Question

Which of the following relation is correct for \(k_{f}\) and \(k_{b}\) in an equilibrium process that contains equal moles of reactants and products. (a) \(k_{f}=k_{b}\) (b) \(k_{f}>k_{b}\) (c) \(k_{f}

Short answer

At equilibrium with equal moles of reactants and products, the rate constants are equal, so the correct relation is (a) kf=kb.

Step-by-step solution

Understand equilibrium processes

For an equilibrium process, the rate of the forward reaction (turning reactants into products, characterized by the rate constant kf) is equal to the rate of the backward reaction (turning products back into reactants, characterized by the rate constant kb) when the system is at equilibrium. At this point, the amount of reactants and products remains constant over time.

Analyze the given system

The exercise states that the system contains equal moles of reactants and products, suggesting that the system is at equilibrium. Given that the rate of the forward and backward reactions must be equal at equilibrium, their rate constants must be related to each other to maintain that balance.

Relate rate constants at equilibrium

Since the rates of the forward and backward reactions are equal at equilibrium and the system has equal moles of reactants and products, the rate constants kf and kb must also be equal to sustain this balance. Therefore, for an equilibrium process with equal moles of reactants and products, the correct relationship between the rate constants kf and kb will be kf=kb.

Key concepts

Chemical Equilibrium

At the heart of many chemical processes is the concept of chemical equilibrium, a state where the rates of the forward and backward reactions are equal, resulting in no net change in the concentration of reactants and products over time.

This balance does not imply that the reactions have stopped but rather that they continue to occur at an equal pace. For students getting to grips with this idea, it's crucial to visualize it as a dynamic seesaw, constantly in motion, but perfectly balanced. When a reaction reaches this point, it's said to be in a state of equilibrium.

Moreover, for equilibrium to exist, certain conditions must be met, including a closed system and constant conditions such as temperature and pressure. Remember, equilibrium can be disturbed by changing these conditions, leading to a shift in the equilibrium position favoring either the forward or the backward reaction. This is known as Le Chatelier's Principle.

Forward and Backward Reactions

Now, let's delve into the forward and backward reactions that drive chemical equilibrium. A forward reaction converts reactants into products, whereas a backward reaction does precisely the opposite.

It's helpful to imagine these reactions as two teams in a tug-of-war contest, with each side pulling with equal force at equilibrium. When they pull with different strengths, one side might gain ground, analogous to how the concentration of reactants or products changes when a system is not at equilibrium.

Understanding Equal Rates

Referring back to the exercise, it implies an equilibrium scenario. This means the tug-of-war has reached a stalemate, indicating the teams (forward and backward reactions) are equally matched. This does not depend solely on the quantities of reactants and products but also on how forcefully they 'pull', that is, how fast they react, which related directly to their rate constants.

Rate Constant

Finally, let's explore the rate constant. It's a measure of how quickly a given reaction proceeds. A higher rate constant indicates a faster reaction, whether we're talking about forward direction (forming products from reactants, represented by the rate constant kf) or the backward direction (reforming reactants from the products, represented by the rate constant kb).

Consider the rate constant as the inherent strength of each team in our tug-of-war analogy. When presented with equal moles of reactants and products at equilibrium (equal force from both teams), the forward and backward rate constants must be equal, as is correctly identified in option (a) of our exercise. This equivalence maintains the equilibrium 'tie' without allowing either team to gain a sudden advantage.

The rate constants are pivotal in determining the velocity of reactions and hence the time it takes to reach equilibrium. It's worth noting that while the concentrations of reactants and products influence the rates of the forward and backward reactions, the intrinsic rate constants remain unaffected by concentrations and can only change with temperature.