Iodine atoms combine to form I₂ in liquid hexane solvent with a rate constant of 1.5⨉10¹⁰ L/mols. The reaction is second order in I. Since the reaction occurs so quickly, the only way to study the reaction is to create iodine atoms almost instantaneously, usually by photochemical decomposition of I₂. Suppose a flash of light creates an initial [I] concentration of 0.0100 M. How long will it take for 95% of the newly created iodine atoms to recombine to form I₂?

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Identify the order of the reaction. The problem states that the reaction is second order in I, which means the rate law is: \( \text{Rate} = k[I]^2 \).

Use the integrated rate law for a second-order reaction: \( \frac{1}{[I]} = kt + \frac{1}{[I]_0} \), where \([I]_0\) is the initial concentration and \([I]\) is the concentration at time \(t\).

Determine the final concentration \([I]\) when 95% of iodine atoms have recombined. Since 95% recombine, 5% remain, so \([I] = 0.05 \times [I]_0 = 0.05 \times 0.0100\, \text{M} = 0.0005\, \text{M}\).

Substitute the known values into the integrated rate law: \( \frac{1}{0.0005} = (1.5 \times 10^{10}\, \text{L/mol s}) \cdot t + \frac{1}{0.0100} \).

Solve for \(t\) to find the time it takes for 95% of the iodine atoms to recombine.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Second-Order Reactions

A second-order reaction is one where the rate of reaction is proportional to the square of the concentration of one reactant or to the product of the concentrations of two reactants. In this case, the reaction involving iodine atoms is second order in I, meaning that the rate of formation of I2 depends on the concentration of I raised to the second power. This relationship is crucial for calculating the time it takes for a certain percentage of reactants to convert into products.

Rate Constant (k)

The rate constant (k) is a proportionality factor in the rate equation that is specific to a given reaction at a specific temperature. For the reaction in question, the rate constant is given as 1.5×10^10 L/mol·s, indicating a very fast reaction. Understanding the significance of the rate constant helps in determining how quickly the reaction proceeds and is essential for calculating the time required for a certain concentration change.

Integrated Rate Law

The integrated rate law for a second-order reaction can be expressed as 1/[A] = 1/[A₀] + kt, where [A] is the concentration at time t, [A₀] is the initial concentration, k is the rate constant, and t is time. This equation allows us to calculate the time required for a specific change in concentration, such as the time it takes for 95% of iodine atoms to recombine into I2. Mastery of this concept is essential for solving the problem presented.