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Ch.14 - Chemical Kinetics
Chapter 14, Problem 116b

Enzymes are often described as following the two-step mechanism: E + S Δ ES 1fast2 ES ¡ E + P 1slow2 where E = enzyme, S = substrate, ES = enzyme9substrate complex, and P = product. (b) Molecules that can bind to the active site of an enzyme but are not converted into product are called enzyme inhibitors. Write an additional elementary step to add into the preceding mechanism to account for the reaction of E with I, an inhibitor.

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Identify the components involved in the reaction: E (enzyme), S (substrate), ES (enzyme-substrate complex), P (product), and I (inhibitor).
Understand that the inhibitor (I) binds to the enzyme (E) at the active site, preventing the substrate (S) from binding.
Write the elementary step for the binding of the inhibitor to the enzyme: E + I \rightleftharpoons EI.
Recognize that the formation of the enzyme-inhibitor complex (EI) is a reversible process, similar to the formation of the enzyme-substrate complex (ES).
Note that the presence of the inhibitor affects the overall reaction rate by reducing the availability of the enzyme for the substrate.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Enzyme-Substrate Complex Formation

The enzyme-substrate complex (ES) is a transient molecular structure formed when an enzyme (E) binds to its substrate (S). This interaction is crucial for catalysis, as it stabilizes the transition state and lowers the activation energy required for the reaction to proceed. Understanding this step is essential for analyzing how inhibitors can affect enzyme activity.
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Complex Ions and Formation Constant

Enzyme Inhibition

Enzyme inhibitors are molecules that bind to enzymes and decrease their activity. They can bind to the active site, preventing substrate binding, or to other sites, altering enzyme conformation. Recognizing the role of inhibitors is vital for modifying the reaction mechanism, as they can significantly impact the formation of the enzyme-substrate complex and the overall reaction rate.

Reaction Mechanism

A reaction mechanism describes the step-by-step sequence of elementary reactions that lead to the formation of products from reactants. In the context of enzyme kinetics, adding an elementary step to account for the interaction between the enzyme and an inhibitor (I) is necessary to fully understand how the inhibitor affects the overall reaction pathway and the dynamics of enzyme activity.
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Related Practice
Textbook Question

Platinum nanoparticles of diameter 2 nm are important catalysts in carbon monoxide oxidation to carbon dioxide. Platinum crystallizes in a face-centered cubic arrangement with an edge length of 3.924 Å. (c) Using your results from (a) and (b), calculate the percentage of Pt atoms that are on the surface of a 2.0-nm nanoparticle.

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Textbook Question

One of the many remarkable enzymes in the human body is carbonic anhydrase, which catalyzes the interconversion of carbon dioxide and water with bicarbonate ion and protons. If it were not for this enzyme, the body could not rid itself rapidly enough of the CO2 accumulated by cell metabolism. The enzyme catalyzes the dehydration (release to air) of up to 107 CO2 molecules per second. Which components of this description correspond to the terms enzyme, substrate, and turnover number?

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Open Question
Suppose that, in the absence of a catalyst, a certain biochemical reaction occurs x times per second at normal body temperature 37 °C. In order to be physiologically useful, the reaction needs to occur 5000 times faster than when it is uncatalyzed. By how many kJ/mol must an enzyme lower the activation energy of the reaction to make it useful?
Open Question
Dinitrogen pentoxide (N2O5) decomposes in chloroform as a solvent to yield NO2 and O2. The decomposition is first order with a rate constant at 45 _x001E_C of 1.0 * 10^-5 s^-1. Calculate the partial pressure of O2 produced from 1.00 L of 0.600 M N2O5 solution at 45 _x001E_C over a period of 20.0 h if the gas is collected in a 10.0-L container. (Assume that the products do not dissolve in chloroform.)
Textbook Question

The reaction between ethyl iodide and hydroxide ion in ethanol 1C2H5OH2 solution, C2H5I1alc2 + OH- 1alc2 ¡ C2H5OH1l2 + I - 1alc2, has an activation energy of 86.8 kJ>mol and a frequency factor of 2.10 * 1011 M-1 s-1. (c) Which reagent in the reaction is limiting, assuming the reaction proceeds to completion?

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Textbook Question

The reaction between ethyl iodide and hydroxide ion in ethanol 1C2H5OH2 solution, C2H5I1alc2 + OH- 1alc2 ¡ C2H5OH1l2 + I - 1alc2, has an activation energy of 86.8 kJ>mol and a frequency factor of 2.10 * 1011 M-1 s-1. (d) Assuming the frequency factor and activation energy do not change as a function of temperature, calculate the rate constant for the reaction at 50 C.

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