Some reactions are so rapid that they are said to be diffusion-controlled; that is, the reactants react as quickly as they can collide. An example is the neutralization of H₃O⁺ by OH^-, which has a second-order rate constant of 1.3⨉10¹¹ M^-1 s^-1 at 25 °C. (b) Under normal laboratory conditions, would you expect the rate of the acid–base neutralization to be limited by the rate of the reaction or by the speed of mixing?

검증된 단계별 안내

Identify the type of reaction: The problem describes a diffusion-controlled reaction, which means the reaction rate is determined by how quickly the reactants can collide.

Understand the given rate constant: The second-order rate constant is given as \(1.3 \times 10^{11} \text{ M}^{-1} \text{s}^{-1}\), which is extremely high, indicating a very fast reaction.

Consider the factors affecting reaction rate: In diffusion-controlled reactions, the rate is limited by the diffusion of reactants through the solution rather than the intrinsic chemical reaction rate.

Evaluate the laboratory conditions: Under normal laboratory conditions, mixing can be a limiting factor if it is not done efficiently, as the reactants need to be brought into contact quickly to maintain the high reaction rate.

Conclude based on diffusion control: Since the reaction is diffusion-controlled, the speed of mixing is more likely to limit the rate of the reaction than the intrinsic reaction rate itself, given the high rate constant.

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Diffusion-Controlled Reactions

Diffusion-controlled reactions occur when the rate of reaction is limited by the rate at which reactants diffuse together. In such cases, the reaction proceeds as quickly as the molecules can collide, making the reaction rate highly dependent on the concentration of the reactants and their mobility in the solution.

Second-Order Kinetics

Second-order reactions are characterized by a rate that depends on the concentration of two reactants or the square of the concentration of one reactant. The rate constant for a second-order reaction, like the neutralization of H3O+ by OH-, is expressed in units of M^-1 s^-1, indicating that the reaction rate increases significantly with higher concentrations of the reactants.

Mixing and Reaction Rates

In laboratory settings, the efficiency of mixing can significantly influence reaction rates, especially for fast reactions. If mixing is inadequate, the reactants may not collide frequently enough to react, potentially limiting the overall reaction rate despite the inherent speed of the reaction itself. Thus, effective mixing is crucial for maximizing the rate of diffusion-controlled reactions.

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교과서 질문

Some reactions are so rapid that they are said to be diffusion-controlled; that is, the reactants react as quickly as they can collide. An example is the neutralization of H₃O⁺ by OH^-, which has a second-order rate constant of 1.3⨉10¹¹ M^-1 s^-1 at 25 °C. (a) If equal volumes of 2.0 M HCl and 2.0 M NaOH are mixed instantaneously, how much time is required for 99.999% of the acid to be neutralized?

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교과서 질문

The half-life for the first-order decomposition of N2O4 is 1.3 * 10-5 s. N2O41g2S 2 NO21g2 If N2O4 is introduced into an evacuated flask at a pressure of 17.0 mm Hg, how many seconds are required for the pressure of NO2 to reach 1.3 mm Hg?

1180

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교과서 질문

The reaction 2 NO1g2 + O21g2S 2 NO21g2 has the thirdorder rate law rate = k3NO423O24, where k = 25 M-2 s-1. Under the condition that 3NO4 = 2 3O24, the integrated rate law is 13O242 = 8 kt +113O24022 What are the concentrations of NO, O2, and NO2 after 100.0 s if the initial concentrations are 3NO4 = 0.0200 M and 3O24 = 0.0100 M?

315

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교과서 질문

Assume that you are studying the first-order conversion of a reactant X to products in a reaction vessel with a constant volume of 1.000 L. At 1 p.m., you start the reaction at 25 °C with 1.000 mol of X. At 2 p.m., you find that 0.600 mol of X remains, and you immediately increase the temperature of the reaction mixture to 35 °C. At 3 p.m., you discover that 0.200 mol of X is still present. You want to finish the reaction by 4 p.m. but need to continue it until only 0.010 mol of X remains, so you decide to increase the temperature once again. What is the minimum temperature required to convert all but 0.010 mol of X to products by 4 p.m.?

486

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