Chapter 13

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 \(240 \mathrm{~s} ?\)

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.

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?

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?

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 \(K_{m}\).

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?

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.

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?

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}<

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?

\({ }^{60} \mathrm{Co}\) is a long-lived isotope \(\left(t_{1 / 2}=5.3 \mathrm{yr}\right)\) frequently used as a radiotracer. The activity in a 5.00 -mL sample of a solution of \({ }^{60} \mathrm{Co}\) is \(2.1 \times 10^{7}\) disintegrations/sec. What is the molar concentration of \({ }^{60} \mathrm{Co}\) in the sample?

The concentration of \(\mathrm{Ni}\) in a new alloy is determined by a neutron activation analysis. A 0.500 -g sample of the alloy and a 1.000 -g sample of a standard alloy that is \(5.93 \% \mathrm{w} / \mathrm{w} \mathrm{Ni}\) are irradiated with neutrons in a nuclear reactor. When irradiation is complete, the sample and the standard are allowed to cool and their gamma ray activities measured. Given that the activity is \(1020 \mathrm{cpm}\) for the sample and \(3540 \mathrm{cpm}\) for the standard, determine the \(\% \mathrm{w} / \mathrm{w} \mathrm{Ni}\) in the alloy.

The vitamin \(\mathrm{B}_{12}\) content of a multivitamin tablet is determined by the following procedure. A sample of 10 tablets is dissolved in water and diluted to volume in a 100 -mL volumetric flask. A 50.00 -mL portion is removed and \(0.500 \mathrm{mg}\) of radioactive vitamin \(\mathrm{B}_{12}\) having an activity of 572 cpm is added as a tracer. The sample and tracer are homogenized and the vitamin \(\mathrm{B}_{12}\) isolated and purified, producing \(18.6 \mathrm{mg}\) with an activity of 361 cpm. Calculate the milligrams of vitamin \(\mathrm{B}_{12}\) in a multivitamin tablet.

The steady state activity for \({ }^{14} \mathrm{C}\) in a sample is 13 cpm per gram of carbon. If counting is limited to \(1 \mathrm{hr}\), what mass of carbon is needed to give a percent relative standard deviation of \(1 \%\) for the sample's activity? How long must we monitor the radioactive decay from a 0.50 -g sample of carbon to give a percent relative standard deviation of \(1.0 \%\) for the activity?

To improve the sensitivity of a FIA analysis you might do any of the following: inject a larger volume of sample, increase the flow rate, decrease the length and the diameter of the manifold's tubing, or merge separate channels before injecting the sample. For each action, explain why it leads to an improvement in sensitivity.

The concentration of chloride in seawater is determined by a flow injection analysis. The analysis of a set of calibration standards gives the following results. $$ \begin{array}{cccc} {\left[\mathrm{Cl}^{-}\right](\mathrm{ppm})} & \text { absorbance } & {\left[\mathrm{Cl}^{-}\right](\mathrm{ppm})} & \text { absorbance } \\ \hline 5.00 & 0.057 & 40.00 & 0.478 \\ 10.00 & 0.099 & 50.00 & 0.594 \\ 20.00 & 0.230 & 75.00 & 0.840 \\ 30.00 & 0.354 & & \end{array} $$ A 1.00-mL sample of seawater is placed in a 500 -mL volumetric flask and diluted to volume with distilled water. When injected into the flow injection analyzer an absorbance of 0.317 is measured. What is the concentration of \(\mathrm{Cl}^{-}\) in the sample?

Ramsing and co-workers developed an FIA method for acid-base titrations using a carrier stream that is \(2.0 \times 10^{-3} \mathrm{M} \mathrm{NaOH}\) and that contains the acid-base indicator bromothymol blue. \({ }^{25}\) Standard solutions of \(\mathrm{HCl}\) were injected, and the following values of \(\Delta t\) were measured from the resulting fiagrams. $$ \begin{array}{cccc} {[\mathrm{HCl}](\mathrm{M})} & \Delta t(s) & {[\mathrm{HCl}](\mathrm{M})} & \Delta t(s) \\ \hline 0.008 & 3.13 & 0.080 & 7.71 \\ 0.010 & 3.59 & 0.100 & 8.13 \\ 0.020 & 5.11 & 0.200 & 9.27 \\ 0.040 & 6.39 & 0.400 & 10.45 \\ 0.060 & 7.06 & 0.600 & 11.40 \end{array} $$ A sample with an unknown concentration of \(\mathrm{HCl}\) is analyzed five times, giving values of \(7.43,7.28,7.41,7.37,\) and \(7.33 \mathrm{~s}\) for \(\Delta t .\) Determine the concentration of \(\mathrm{HCl}\) in the sample.

