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Chapter 14: Problem 70

The first-order rate constant for the dehydration of carbonic acid: $$ \mathrm{H}_{2} \mathrm{CO}_{3} \longrightarrow \mathrm{CO}_{2}+\mathrm{H}_{2} \mathrm{O} $$ is about \(1 \times 10^{2} \mathrm{~s}^{-1}\). In view of this rather high rate constant, explain why it is necessary to have the enzyme carbonic anhydrase to enhance the rate of dehydration in the lungs.

Short Answer

Expert verified
Carbonic anhydrase accelerates CO2 removal, matching physiological demands despite a high intrinsic rate.

Step by step solution

01

Understand the Chemical Reaction

The dehydration of carbonic acid is a chemical reaction where carbonic acid (\(\mathrm{H}_{2} \mathrm{CO}_{3}\)) splits into carbon dioxide (\(\mathrm{CO}_{2}\)) and water (\(\mathrm{H}_{2}\mathrm{O}\)). The transformation can be represented as: \[\mathrm{H}_{2} \mathrm{CO}_{3} \rightarrow \mathrm{CO}_{2} + \mathrm{H}_{2} \mathrm{O}.\] This process is significant in various biological systems, particularly in the context of respiration.
02

Analyze the Role of the Rate Constant

The first-order rate constant \(k\) for this reaction is given as \(1 \times 10^{2} \, \mathrm{s}^{-1}\). This indicates that the reaction proceeds at a relatively fast pace under normal conditions due to the high value of \(k\). First-order reactions have rate laws of the form \(\text{Rate} = k[\text{Reactant}]\), thus, suggesting the reaction does not necessitate catalysis under basic chemical conditions.
03

Examine Biological Relevance in the Lungs

In biological systems, such as the human lungs, rapid elimination of \(\mathrm{CO}_{2}\) formed is crucial for maintaining proper gas exchange and systemic pH balance. Despite a high rate constant under chemical conditions, physiological reactions may demand even greater speed to meet biological needs. This situation arises because living systems operate under different constraints than simple chemical reactions, such as the need to quickly expel CO2 initially dissolved in blood.
04

Discuss the Role of Carbonic Anhydrase

Carbonic anhydrase is the enzyme that catalyzes the hydration and dehydration of carbonic acid in the blood, enhancing the reaction rate beyond the capability of the intrinsic rate constant alone. Although the rate constant is high, the enzyme ensures the reaction proceeds at optimal physiological rates necessary for efficient respiratory function, facilitating rapid removal of carbon dioxide from the bloodstream into lung air spaces.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Dehydration of Carbonic Acid
Dehydration of carbonic acid is a chemical process where carbonic acid (\(\mathrm{H}_{2} \mathrm{CO}_{3}\)) breaks down into carbon dioxide (\(\mathrm{CO}_{2}\)) and water (\(\mathrm{H}_{2}\mathrm{O}\)). This reaction plays a crucial role in our body's respiratory system, especially in the lungs.
  • The chemical equation is: \(\mathrm{H}_{2} \mathrm{CO}_{3} \rightarrow \mathrm{CO}_{2} + \mathrm{H}_{2} \mathrm{O}\).
  • This transformation helps in expelling \(\mathrm{CO}_{2}\), a waste product, from our body.
  • The reaction naturally occurs quite fast, with a rate constant indicating a speedy process even without extra help.
However, despite this inherent speed, our body sometimes needs it to be even faster, especially during vigorous activities. That鈥檚 where enzyme catalysis steps in.
Reaction Rate Constant
A reaction rate constant is a numerical value that provides insight into how fast a particular reaction occurs. For the dehydration of carbonic acid, this rate constant is quite high, at \(1 \times 10^{2} \, \mathrm{s}^{-1}\).
  • This means the reaction is fast under normal conditions.
  • A high rate constant like this suggests that plenty of carbon dioxide is naturally being produced and released.
In the context of this reaction, the term "first-order" is important. It implies that the reaction speed is directly proportional to the concentration of the carbonic acid. Despite the fast natural speed, the biological process demands even more rapid rates for efficient gas exchange in the body.
Enzyme Catalysis
Enzyme catalysis is the acceleration of chemical reactions by enzymes. In our bodies, enzymes serve as incredible natural catalysts. One such enzyme is carbonic anhydrase, which plays a crucial role in speeding up the dehydration of carbonic acid.
  • This enzyme enhances the reaction rate much further than the intrinsic rate constant would allow.
  • It ensures efficient functioning of respiratory processes by processing reactions faster than they'd proceed under typical conditions.
Thanks to carbonic anhydrase, the chemical conversion necessary for breathing happens swiftly, supporting vital physiological functions and maintaining balance in the bloodstream.
Gas Exchange
Gas exchange in the lungs involves swapping of \(\mathrm{O}_{2}\) (oxygen) and \(\mathrm{CO}_{2}\) (carbon dioxide) between the bloodstream and the air we breathe.
  • This process helps to deliver oxygen to cells for energy production while removing \(\mathrm{CO}_{2}\), a by-product of cellular respiration.
  • Efficiency in gas exchange is critical to maintain life-sustaining processes.
Fast and effective removal of \(\mathrm{CO}_{2}\) is important to ensure our body functions smoothly, explaining why enzymes like carbonic anhydrase are so important. They make this crucial conversion process ultrafast, thus, supporting the respiratory system's needs at all times.
Respiratory System
The respiratory system is integral to our survival, responsible for taking in oxygen and expelling carbon dioxide from the body. It consists of organs such as the lungs and airways, which collaborate to ensure effective breathing.
  • Carbonic anhydrase assists the respiratory system by accelerating the conversion of carbon dioxide, enabling quicker release from the bloodstream into the lungs.
  • This efficient processing means that your body can handle different activity levels without problems related to \(\mathrm{CO}_{2}\) buildup.
Without such enzymatic boosts, maintaining the balance of gases during everyday activities or intense exercise would be far less efficient. Thus, carbonic anhydrase plays a vital role in keeping our respiratory systems running smoothly and effectively.

