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?
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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Get started for freeThe reaction \(2 \mathrm{NO}_{2} \longrightarrow 2 \mathrm{NO}+\mathrm{O}_{2}\) has the rate constant \(k=0.63 \mathrm{M}^{-1} \mathrm{~s}^{-1}\). Based on the units for \(k\), is the reaction first or second order in \(\mathrm{NO}_{2} ?\) If the initial concentration of \(\mathrm{NO}_{2}\) is \(0.100 \mathrm{M}\), how would you determine how long it would take for the concentration to decrease to \(0.025 \mathrm{M} ?\)
As described in Exercise \(14.37\), the decomposition of sulfuryl chloride \(\left(\mathrm{SO}_{2} \mathrm{Cl}_{2}\right)\) is a first-order process. The rate constant for the decomposition at \(660 \mathrm{~K}\) is \(4.5 \times 10^{-2} \mathrm{~s}^{-1}\). (a) If we begin with an initial \(\mathrm{SO}_{2} \mathrm{Cl}_{2}\) pressure of 375 torr, what is the pressure of this substance after 65 s? (b) At what time will the pressure of \(\mathrm{SO}_{2} \mathrm{Cl}_{2}\) decline to one-tenth its initial value?
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.
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?
The first-order rate constant for reaction of a particular organic compound with water varies with temperature as follows: $$ \begin{array}{ll} \hline \text { Temperature (K) } & \text { Rate Constant (s }^{-1} \text { ) } \\\ \hline 300 & 3.2 \times 10^{-11} \\ 320 & 1.0 \times 10^{-9} \\ 340 & 3.0 \times 10^{-8} \\ 355 & 2.4 \times 10^{-7} \\ \hline \end{array} $$ From these data, calculate the activation energy in units of \(\mathrm{kJ} / \mathrm{mol}\).
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