Problem 6 - Chemistry An Atoms First Approach

Question

For the reaction \(A+B \rightarrow C\), explain at least two ways in which the rate law could be zero order in chemical A.

Step-by-Step Solution

Answer

The reaction $A+B \rightarrow C$ can be zero order in chemical A through two approaches: 1. In the presence of a catalyst or an enzyme which saturates with chemical A, the rate of reaction becomes independent of the concentration of A making the reaction zero order with respect to A. 2. If the rate-determining step (slowest step in the reaction mechanism) does not involve chemical A, the rate of the reaction will be independent of the concentration of A, resulting in a zero-order reaction with respect to A.

Step 1: Approach 1: Presence of a catalyst or enzyme which saturates with chemical A

One possible way to make the reaction zero order in chemical A is in the presence of a catalyst or an enzyme which can saturate with A. When the concentration of A increases, the catalyst or enzyme-related reaction site becomes saturated with A, so increasing the concentration of A does not affect the rate of the reaction anymore. The rate of reaction becomes independent of the concentration of A and hence the reaction becomes zero order with respect to chemical A.

Step 2: Approach 2: The rate-determining step does not involve chemical A

Another way to make the reaction zero order in chemical A is if the rate-determining step, which is the slowest step in the reaction mechanism, does not involve chemical A. In a reaction mechanism that has multiple elementary steps, the overall rate law depends on the rate-determining step. If the slowest step in the mechanism does not involve chemical A, the rate of the reaction will be independent of the concentration of chemical A. In this scenario, the reaction order will be zero with respect to chemical A. These are two possible ways for the reaction between A and B to be zero order in chemical A. It is important to remember that the reaction order is determined by the reaction mechanism and cannot be predicted solely based on the balanced chemical equation.

Key Concepts

Reaction Mechanism

In chemistry, the reaction mechanism is a step-by-step sequence of elementary reactions by which a chemical change occurs. Understanding the mechanism helps to identify how different reaction components interact and transform.
A chemical reaction isn't always a one-step process but can involve multiple stages, moving from reactants to products.
This sequence of steps is termed the mechanism of the reaction.

• Each elementary step is a smaller reaction that includes just a few molecules.
• Steps can vary in how quickly they occur; some are fast while others are slow.
• The slowest step plays a crucial role in defining the rate of the entire reaction.

The entire sequence is necessary to fully understand how a given reaction occurs and to derive the reaction's overall rate law.

Catalyst

A catalyst is a substance that speeds up a chemical reaction without being consumed in the process. Catalysts function by lowering the activation energy of a reaction, which allows the reaction to proceed more quickly.
In some cases, a catalyst may become saturated with one of the reactants, affecting the rate order of a reaction.

• They provide an alternative pathway with a lower activation energy.
• They increase the reaction rate but do not alter the position of equilibrium.
• They are specific to certain reactions, meaning a catalyst used for one may not work for another.

In zero order kinetics, the presence of a catalyst can mean that even when the concentration of one reactant increases, it does not affect the reaction rate if the catalyst is already saturated.

Rate-Determining Step

The rate-determining step is the slowest step in a reaction mechanism and it effectively sets the pace of the entire reaction. It's the bottleneck of the process, providing a cap on how fast the overall reaction can proceed.

• If a particular step in a reaction is much slower relative to others, it will determine the reaction's rate.
• The reaction order is significantly impacted by the rate-determining step.
• In some reactions, none of the reactants might directly participate in this slow step.

Due to its slow nature, only components involved in this step influence the reaction’s rate law, making it crucial in determining the reaction's kinetics.

Enzyme Saturation

Enzymes are biological catalysts that significantly increase reaction rates. Enzyme saturation occurs when all enzyme molecules are occupied with substrate molecules, and adding more substrate won't further increase the rate of reaction.

• At low substrate concentrations, increases in concentration lead to proportional increases in reaction rate.
• Once saturation is reached, the enzymes can't work any faster, regardless of the substrate availability.
• This is akin to a busy highway where adding more cars doesn't improve traffic flow once capacity is reached.

In terms of reaction kinetics, enzyme saturation often results in the reaction proceeding at a constant rate, typical of zero order reactions.