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Most popular questions from this chapter

For the reaction \(\mathrm{X}_{2}+\mathrm{Y}+\mathrm{Z} \longrightarrow \mathrm{XY}+\mathrm{XZ},\) it is found that doubling the concentration of \(\mathrm{X}_{2}\) doubles the reaction rate, tripling the concentration of \(Y\) triples the rate, and doubling the concentration of \(Z\) has no effect. (a) What is the rate law for this reaction? (b) Why is it that the change in the concentration of \(Z\) has no effect on the rate? (c) Suggest a mechanism for the reaction that is consistent with the rate law.

Classify the following elementary reactions as unimolecular, bimolecular, or termolecular: (a) \(2 \mathrm{NO}+\mathrm{Br}_{2} \longrightarrow 2 \mathrm{NOBr}\) (b) \(\mathrm{CH}_{3} \mathrm{NC} \longrightarrow \mathrm{CH}_{3} \mathrm{CN}\) (c) \(\mathrm{SO}+\mathrm{O}_{2} \longrightarrow \mathrm{SO}_{2}+\mathrm{O}\)

The activation energy for the decomposition of hydrogen peroxide: $$ 2 \mathrm{H}_{2} \mathrm{O}_{2}(a q) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(l)+\mathrm{O}_{2}(g) $$ is \(42 \mathrm{~kJ} / \mathrm{mol}\), whereas when the reaction is catalyzed by the enzyme catalase, it is \(7.0 \mathrm{~kJ} / \mathrm{mol}\). Calculate the temperature that would cause the uncatalyzed decomposition to proceed as rapidly as the enzyme-catalyzed decomposition at \(20^{\circ} \mathrm{C}\). Assume the frequency factor A to be the same in both cases.

The decomposition of \(\mathrm{N}_{2} \mathrm{O}\) to \(\mathrm{N}_{2}\) and \(\mathrm{O}_{2}\) is a first-order reaction. At \(730^{\circ} \mathrm{C}\) the half-life of the reaction is \(3.58 \times 10^{3}\) min. If the initial pressure of \(\mathrm{N}_{2} \mathrm{O}\) is 2.10 atm at \(730^{\circ} \mathrm{C},\) calculate the total gas pressure after one half-life. Assume that the volume remains constant.

A flask contains a mixture of compounds \(\mathrm{A}\) and \(\mathrm{B}\). Both compounds decompose by first-order kinetics. The half-lives are 50.0 min for \(\mathrm{A}\) and 18.0 min for \(\mathrm{B}\). If the concentrations of \(\mathrm{A}\) and \(\mathrm{B}\) are equal initially, how long will it take for the concentration of \(\mathrm{A}\) to be four times that of \(\mathrm{B}\) ?
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