Milardovíc and colleagues used a flow injection analysis method with an amperometric biosensor to determine the concentration of glucose in blood. \(^{26}\) Given that a blood sample that is \(6.93 \mathrm{mM}\) in glucose has a signal of \(7.13 \mathrm{nA}\), what is the concentration of glucose in a sample of blood if its signal is \(11.50 \mathrm{nA}\) ?

Fernández-Abedul and Costa-García developed an FIA method to determine cocaine in samples using an amperometric detector. \(^{27}\) The following signals (arbitrary units) were collected for 12 replicate injections of a \(6.2 \times 10^{-6} \mathrm{M}\) sample of cocaine, \(\mathrm{C}_{17} \mathrm{H}_{21} \mathrm{NO}_{4}\). \(\begin{array}{lll}24.5 & 24.1 & 24.1 \\ 23.8 & 23.9 & 25.1 \\ 23.9 & 24.8 & 23.7 \\ 23.3 & 23.2 & 23.2\end{array}\) (a) What is the relative standard deviation for this sample? (b) The following calibration data are available $$ \begin{array}{cc} \text { [cocaine] }(\mu \mathrm{M}) & \text { signal (arb. units) } \\ \hline 0.18 & 0.8 \\ 0.36 & 2.1 \\ 0.60 & 2.4 \\ 0.81 & 3.2 \\ 1.0 & 4.5 \\ 2.0 & 8.1 \\ 4.0 & 14.4 \\ 6.0 & 21.6 \\ 8.0 & 27.1 \\ 10.0 & 32.9 \end{array} $$ In a typical analysis a 10.0 -mg sample is dissolved in water and diluted to volume in a \(25-\mathrm{mL}\) volumetric flask. A \(125-\mu \mathrm{L}\) aliquot is transferred to a \(25-\mathrm{mL}\) volumetric flask and diluted to volume with a \(\mathrm{pH} 9\) buffer. When injected into the flow injection apparatus a signal of 21.4 (arb. units) is obtained. What is the \(\% \mathrm{w} / \mathrm{w}\) cocaine in the sample?

Holman, Christian, and Ruzicka described an FIA method to determine the concentration of \(\mathrm{H}_{2} \mathrm{SO}_{4}\) in nonaqueous solvents. \({ }^{28}\) Agarose beads \((22-45 \mu \mathrm{m}\) diameter \()\) with a bonded acid- base indicator are soaked in \(\mathrm{NaOH}\) and immobilized in the detector's flow cell. Samples of \(\mathrm{H}_{2} \mathrm{SO}_{4}\) in \(n\) -butanol are injected into the carrier stream. As a sample passes through the flow cell, an acid-base reaction takes place between \(\mathrm{H}_{2} \mathrm{SO}_{4}\) and \(\mathrm{NaOH}\). The endpoint of the neutralization reaction is signaled by a change in the bound indicator's color and is detected spectrophotometrically. The elution volume needed to reach the titration's endpoint is inversely proportional to the concentration of \(\mathrm{H}_{2} \mathrm{SO}_{4} ;\) thus, a plot of endpoint volume versus \(\left[\mathrm{H}_{2} \mathrm{SO}_{4}\right]^{-1}\) is linear. The following data is typical of that obtained using a set of external standards. $$ \begin{array}{cc} {\left[\mathrm{H}_{2} \mathrm{SO}_{4}\right](\mathrm{mM})} & \text { end point volume }(\mathrm{mL}) \\ \hline 0.358 & 0.266 \\ 0.436 & 0.227 \\ 0.560 & 0.176 \\ 0.752 & 0.136 \\ 1.38 & 0.075 \\ 2.98 & 0.037 \\ 5.62 & 0.017 \end{array} $$ What is the concentration of \(\mathrm{H}_{2} \mathrm{SO}_{4}\) in a sample if its endpoint volume is \(0.157 \mathrm{~mL}\) ?