Problem 61 - Basic Principles of Organic Chemistry

Question

The rate of addition of dimethylmagnesium to excess diphenylmethanone (benzophenone) in diethyl ether initially is cleanly second order, that is, first order in ketone and first order in \(\left(\mathrm{CH}_{3}\right)_{2} \mathrm{Mg}\). As the reaction proceeds, the rate no longer follows a strictly second-order rate overall. Suggest how the apparent specific rate could change as the reaction proceeds.

Step-by-Step Solution

Answer

As the reaction proceeds, complex formation or product inhibition may cause the specific rate to deviate from second-order kinetics.

Step 1: Understand Initial Rate Order

The exercise states that the initial reaction is first order in both the ketone and dimethylmagnesium. This gives us a second-order reaction overall. The rate law can be written as: \( \text{Rate} = k[A][B] \), where \( [A] \) and \( [B] \) represent the concentrations of the ketone and dimethylmagnesium, respectively, and \( k \) is the rate constant.

Step 2: Consider Reaction Progress

As the reaction progresses, concentrations of reactants change. Initially, when both reactants are abundant, the rate follows second-order kinetics. As the reaction proceeds, one or both concentrations decrease, which could lead to deviation from strict second-order behavior.

Step 3: Investigate Possible Complex Formation

The reaction might form intermediate complexes that alter the kinetic order. For example, intermediates may sequester reactants or catalysts (e.g., the formation of by-products or complexation with the ether solvent), reducing the available concentration of active species for the reaction.

Step 4: Assess Product Inhibition

The reaction products could act as inhibitors, slowing the reaction rate as they accumulate. This could alter the apparent rate law from its original kinetic order. Product molecules might interact with active sites or reactants, modifying accessible concentrations.

Step 5: Evaluate Catalyst or Solvent Effects

The effect of the solvent (diethyl ether) might change over the course of the reaction due to the formation of solvates or other complexes. The reaction rate could be altered by changes in the effective concentration of reactants due to the solvent effects.

Step 6: Postulate Specific Rate Change

With the above considerations, the specific rate may become lower than expected from strict second-order kinetics. This could be due to decreased reactant concentrations, formation of intermediates or complexes, or interaction with products altering reaction pathways.

Key Concepts

Rate Law

A rate law is crucial to understanding how the concentration of reactants affects the rate of a chemical reaction. It expresses the relationship in a mathematical form. For the given reaction involving dimethylmagnesium and diphenylmethanone, the initial rate law is expressed as:

• Rate = \( k[A][B] \)

Here, \( [A] \) and \( [B] \) are the concentrations of the ketone and dimethylmagnesium at the start. The rate constant \( k \) remains constant at a constant temperature.
This equation suggests that the reaction is of order one in each reactant, making it second-order in total. By monitoring how changing reactant concentrations impacts the rate, chemists can deduce the reaction mechanism and estimate reaction kinetics.

Second-Order Reaction

A second-order reaction is characterized by the rate being proportional to the square of the concentration of one reactant or the product of the concentrations of two reactants. In this scenario, the initial rate is second-order because it is first-order in each reactant:

• Rate \( = k[A][B] \)

As the reaction progresses, keeping track of changes becomes important. Either concentration change or interactions in the reaction environment can make the rate law appear to shift as the reaction moves forward. This highlights how kinetic order is reliant on the initial conditions and possible adjustments during the reaction process.

Reaction Intermediates

Reaction intermediates are species that form during a reaction pathway, potentially altering kinetics. They don’t appear in the net equation since they are often transient. If the dimethylmagnesium and diphenylmethanone reaction forms intermediates, these could influence the rate unexpectedly. Intermediates can:

• Bind to the reactants, affecting their availability.
• Form complexes that are less reactive.

Intermediates might arise due to complexity in the reaction or interaction with solvents like diethyl ether. These changes can modify the effective reaction pathway, suggesting why the observed kinetics might differ from the anticipated second-order.

Product Inhibition

Product inhibition occurs when the accumulation of products hinders the reaction’s progress. This is a critical factor that can alter reaction kinetics. As products of a reaction build up:

• They may bind to active sites intended for reactants.
• Interference with further reaction steps might happen, thus slowing the rate.

For the reaction of dimethylmagnesium with diphenylmethanone, if products accumulate at significant levels, they might act as inhibitors. This creates an apparent change in rate, where the attention is shifting from initial reactants to managing the concentration and participation of the emerging products. This phenomenon underscoring why a reaction initially follows a second-order rate law and may deviate with progression.