# 3.E: The Vocabulary of Analytical Chemistry (Exercises)

1. When working with a solid sample, it often is necessary to bring the analyte into solution by digesting the sample with a suitable solvent. Any remaining solid impurities are removed by filtration before continuing with the analysis. In a typical total analysis method, the procedure might read

After digesting the sample in a beaker, remove any solid impurities by passing the solution containing the analyte through filter paper, collecting the filtrate in a clean Erlenmeyer flask. Rinse the beaker with several small portions of solvent, passing these rinsings through the filter paper and collecting them in the same Erlenmeyer flask. Finally, rinse the filter paper with several portions of solvent, collecting the rinsings in the same Erlenmeyer flask.

For a typical concentration method, however, the procedure might state

After digesting the sample in a beaker, remove any solid impurities by filtering a portion of the solution containing the analyte. Collect and discard the first several mL of filtrate before collecting a sample of approximately 5 mL for further analysis.

Explain why these two procedures are different.

2. A certain concentration method works best when the analyte’s concentration is approximately 10 ppb.

1. If the method requires a sample of 0.5 mL, about what mass of analyte is being measured?
2. If the analyte is present at 10% w/v, how would you prepare the sample for analysis?
3. Repeat for the case where the analyte is present at 10% w/w.
4. Based on your answers to parts (a)–(c), comment on the method’s suitability for the determination of a major analyte.

3. An analyst needs to evaluate the potential effect of an interferent, I, on the quantitative analysis for an analyte, A. She begins by measuring the signal for a sample in which the interferent is absent and the analyte is present with a concentration of 15 ppm, obtaining an average signal of 23.3 (arbitrary units). When analyzing a sample in which the analyte is absent and the interferent is present with a concentration of 25 ppm, she obtains an average signal of 13.7.

1. What is the sensitivity for the analyte?
2. What is the sensitivity for the interferent?
3. What is the value of the selectivity coefficient?
4. Is the method more selective for the analyte or the interferent?
5. What is the maximum concentration of interferent relative to that of the analyte (i.e. [interferent]/[analyte]), if the error in the analysis is to be less than 1%?

4. A sample was analyzed to determine the concentration of an analyte. Under the conditions of the analysis the sensitivity is 17.2 ppm-1. What is the analyte’s concentration if Stotal is 35.2 and Sreag is 0.6?

5. A method for the analysis of Ca2+ in water suffers from an interference in the presence of Zn2+. When the concentration of Ca2+ is 50 times greater than that of Zn2+, an analysis for Ca2+ gives a relative error of –2.0%. What is the value of the selectivity coefficient for this method?

6. The quantitative analysis for reduced glutathione in blood is complicated by the presence of many potential interferents. In one study, when analyzing a solution of 10 ppb glutathione and 1.5 ppb ascorbic acid, the signal was 5.43 times greater than that obtained for the analysis of 10 ppb glutathione.12 What is the selectivity coefficient for this analysis? The same study found that when analyzing a solution of 350 ppb methionine and 10 ppb glutathione the signal was 0.906 times less than that obtained for the analysis of 10 ppb glutathione. What is the selectivity coefficient for this analysis? In what way do these interferents behave differently?

7. Oungpipat and Alexander described a method for determining the concentration of glycolic acid (GA) in a variety of samples, including physiological fluids such as urine.13 In the presence of only GA, the signal is given as

$S_\textrm{samp,1}=k_\ce{GA}C_\ce{GA}$

and in the presence of both glycolic acid and ascorbic acid (AA), the signal is

$S_\textrm{samp,2}=k_\ce{GA}C_\ce{GA}+ k_\ce{AA}C_\ce{AA}$

When the concentration of glycolic acid is 1.0 × 10–4 M and the concentration of ascorbic acid is 1.0 × 10–5 M, the ratio of the two signals was found to be

$\dfrac{S_\textrm{samp,2}}{S_\textrm{samp,1}} = 1.44$

1. Using the ratio of the two signals, determine the value of the selectivity ratio KGA,AA.
2. Is the method more selective toward glycolic acid or ascorbic acid?
3. If the concentration of ascorbic acid is 1.0 × 10–5 M, what is the smallest concentration of glycolic acid that can be determined such that the error introduced by failing to account for the signal from ascorbic acid is less than 1%?

8. Ibrahim and co-workers developed a new method for the quantitative analysis of hypoxanthine, a natural compound of some nucleic acids.14 As part of their study they evaluated the method’s selectivity for hypoxanthine in the presence of several possible interferents, including ascorbic acid.

1. When analyzing a solution of 1.12 × 10–6 M hypoxanthine the authors obtained a signal of 7.45 × 10–5 amps. What is the sensitivity for hypoxanthine? You may assume that the signal has been corrected for the method blank.
2. When a solution containing 1.12 × 10–6 M hypoxanthine and 6.5 × 10–5 M ascorbic acid was analyzed a signal of 4.04 × 10–5 amps was obtained. What is the selectivity coefficient for this method?
3. Is the method more selective for hypoxanthine or for ascorbic acid?
4. What is the largest concentration of ascorbic acid that may be present if a concentration of 1.12 × 10–6 M hypoxanthine is to be determined within ±1%?

9. Examine a procedure from Standard Methods for the Analysis of Waters and Wastewaters (or another manual of standard analytical methods) and identify the steps taken to compensate for interferences, to calibrate equipment and instruments, to standardize the method and to acquire a representative sample.

## 3.8.3 Solutions to Practice Exercises

### Practice Exercise 3.1

Since the signal for Ag+ in the presence of Ni2+ is given as a relative error, the fact that are not given absolute signals is of no consequence. Instead, we will assign a value of 100 as the signal for 1 × 10–9 M Ag+. With a relative error of +4.9%, the signal for the solution of 1 × 10–9 M Ag+ and 1.1 × 10–7 M Ni2+ is 104.9. The sensitivity for Ag+ is determined using the solution that does not contain Ni2+.

$k_\ce{Ag} = \dfrac{S_\ce{Ag}}{C_\ce{Ag}} = \mathrm{\dfrac{100}{1×10^{−9}\: M} = 1.0 ×10^{11}\: M^{−1}}$

Substituting into equation 3.4 values for kAg, Ssamp for the solution containing Ag+ and Ni2+, and the concentrations of Ag+ and Ni2+

$\mathrm{\mathit{S}_{samp} = 104.9 = (1.0 ×10^{11}\: M^{−1})×(1.0 ×10^{−9}\: M) + \mathit{k}_{Ni}×(1.1×10^{−7}\: M)}$

and solving gives kNi as 4.5 × 107 M–1. The selectivity coefficient is

$\mathrm{\mathit{K}_{Ag,Ni} =\dfrac{\mathit{k}_{Ni}}{\mathit{k}_{Ag}} = \dfrac{4.5×10^7\: M^{−1}}{1.0×10^{11}\: M^{−1}} = 4.5×10^{−4}}$

$K_\textrm{Ag,Hg}×C_\ce{Hg}=−0.01×C_\ce{Ag}$