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Chapter 14: Problem 54

The concentrations of enzymes in cells are usually quite small. What is the biological significance of this fact?

Short Answer

Expert verified
The small concentrations of enzymes in cells are biologically significant because it highlights their efficiency. They can catalyze a high number of reactions even in small quantities, allowing the body to conserve resources and regulate reactions to maintain homeostasis.

Step by step solution

01

Understand the Role of Enzymes

Enzymes are biological catalysts that speed up chemical reactions in the body. They function by reducing the activation energy necessary for reactions to proceed.
02

Discuss the Implications of Enzyme Concentrations

The small concentration of enzymes in cells means that these catalysts are highly efficient. Even in small quantities, they are capable of catalyzing a large number of reactions.
03

Link to Biological Significance

The biological significance of this fact is multifold. First, the efficiency of enzymes allows the body to carry out vital functions while conserving resources. Second, their small concentrations ensure that reactions are regulated and do not proceed at a pace that could be harmful to the cell or organism. This is vital for maintaining homeostasis in biological systems.

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Most popular questions from this chapter

What are the units of the rate constant for a thirdorder reaction?

Polyethylene is used in many items such as water pipes, bottles, electrical insulation, toys, and mailer envelopes. It is a polymer, a molecule with a very high molar mass made by joining many ethylene molecules (the basic unit is called a monomer) together (see p. 369 ). The initiation step is $$ \mathrm{R}_{2} \stackrel{k_{1}}{\longrightarrow} 2 \mathrm{R} \cdot \quad \text { initiation } $$ The \(\mathrm{R}\) - species (called a radical) reacts with an ethylene molecule \((\mathrm{M})\) to generate another radical $$ \mathrm{R} \cdot+\mathrm{M} \longrightarrow \mathrm{M}_{1} \cdot $$ Reaction of \(\mathrm{M}_{1}\). with another monomer leads to the growth or propagation of the polymer chain: $$ \mathrm{M}_{1} \cdot+\mathrm{M} \stackrel{k_{\mathrm{p}}}{\longrightarrow} \mathrm{M}_{2} \cdot \quad \text { propagation } $$ This step can be repeated with hundreds of monomer units. The propagation terminates when two radicals combine $$ \mathrm{M}^{\prime} \cdot+\mathrm{M}^{\prime \prime} \cdot \stackrel{k_{t}}{\longrightarrow} \mathrm{M}^{\prime}-\mathrm{M}^{\prime \prime} \quad \text { termination } $$ (a) The initiator used in the polymerization of ethylene is benzoyl peroxide \(\left[\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{COO}\right)_{2}\right]:\) $$ \left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{COO}\right)_{2} \longrightarrow 2 \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{COO} \cdot $$ This is a first-order reaction. The half-life of benzoyl peroxide at \(100^{\circ} \mathrm{C}\) is \(19.8 \mathrm{~min} .\) (a) Calculate the rate constant (in \(\min ^{-1}\) ) of the reaction. (b) If the half-life of benzoyl peroxide is \(7.30 \mathrm{~h}\) or \(438 \mathrm{~min},\) at \(70^{\circ} \mathrm{C},\) what is the activation energy (in \(\mathrm{kJ} / \mathrm{mol}\) ) for the decomposition of benzoyl peroxide? (c) Write the rate laws for the elementary steps in the above polymerization process and identify the reactant, product, and intermediates. (d) What condition would favor the growth of long high-molar-mass polyethylenes?

Reactions can be classified as unimolecular, bimolecular, and so on. Why are there no zero-molecular reactions?

Consider this elementary step: $$ X+2 Y \longrightarrow X Y_{2} $$ (a) Write a rate law for this reaction. (b) If the initial rate of formation of \(\mathrm{XY}_{2}\) is \(3.8 \times 10^{-3} \mathrm{M} / \mathrm{s}\) and the initial concentrations of \(X\) and \(Y\) are \(0.26 M\) and \(0.88 M\), what is the rate constant of the reaction?

Define the half-life of a reaction. Write the equation relating the half-life of a first-order reaction to the rate constant.
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