Problem 87 - A Complete Resource Book in Chemistry for JEE Main

Question

One mole of \(\mathrm{A}(\mathrm{g})\) is heated to \(200{ }^{\circ} \mathrm{C}\) in a one litre closed flask, till the following equilibrium is reached. \(\mathrm{A}(\mathrm{g}) \rightleftharpoons \mathrm{B}(\mathrm{g})\) The rate of forward reaction at equilibrium is \(0.02 \mathrm{~mol}\) \(\mathrm{L}^{-1} \min ^{-1}\). What is the rate (in \(\mathrm{mol} \mathrm{L}^{-1}, \mathrm{~min}^{-1}\) ) of the backward reaction at equilibrium? (a) \(0.04\) (b) \(0.01\) (c) \(0.02\) (d) 1

Step-by-Step Solution

Answer

The rate of the backward reaction at equilibrium is \(0.02 \text{ mol L}^{-1} \text{ min}^{-1}\).

Step 1: Understanding Chemical Equilibrium

At equilibrium, the rate of the forward reaction equals the rate of the backward reaction. For the reaction \( \text{A}(\text{g}) \rightleftharpoons \text{B}(\text{g}) \), this means the rate at which A turns into B is the same as the rate at which B turns back into A.

Step 2: Analyzing Forward Reaction Rate

The rate of the forward reaction at equilibrium is given as \(0.02 \text{ mol L}^{-1} \text{ min}^{-1}\). This implies that at equilibrium, every minute, 0.02 moles of A are converted to B per liter.

Step 3: Concluding Backward Reaction Rate

Since at equilibrium, the rate of the forward reaction equals the rate of the backward reaction, the backward reaction rate must also be \(0.02 \text{ mol L}^{-1} \text{ min}^{-1}\). This means 0.02 moles of B are being converted back to A per liter every minute.

Key Concepts

Forward Reaction

In any chemical equilibrium, the forward reaction is crucial to understand. The forward reaction is the process where reactants turn into products. For instance, in the reaction \(\mathrm{A(g)} \rightarrow \mathrm{B(g)}\), "forward" refers to the conversion of \(A\) into \(B\). This transformation is driven by various factors, including temperature and concentration of reactants.

• The forward reaction rate measures how quickly reactants are converted to products over time. In our example, at equilibrium, 0.02 moles of \(A\) are converted into \(B\) per liter every minute.
• As a reaction progresses toward equilibrium, the forward reaction initially occurs faster than the backward reaction, gradually slowing down until both rates are equal.

Understanding the forward reaction's rate is vital because it helps predict how fast a reaction reaches equilibrium and how much product can be expected.

Backward Reaction

The backward or reverse reaction is simply the opposite of the forward reaction. It involves the conversion of products back into reactants. In the equilibrium given, this would be \(\mathrm{B(g)} \rightarrow \mathrm{A(g)}\).

• At equilibrium, the backward reaction occurs at the same rate as the forward reaction, ensuring no net change in the concentrations of reactants and products.
• In the scenario where 0.02 moles of \(A\) turn into \(B\) every minute, exactly 0.02 moles of \(B\) convert back to \(A\) per minute at equilibrium. This balance maintains the stability of the system.

This concept highlights the dynamic nature of equilibrium, where reactions continue to occur, but without any overall change in concentration of reactants and products.

Reaction Rate

Reaction rate is a measure of how quickly a chemical reaction occurs. This rate can differ between reactions and is influenced by several factors, such as temperature, pressure, and concentration of reactants. In the context of our exercise, the reaction rate is expressed as \(\text{mol L}^{-1} \text{ min}^{-1}\), representing the moles of substance transformed per unit volume per unit time.

• At equilibrium, both the forward and backward reaction rates are equal. This equality ensures that the system’s concentrations remain constant over time.
• In practice, determining reaction rates involves measuring how quickly reactants are consumed or products are formed.

Understanding reaction rates can help predict the duration required to reach equilibrium and the conditions under which a reaction will proceed most efficiently.

Equilibrium Constant

The equilibrium constant \(K\), is a number that provides insight into the composition of a reaction mixture at equilibrium. It is essential for understanding the extent of a reaction and the concentrations of reactants and products at equilibrium.

• The equilibrium constant is calculated using the concentrations of products and reactants, typically portrayed as \(K = \frac{[\text{products}]}{[\text{reactants}]}\). This ratio reflects the balance between the forward and backward reaction rates.
• If \(K\) is much greater than 1, this suggests that the products dominate at equilibrium, whereas if \(K\) is less than 1, the reactants are more plentiful.

The equilibrium constant is a fixed value at a given temperature and is unaffected by the initial concentrations of the reactants or products. It serves as a fundamental aspect of understanding and predicting the behavior of chemical systems in equilibrium.