equilibrium assuming that the reaction has the same molar coefficients for reactants and products. Since the rate of the forward reaction is double that of the backward reaction, the ratio of the forward reaction rate to the backward reaction rate is \(2/1 = 2\).

Pinpointing the Correct Answer

Since the ratio of the forward to backward reaction rates is 2 (which is also the value of the equilibrium constant \(K_{\text {equilibrium}}\)), the correct answer is \(K = 2\).

Key concepts

Forward Reaction Rate

In chemistry, understanding the concept of reaction rates is crucial. The forward reaction rate refers to how fast the reactants are converted into products in a given chemical reaction. This is the initial direction in which reactants react to form products. The speed at which this conversion happens depends on factors such as temperature, pressure, and concentration of the reactants.
The forward reaction rate can often increase if the conditions favor the formation of products. For instance, if you increase the concentration of reactants or the temperature of the surroundings, you'll likely notice that the forward reaction accelerates. This change is due to more frequent and energetic collisions among molecules leading to more successful reactions.

• Higher concentration of reactants usually leads to a higher forward reaction rate.
• Increased temperature can also boost the reaction speed.
• The presence of a catalyst can further accelerate the forward reaction rate.

Ultimately, understanding the forward reaction's rate helps us predict how quickly a reaction will proceed towards equilibrium.

Backward Reaction Rate

The backward reaction rate is essentially how quickly the products of a reaction revert to form the original reactants. In reversible reactions, both forward and backward reactions occur simultaneously. However, initially, the forward reaction is typically faster, progressing towards equilibrium.
At equilibrium, the rate of the backward reaction equals that of the forward reaction, meaning products are formed and consumed at the same rate. Factors affecting the backward reaction rate are similar to those impacting the forward reaction and may include concentration, temperature, and even catalysts. This rate is essential in determining the dynamics of reversible reactions:

• Higher concentration of products can increase the backward reaction rate.
• Regulating the temperature can affect the reaction rate both forward and backward.
• Catalysts can increase the rate of the backward reaction without being consumed.

Understanding these rates helps in manipulating reaction conditions to favor the desired reaction direction.

Reaction Equilibrium

Reaction equilibrium is a state in a reversible reaction where the rate of the forward reaction is equal to the rate of the backward reaction. At this point, the concentrations of reactants and products remain constant over time, though not necessarily equal. This dynamic equilibrium indicates a balance, despite the continuous transformation of reactants to products and vice versa.
Equilibrium is described by the equilibrium constant, denoted as \( K \), which is calculated using the ratio of the product concentrations to reactant concentrations, each raised to the power of their respective coefficients in the balanced chemical equation. For a reaction to reach equilibrium:

• The rates of the forward and backward reactions must be equal.
• Concentration of reactants and products cease to change.
• Altering external conditions like temperature can shift the equilibrium position.

Thus, understanding reaction equilibrium allows chemists to predict the outcome of reactions and manipulate them to obtain desired concentrations of products.