Question

Hydrogen peroxide and the iodide ion react in acidic solution as follows: $$\mathrm{H}_{2} \mathrm{O}_{2}(a q)+3 \mathrm{I}^{-}(a q)+2 \mathrm{H}^{+}(a q) \longrightarrow \mathrm{I}_{3}^{-}(a q)+2 \mathrm{H}_{2} \mathrm{O}(l)$$ The kinetics of this reaction were studied by following the decay of the concentration of \(\mathrm{H}_{2} \mathrm{O}_{2}\) and constructing plots of \(\ln \left[\mathrm{H}_{2} \mathrm{O}_{2}\right]\) versus time. All the plots were linear and all solutions had \(\left[\mathrm{H}_{2} \mathrm{O}_{2}\right]_{0}=8.0 \times 10^{-4} \mathrm{mol} / \mathrm{L} .\) The slopes of these straight lines depended on the initial concentrations of \(\mathrm{I}^{-}\) and \(\mathrm{H}^{+} .\) The results follow: The rate law for this reaction has the form $$\text { Rate }=\frac{-\Delta\left[\mathrm{H}_{2} \mathrm{O}_{2}\right]}{\Delta t}=\left(k_{1}+k_{2}\left[\mathrm{H}^{+}\right]\right)\left[\mathrm{I}^{-}\right]^{m}\left[\mathrm{H}_{2} \mathrm{O}_{2}\right]^{n}$$ a. Specify the order of this reaction with respect to \(\left[\mathrm{H}_{2} \mathrm{O}_{2}\right]\) and \(\left[\mathrm{I}^{-}\right]\) b. Calculate the values of the rate constants, \(k_{1}\) and \(k_{2}\) c. What reason could there be for the two-term dependence of the rate on \(\left[\mathrm{H}^{+}\right] ?\)

Short answer

The order of the reaction with respect to H₂O₂ is 1, and with respect to I⁻ is m, as denoted by the rate law equation: Rate = \((k_{1}+k_{2}[H^{+}])[I^{-}]^{m}[H_{2}O_{2}]\). However, specific data is needed to calculate the values of the rate constants, k₁ and k₂. The two-term dependence of the rate on [H⁺] could be due to either the existence of a parallel reaction or the existence of a pre-equilibrium.

Step-by-step solution

Determine the order of the reaction with respect to H₂O₂ and I⁻

To determine the order of the reaction with respect to H₂O₂ and I⁻, we need to examine the rate law equation given: Rate = \(-\Delta[H_{2}O_{2}]/\Delta t = (k_{1}+k_{2}[H^{+}])[I^{-}]^{m}[H_{2}O_{2}]^{n}\) Since the plots of ln[H₂O₂] vs time were linear, this indicates that the decay of the H₂O₂ concentration is a first-order reaction. Therefore, we can conclude that n = 1. Now let's look at the relationship between [H₂O₂] and [I⁻]. Since the initial [H₂O₂] remains constant at 8.0 x 10⁻⁴ mol/L, the rate law equation also indicates a direct proportionality between the rate and [I⁻]^m. Thus, our rate law simplifies to: Rate = \((k_{1}+k_{2}[H^{+}])[I^{-}]^{m}[H_{2}O_{2}]\)

Calculate the values of the rate constants k₁ and k₂

We do not have the direct experimental data for the slopes, [H⁺], and [I⁻] concentrations in the given problem. Based on the experimental data we are supposed to have, we could create a linear regression for different initial [I⁻] and [H⁺] concentrations and find the slopes to determine the values of k₁ and k₂. In general, the procedure to find k₁ and k₂ would be: 1. For each set of [I⁻], and [H⁺], find the slope (let's call it S) from the linear plots of ln[H₂O₂] vs time. 2. Use the equation S = (k₁ + k₂[H⁺])[I⁻]^m to solve for k₁ and k₂ simultaneously with different sets of initial [I⁻], and [H⁺]. However, as no data is provided, we cannot calculate k₁ and k₂. Please provide the data to proceed with the calculations.

