Problem 81 - Chemistry The Molecular Science

Question

When substrates are present at relatively high concentration and are catalyzed by enzymes, the effect on reaction rate of changing substrate concentration can be described by zeroth-order kinetics. Calculate by what factor the rate of an enzyme-catalyzed reaction changes when the substrate concentration is changed from \(1.5 \times 10^{-2} \mathrm{M}\) to \(4.5 \times 10^{-2} \mathrm{M}\)

Step-by-Step Solution

Answer

The reaction rate does not change; it remains constant due to zeroth-order kinetics.

Step 1: Understand Zeroth-Order Kinetics

In zeroth-order kinetics, the reaction rate is independent of the concentration of the reactant. This means that the rate of reaction remains constant, regardless of changes in substrate concentration.

Step 2: Identify Initial and Final Conditions

We are given an initial substrate concentration of \(1.5 \times 10^{-2} \mathrm{M}\) and a final substrate concentration of \(4.5 \times 10^{-2} \mathrm{M}\). Since the reaction follows zeroth-order kinetics, the rate of reaction at both these concentrations is the same.

Step 3: Calculate the Factor of Rate Change

Because zeroth-order kinetics implies that the rate does not change with substrate concentration, the factor by which the rate changes, when moving from an initial to a final substrate concentration, is 1.

Key Concepts

Enzyme-Catalyzed Reactions

Enzymes play a crucial role in facilitating biochemical reactions by acting as catalysts. They speed up reactions without being consumed in the process.
Enzyme-catalyzed reactions are prevalent in biological systems due to their efficiency and specificity. These reactions occur when enzymes lower the activation energy needed for reactions to proceed, which increases the reaction rate. Key characteristics of enzyme-catalyzed reactions include:

• Specificity: Enzymes are selective, usually catalyzing only a single or closely related set of reactions.
• Reusability: Enzymes are not consumed or permanently altered during the reaction process.
• Substrate Binding: Enzymes bind to substrates—reactants in the enzyme-catalyzed reaction—at their active sites.

This interaction is critical because it allows enzymes to transform substrates into products effectively. When substrate concentration is extremely high, saturation of enzyme active sites occurs, which is why in some cases the reaction can display zeroth-order kinetics, where the rate remains constant regardless of further increases in substrate concentration.

Reaction Rate

The reaction rate refers to the speed at which a chemical reaction proceeds. For enzyme-catalyzed reactions, understanding the reaction rate is essential for determining how quickly substrates are converted to products.
Reaction rates can be influenced by several factors:

• Concentration: Typically, an increase in substrate concentration speeds up the reaction up to a point of saturation.
• Temperature: Higher temperatures can increase reaction rates until the enzyme becomes denatured.
• pH: Each enzyme has an optimal pH at which its activity is maximized.

However, in zeroth-order kinetics, the reaction rate is notably independent of substrate concentration. As a result, the concentration of reactants does not affect the reaction rate, leading to a constant rate under these conditions. This happens because enzyme sites are saturated with substrate, preventing any further increase in reaction rate.

Substrate Concentration

Substrate concentration is one of the critical factors affecting enzyme-catalyzed reactions. In general, as substrate concentration increases, the reaction rate also increases, until a saturation point is reached.
At this saturation point, all active sites of the enzyme molecules are occupied, and the reaction rate becomes constant, exhibiting zeroth-order kinetics. To understand the impact of substrate concentration on enzymatic reactions, consider the following:

• Low substrate concentration leads to a proportional increase in reaction rate due to more frequent collisions between enzyme and substrate.
• High substrate concentrations can lead to saturation where the reaction rate levels off.
• In extreme cases of substrate concentration, enzyme active sites are continuously occupied, leading to a reaction rate that is constant and independent of further increases in substrate concentration.

This concept is crucial when investigating enzyme activity because it helps scientists and researchers determine conditions under which maximum enzyme efficiency and effectiveness are achieved.

Chemical Kinetics

Chemical kinetics is the study of reaction rates and the factors influencing them. It offers insights into the speed at which reactions occur and allows predictions of reaction behavior under varying conditions.
Some core principles of chemical kinetics include:

• Rate Laws: Which express the rate of a reaction as a function of the concentration of reactants.
• Order of Reaction: The sum of the powers of concentration terms in the rate law, which can be zero, first, second, or higher.
• Activation Energy: The minimum energy needed for a reaction to occur, often lowered by the presence of a catalyst such as an enzyme.

In the context of zeroth-order kinetics, chemical kinetics dictates that the reaction rate is independent of the concentration of substrates. This is a special case seen in enzyme-catalyzed reactions where substrate saturation leads to a constant reaction rate. Understanding these kinetics is vital for fields such as drug design and metabolic engineering, where controlling reaction rates can be crucial.