The rate constant for the uncatalyzed reaction of two molecules of glycine ethyl ester to form glycylglycine ethyl ester is 0.6 M^-1 s^-1. In the presence of Co²⁺, the rate constant is 1.5 × 10⁶ M^-1 s^-1. What rate enhancement does the catalyst provide?

검증된 단계별 안내

Understand the problem: The question asks for the rate enhancement provided by the catalyst. This is calculated by comparing the rate constant of the catalyzed reaction to the rate constant of the uncatalyzed reaction.

Identify the given values: The rate constant for the uncatalyzed reaction is k₁ = 0.6 M⁻¹s⁻¹, and the rate constant for the catalyzed reaction is k₂ = 1.5 × 10⁶ M⁻¹s⁻¹.

Set up the formula for rate enhancement: Rate enhancement is defined as the ratio of the catalyzed rate constant to the uncatalyzed rate constant. Mathematically, this is expressed as:

\frac{k₂}{k₁}

Substitute the given values into the formula: Replace k₁ and k₂ with their respective values in the formula:

\frac{1.5}{\times} 0.6

Simplify the expression to find the rate enhancement: Perform the division to calculate the ratio, which will give the magnitude of the rate enhancement provided by the catalyst.

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주요 개념

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Rate Constant

The rate constant (k) is a proportionality factor in the rate equation of a chemical reaction, indicating the speed at which reactants are converted to products. It is specific to a given reaction at a particular temperature and is influenced by factors such as concentration and the presence of catalysts. In this question, the rate constants for both the uncatalyzed and catalyzed reactions are provided, which are essential for calculating the rate enhancement.

Catalysis

Catalysis is the process by which the rate of a chemical reaction is increased by the presence of a catalyst, which is a substance that is not consumed in the reaction. Catalysts work by providing an alternative reaction pathway with a lower activation energy, allowing the reaction to proceed more quickly. In this scenario, Co2+ acts as a catalyst, significantly increasing the rate constant from 0.6 M - 1s - 1 to 1.5 * 10^6 M - 1s - 1.

Rate Enhancement

Rate enhancement refers to the factor by which a catalyst increases the rate of a reaction compared to the uncatalyzed reaction. It is calculated by dividing the rate constant of the catalyzed reaction by that of the uncatalyzed reaction. In this case, the rate enhancement can be determined by taking the ratio of the two given rate constants, illustrating the effectiveness of the catalyst in accelerating the reaction.

The rate constant for the uncatalyzed reaction of two molecules of glycine ethyl ester to form glycylglycine ethyl ester is 0.6 M-1 s-1. In the presence of Co2+, the rate constant is 1.5 × 106 M-1 s-1. What rate enhancement does the catalyst provide?