Explain the two-term dependence of the rate on [H⁺]

Based on the given rate law (k₁ + k₂[H⁺]), it is clear that there are two contributions to the rate of the reaction that are affected by [H⁺] concentration. This two-term dependence could be due to two different reasons: 1. Existence of a parallel reaction: The hydrogen peroxide reaction with the iodide ion may be happening through two separate pathways that have different dependencies on [H⁺]. One reaction pathway may have no dependence on [H⁺] (k₁ term), while the other pathway may have a direct dependence on [H⁺] (k₂[H⁺] term). Both pathways will contribute to the overall rate of the reaction. 2. Existence of a pre-equilibrium: There could be an initial fast equilibrium reaction between H₂O₂, I⁻, and H⁺ producing an intermediate. This equilibrium could be described by the k₁ term. This intermediate then may further react to form the products at a rate that depends on [H⁺], giving rise to the k₂[H⁺] term in the rate law.

Key concepts

Rate Law

The rate law is a formula that helps us understand the speed or rate at which a chemical reaction occurs.
It is expressed as an equation that relates the concentration of reactants to the rate of the reaction. In the given reaction of hydrogen peroxide with iodide ions, the rate law is provided in a specific form:
\[ \text{Rate} = (k_{1} + k_{2}[H^{+}])[I^{-}]^{m}[H_{2}O_{2}]^{n} \] The given rate law suggests that the reaction rate depends on the concentrations of iodide ions \([I^-]\) and hydrogen peroxide \([H_{2}O_{2}]\). There are also two rate constants, \(k_{1}\) and \(k_{2}\), involved that depend on the hydrogen ion concentration \([H^+]\).
Understanding the components of a rate law helps to predict how changing conditions, like concentration of reactants or presence of catalysts, might affect the reaction rate.

Reaction Order

The order of a reaction provides insight into how the concentration of each reactant influences the rate of the reaction.
For hydrogen peroxide, the reaction was found to be first-order with respect to \([H_{2}O_{2}]\). This is because the plot of \(\ln[H_{2}O_{2}]\) versus time is linear, indicating a direct proportion. So, \(n = 1\) for \([H_{2}O_{2}]\).
For the iodide ion \([I^-]\), the rate law indicates a dependence on \([I^-]^{m}\), where \(m\) denotes the reaction order for \([I^-]\).
The reaction order can help chemists determine how sensitive the reaction rate is to changes in reactant concentrations.

• First-order reactions mean the rate doubles if the concentration doubles.
• Second-order implies the rate quadruples if the concentration doubles.

Understanding reaction order is essential for controlling and optimizing chemical processes in industrial applications.

Reaction Mechanisms

Reaction mechanisms provide a detailed step-by-step description of the molecular events in a chemical reaction.
It includes all the elementary steps leading from reactants to products and helps to identify possible intermediates.
In the hydrogen peroxide reaction, there's a suggestion of two pathways due to the dual dependence on \([H^+]\), which might imply the involvement of parallel reactions or intermediate species.- **Parallel Pathway Hypothesis:** Suggests that there are two different reactions pathways, one unaffected by \([H^+]\) (related to \(k_{1}\)), and another that increases with \([H^+]\) (associated with \(k_{2}[H^{+}])\).
- **Pre-Equilibrium Concept:** In this scenario, there's an initial fast reversible reaction that forms an intermediate, which then reacts further to form products.
Understanding reaction mechanisms is crucial for predicting the behavior of the reaction under different conditions and for synthesizing new compounds efficiently.

Chemical Equilibrium

Chemical equilibrium occurs when the rate of the forward reaction equals the rate of the backward reaction, resulting in no net change in the concentration of reactants and products. In the context of the reaction kinetics being discussed, if an intermediate is formed via a pre-equilibrium step, then this intermediate might be at equilibrium during the reaction.
When considering the possible pre-equilibrium in the reaction between hydrogen peroxide, iodide ions, and hydrogen ions, the understanding of equilibrium can explain how the concentration of ions doesn't change the rate dramatically after reaching a certain point.

• Equilibrium constant \(K\) expresses the ratio of concentrations of products to reactants at equilibrium.
• Despite changes in concentration, temperature, or pressure, equilibrium helps in maintaining a balance within the reaction system.

Grasping the concept of chemical equilibrium aids in understanding the balance of reversible reactions and is key to performing successful reactions in industrial chemistry.