Problem 16
\({ }^{60} \mathrm{Co}\) 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?
Problem 17
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.
Problem 18
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.
Problem 21
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?
Problem 22
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.
Problem 25
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?
Problem 26
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.
Problem 27
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 \(11.50 \mathrm{nA}\) ?
Problem 28
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?
Problem 29
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 \(0.157 \mathrm{~mL}\) ?
