Problem 3
In the presence of acid, iodide is oxidized by hydrogen peroxide $$ 2 \mathrm{I}^{-}(a q)+\mathrm{H}_{2} \mathrm{O}_{2}(a q)+2 \mathrm{H}_{3} \mathrm{O}^{+}(a q) \longrightarrow 4 \mathrm{H}_{2} \mathrm{O}(l)+\mathrm{I}_{2}(a q) $$ When \(\mathrm{I}^{-}\) and \(\mathrm{H}_{3} \mathrm{O}^{+}\) are present in excess, we can use the reaction's kinetics of the reaction, which is pseudo- first order in \(\mathrm{H}_{2} \mathrm{O}_{2},\) to determine the concentration of \(\mathrm{H}_{2} \mathrm{O}_{2}\) by following the production of \(\mathrm{I}_{2}\) with time. In one analysis the solution's absorbance at \(348 \mathrm{nm}\) was measured after \(240 \mathrm{~s}\). Analysis of a set of standard gives the results shown below. $$ \begin{array}{cc} {\left[\mathrm{H}_{2} \mathrm{O}_{2}\right](\mu \mathrm{M})} & \text { absorbance } \\ \hline 100.0 & 0.236 \\ 200.0 & 0.471 \\ 400.0 & 0.933 \\ 800.0 & 1.872 \end{array} $$ What is the concentration of \(\mathrm{H}_{2} \mathrm{O}_{2}\) in a sample if its absorbance is 0.669 after \(240 \mathrm{~s} ?\)
Problem 5
Malmstadt and Pardue developed a variable time method for the determination of glucose based on its oxidation by the enzyme glucose oxidase. \({ }^{22}\) To monitor the reaction's progress, iodide is added to the samples and standards. The \(\mathrm{H}_{2} \mathrm{O}_{2}\) produced by the oxidation of glucose reacts with \(\mathrm{I}^{-}\), forming \(\mathrm{I}_{2}\) as a product. The time required to produce a fixed amount of \(I_{2}\) is determined spectrophotometrically. The following data was reported for a set of calibration standards $$ \begin{array}{rrrr} \text { [glucose] (ppm) } & & \text { time }(s) & \\ \hline 5.0 & 146.5 & 150.0 & 149.6 \\ 10.0 & 69.2 & 67.1 & 66.0 \\ 20.0 & 34.8 & 35.0 & 34.0 \\ 30.0 & 22.3 & 22.7 & 22.6 \\ 40.0 & 16.7 & 16.5 & 17.0 \\ 50.0 & 13.3 & 13.3 & 13.8 \end{array} $$ To verify the method a standard solution of 20.0 ppm glucose was analyzed in the same way as the standards, requiring \(34.6 \mathrm{~s}\) to produce the same extent of reaction. Determine the concentration of glucose in the standard and the percent error for the analysis.
Problem 6
Deming and Pardue studied the kinetics for the hydrolysis of \(p\) -nitrophenyl phosphate by the enzyme alkaline phosphatase. \({ }^{23}\) The reaction's progress was monitored by measuring the absorbance of \(p\) -nitrophenol, which is one of the reaction's products. A plot of the reaction's rate (with units of \(\mu \mathrm{mol} \mathrm{mL}^{-1} \mathrm{sec}^{-1}\) ) versus the volume, \(V\), in milliliters of a serum calibration standard that contained the enzyme, yielded a straight line with the following equation. $$ \text { rate }=2.7 \times 10^{-7} \mu \mathrm{mol} \mathrm{mL}^{-1} \mathrm{~s}^{-1}+\left(3.485 \times 10^{-5} \mu \mathrm{mol} \mathrm{mL}^{-2} \mathrm{~s}^{-1}\right) V $$ A 10.00 -mL sample of serum is analyzed, yielding a rate of \(6.84 \times 10^{-5}\) \(\mu \mathrm{mol} \mathrm{mL}^{-1} \mathrm{sec}^{-1}\). How much more dilute is the enzyme in the serum sample than in the serum calibration standard?
