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?

Verified step by step guidance

1. 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.
2. 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.
3. 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.
4. 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.
5. 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.

Key Concepts

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.