Chapter 14: Problem 80
There are literally thousands of enzymes at work in complex living systems such as human beings. What properties of the enzymes give rise to their ability to distinguish one substrate from another?
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Chapter 14: Problem 80
There are literally thousands of enzymes at work in complex living systems such as human beings. What properties of the enzymes give rise to their ability to distinguish one substrate from another?
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Enzymes are often described as following the two-step mechanism: $$ \begin{aligned} \mathrm{E}+\mathrm{S} & \rightleftharpoons \mathrm{ES} \text { (fast) } \\ \mathrm{ES} & \ldots \mathrm{E}+\mathrm{P} \text { (slow) } \end{aligned} $$ Where \(\mathrm{E}=\) enzyme, \(\mathrm{S}=\) substrate, and \(\mathrm{P}=\) product. If an enzyme follows this mechanism, what rate law is expected for the reaction?
(a) What is meant by the term elementary reaction? (b) What is the difference between a unimolecular and a bimolecular elementary reaction? (c) What is a reaction mechanism?
One of the many remarkable enzymes in the human body is carbonic anhydrase, which catalyzes the interconversion of carbonic acid with carbon dioxide and water. If it were not for this enzyme, the body could not rid itself rapidly enough of the \(\mathrm{CO}_{2}\) accumulated by cell metabolism. The enzyme catalyzes the dehydration (release to air) of up to \(10^{7} \mathrm{CO}_{2}\) molecules per second. Which components of this description correspond to the terms enzyme, substrate, and turnover number?
Based on their activation energies and energy changes and assuming that all collision factors are the same, which of the following reactions would be fastest and which would be slowest? Explain your answer. (a) \(E_{a}=45 \mathrm{~kJ} / \mathrm{mol} ; \Delta E=-25 \mathrm{~kJ} / \mathrm{mol}\) (b) \(E_{a}=35 \mathrm{~kJ} / \mathrm{mol} ; \Delta E=-10 \mathrm{~kJ} / \mathrm{mol}\) (c) \(E_{a}=55 \mathrm{~kJ} / \mathrm{mol} ; \Delta E=10 \mathrm{~kJ} / \mathrm{mol}\)
Metals often form several cations with different charges. Cerium, for example, forms \(\mathrm{Ce}^{3+}\) and \(\mathrm{Ce}^{4+}\) ions, and thallium forms \(\mathrm{Tl}^{+}\) and \(\mathrm{Tl}^{3+}\) ions. Cerium and thallium ions react as follows: $$ 2 \mathrm{Ce}^{4+}(a q)+\mathrm{Tl}^{+}(a q) \longrightarrow 2 \mathrm{Ce}^{3+}(a q)+\mathrm{Tl}^{3+}(a q) $$ This reaction is very slow and is thought to occur in a single elementary step. The reaction is catalyzed by the addition of \(\mathrm{Mn}^{2+}(a q)\), according to the following mechanism: $$ \begin{aligned} \mathrm{Ce}^{4+}(a q)+\mathrm{Mn}^{2+}(a q) & \longrightarrow \mathrm{Ce}^{3+}(a q)+\mathrm{Mn}^{3+}(a q) \\ \mathrm{Ce}^{4+}(a q)+\mathrm{Mn}^{3+}(a q) & \longrightarrow \mathrm{Ce}^{3+}(a q)+\mathrm{Mn}^{4+}(a q) \\ \mathrm{Mn}^{4+}(a q)+\mathrm{Tl}^{+}(a q) & \longrightarrow \mathrm{Mn}^{2+}(a q)+\mathrm{Tl}^{3+}(a q) \end{aligned} $$ (a) Write the rate law for the uncatalyzed reaction. (b) What is unusual about the uncatalyzed reaction? Why might it be a slow reaction? (c) The rate for the catalyzed reaction is first order in \(\left[\mathrm{Ce}^{4+}\right]\) and first order in \(\left[\mathrm{Mn}^{2+}\right]\). Based on this rate law, which of the steps in the catalyzed mechanism is rate determining? (d) Use the available oxidation states of \(\mathrm{Mn}\) to comment on its special suitability to catalyze this reaction.
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