Problem 7
The following data were collected for a reaction known to be pseudofirst order in analyte, \(A\), during the time in which the reaction is monitored. $$ \begin{array}{cc} \text { time }(s) & {[A]_{t}(\mathrm{mM})} \\ \hline 2 & 1.36 \\ 4 & 1.24 \\ 6 & 1.12 \\ 8 & 1.02 \\ 10 & 0.924 \\ 12 & 0.838 \\ 14 & 0.760 \\ 16 & 0.690 \\ 18 & 0.626 \\ 20 & 0.568 \end{array} $$ What is the rate constant and the initial concentration of analyte in the sample?
Problem 8
The enzyme acetylcholinesterase catalyzes the decomposition of acetylcholine to choline and acetic acid. Under a given set of conditions the enzyme has a \(K_{m}\) of \(9 \times 10^{-5} \mathrm{M}\) and a \(k_{2}\) of \(1.4 \times 10^{4} \mathrm{~s}^{-1}\). What is the concentration of acetylcholine in a sample if the reaction's rate is \(12.33 \mu \mathrm{M} \mathrm{s}^{-1}\) in the presence of \(6.61 \times 10^{-7} \mathrm{M}\) enzyme? You may assume the concentration of acetylcholine is significantly smaller than \(K_{m}\).
Problem 9
The enzyme fumarase catalyzes the stereospecific addition of water to fumarate to form \(\mathrm{L}\) -malate. A standard \(0.150 \mu \mathrm{M}\) solution of fumarase has a rate of reaction of \(2.00 \mu \mathrm{M} \min ^{-1}\) under conditions in which the substrate's concentration is significantly greater than \(K_{m}\). The rate of reaction for a sample under identical condition is \(1.15 \mu \mathrm{M} \mathrm{min}^{-1}\). What is the concentration of fumarase in the sample?
Problem 10
The enzyme urease catalyzes the hydrolysis of urea. The rate of this reaction is determined for a series of solutions in which the concentration of urea is changed while maintaining a fixed urease concentration of \(5.0 \mu \mathrm{M}\). The following data are obtained. $$ \begin{array}{cc} \text { [urea }](\mu \mathrm{M}) & \text { rate }\left(\mu \mathrm{M} \mathrm{s}^{-1}\right) \\ \hline 0.100 & 6.25 \\ 0.200 & 12.5 \\ 0.300 & 18.8 \\ 0.400 & 25.0 \\ 0.500 & 31.2 \\ 0.600 & 37.5 \\ 0.700 & 43.7 \\ 0.800 & 50.0 \\ 0.900 & 56.2 \\ 1.00 & 62.5 \end{array} $$ Determine the values of \(V_{\max }, k_{2}\), and \(K_{m}\) for urease.
Problem 11
To study the effect of an enzyme inhibitor \(V_{\max }\) and \(K_{m}\) are measured for several concentrations of inhibitor. As the concentration of the inhibitor increases \(V_{\max }\) remains essentially constant, but the value of \(K_{m}\) increases. Which mechanism for enzyme inhibition is in effect?
Problem 12
In the case of competitive inhibition, the equilibrium between the enzyme,
\(E,\) the inhibitor, \(I,\) and the enzyme-inhibitor complex, \(E I,\) is described
by the equilibrium constant \(K_{E I}\). Show that for competitive inhibition
the equation for the rate of reaction is
$$
\frac{d[P]}{d t}=\frac{V_{\max }[S]}{K_{m}\left\\{1+\left([I] / K_{E
I}\right)\right\\}+[S]}
$$
where \(K_{I}\) is the formation constant for the \(E I\) complex
$$
E+I \rightleftharpoons E I
$$
You may assume that \(k_{2}<
Problem 13
Analytes \(A\) and \(B\) react with a common reagent \(R\) with first-order kinetics. If \(99.9 \%\) of \(A\) must react before \(0.1 \%\) of \(B\) has reacted, what is the minimum acceptable ratio for their respective rate constants?
