Question

The iodide ion reacts with hypochlorite ion (the active ingredient in chlorine bleaches) in the following way: \(\mathrm{OCl}^{-}+\mathrm{I}^{-} \longrightarrow \mathrm{OI}^{-}+\mathrm{Cl}^{-} .\) This rapid reaction gives the following rate data: (a) Write the rate law for this reaction. (b) Calculate the rate constant. (c) Calculate the rate when \(\left[\mathrm{OCl}^{-}\right]=\) \(2.0 \times 10^{-3} M\) and \(\left[I^{-}\right]=5.0 \times 10^{-4} M\)

Short answer

The rate law for this reaction is Rate = \(k[\mathrm{OCl}^{-}][\mathrm{I}^{-}]\). Unfortunately, the problem statement does not provide enough information to calculate the rate constant (k). If the rate constant were given, we could calculate the rate with the provided concentrations: Rate = \(k(2.0 \times 10^{-3})(5.0 \times 10^{-4})\).

Step-by-step solution

Determine the order of the reaction for OCl- and I-

Based on the information given, the reaction can be written as: \(\mathrm{OCl}^{-}+\mathrm{I}^{-} \longrightarrow \mathrm{OI}^{-}+\mathrm{Cl}^{-}\) Since the problem states that this is a "rapid reaction", we can assume that the reaction is first order with respect to both the OCl- and I- ions. Therefore, the rate law can be written as: Rate = \(k [\mathrm{OCl}^{-}]^m [\mathrm{I}^{-}]^n\) Where k is the rate constant, m and n are the reaction orders with respect to OCl- and I- ions, respectively.

Writing the rate law of the reaction

As assumed earlier, the reaction is first order with respect to both OCl- and I-. So, m = 1, and n = 1. Now, we can write the rate law as: Rate = \(k[\mathrm{OCl}^{-}][\mathrm{I}^{-}]\)

Calculate the rate constant

Unfortunately, the rate constant (k) cannot be calculated without more data, such as the initial reaction rates and concentrations. The prompt does not provide enough data to calculate the rate constant.

Calculating the rate of the reaction under specified conditions

If we assume that we have somehow obtained the rate constant k from additional data, we can calculate the rate of the reaction under the given concentrations of OCl- and I- ions. We were given: \([\mathrm{OCl}^{-}] = 2.0 \times 10^{-3} M\) \([\mathrm{I}^{-}] = 5.0 \times 10^{-4} M\) Plugging these values into the rate law equation: Rate = \(k(2.0 \times 10^{-3})(5.0 \times 10^{-4})\) Rate = \(k \times 10^{-6} \) Given k value, we would be able to determine the rate of the reaction. However, due to insufficient data in the problem, we can't proceed further at this point.

Key concepts

Reaction Order

Understanding the concept of reaction order is a key to mastering chemical kinetics. The reaction order refers to the power to which the concentration of a reactant is raised in the rate law expression. For the reaction between iodide ion \((\mathrm{I}^{-})\) and hypochlorite ion \((\mathrm{OCl}^{-})\), the rate law was found to be:

• Rate = \(k[\mathrm{OCl}^{-}][\mathrm{I}^{-}]\)

Here, the reaction is first order with respect to \(\mathrm{OCl}^{-}\) and also first order with respect to \(\mathrm{I}^{-}\). This implies that the rate of reaction will double if the concentration of either \(\mathrm{OCl}^{-}\) or \(\mathrm{I}^{-}\) is doubled, keeping the other constant.

The overall order of reaction is the sum of individual orders: 1 (for \(\mathrm{OCl}^{-}\)) + 1 (for \(\mathrm{I}^{-}\)) = 2. Knowing the order of reaction helps understand the sensitivity of reaction evolution to changes in concentration, crucial for optimizing chemical processes.

Rate Constant

The rate constant \(k\) is a unique factor in the rate law which provides insights into the reaction's speed under specific conditions. For the given exercise, it's crucial to recognize that the rate constant's value is a "constant" at a fixed temperature, but it changes if the temperature varies. The rate constant can only be determined experimentally by measuring initial rates under known concentrations.

In the example provided, determining \(k\) was not possible without sufficient experimental data like initial concentration and rate measurements. However, once \(k\) is known, it allows for calculating the rate of reaction under different conditions using the formula:

• Rate = \(k[\mathrm{OCl}^{-}][\mathrm{I}^{-}]\)

The units of \(k\) depend on the overall order of reaction, which for this second-order reaction would be \(M^{-1}s^{-1}\). Understanding and calculating \(k\) is fundamental for predicting how changes in concentration affect reaction rates.

Concentration

Concentration reflects the amount of a substance present in a specific volume of solution, typically expressed in molarity (M = moles per liter). In chemical kinetics, concentration plays a dual role. First, it affects how fast a reaction occurs, and second, it helps define the form of the rate law.

In our context, the concentrations of \(\mathrm{OCl}^{-}\) and \(\mathrm{I}^{-}\) directly impact the reaction rate as seen in:

• Rate = \(k[\mathrm{OCl}^{-}][\mathrm{I}^{-}]\)

Experimental data often illustrate how varying the concentration of each reactant influences the rate. For example, doubling the concentration of either reactant in a first-order reaction doubles the reaction rate, assuming other conditions remain constant.

Through concentration, chemists can manipulate reaction conditions to enhance desirable rates, making understanding this concept essential for practical applications in chemical industries.