Question 14.6: The concentration of trace metals in sediment samples collec...
The concentration of trace metals in sediment samples collected from rivers and lakes can be determined by extracting with acid and analyzing the extract by atomic absorption spectrophotometry. One procedure calls for an overnight extraction with dilute \mathrm{HCl} or \mathrm{HNO}_{3}. The samples are placed in plastic bottles with 25 \mathrm{~mL} of acid and extracted on a shaking table at a moderate speed and ambient temperature. To determine the ruggedness of the method, the effect of a change in level for the following factors was studied using the experimental design shown in Table 14.6.
\begin{array}{lll}\text { Factor A – extraction time } & A=24 \mathrm{~h} & a=12 \mathrm{~h} \\ \text { Factor B – shaking speed } & B=\text { medium } & b=\text { high } \\ \text { Factor C – acid type } & C=\mathrm{HCl} & c=\mathrm{HNO}_{3} \\ \text { Factor D – acid concentration } & D=0.1 \mathrm{M} & d=0.05 \mathrm{M} \\ \text { Factor E – volume of acid } & E=25 \mathrm{~mL} & e=35 \mathrm{~mL} \\ \text { Factor F – type of container } & F=\text { plastic } & f=\text { glass } \\ \text { Factor G – temperature } & G=\text { ambient } & g=25^{\circ} \mathrm{C}\end{array}
A standard sample containing a known amount of analyte was carried through the procedure. The percentage of analyte actually found in the eight trials were found to be
\begin{array}{llll} R_{1}=98.9 & R_{2}=99.0 & R_{3}=97.5 & R_{4}=97.7 \\ R_{5}=97.4 & R_{6}=97.3 & R_{7}=98.6 & R_{8}=98.6 \end{array}
Determine which factors, if any, appear to have a significant effect on the response, and estimate the method’s expected standard deviation.
Table 14.6 Experimental Design for a Ruggedness Test Involving Seven Factors
| Run | Factor | Response | ||||||
| A | B | C | D | E | F | G | ||
| 1 | A | B | C | D | E | F | G | R1 |
| 2 | A | B | c | D | e | f | g | R2 |
| 3 | A | b | C | d | E | f | g | R3 |
| 4 | A | b | c | d | e | F | G | R4 |
| 5 | a | B | C | d | e | F | g | R5 |
| 6 | a | B | c | d | E | f | G | R6 |
| 7 | a | b | C | D | e | f | G | R7 |
| 8 | a | b | c | D | E | F | g | R8 |
The effect of a change in level for each factor is calculated using equation 14.15
E_{\mathrm{f}}\,=\,{\frac{\left(\sum R_{i}\right)_{\mathrm{upper\,case}}}{4}}-{\frac{\left(\sum R i\right)_{\mathrm{lower\,case}}}{4}} (14.15)
\begin{aligned} & E_{\mathrm{A}}=\frac{R_{1}+R_{2}+R_{3}+R_{4}}{4}-\frac{R_{5}+R_{6}+R_{7}+R_{8}}{4}=0.30 \\ & E_{\mathrm{B}}=\frac{R_{1}+R_{2}+R_{5}+R_{6}}{4}-\frac{R_{3}+R_{4}+R_{7}+R_{8}}{4}=0.05 \\ & E_{\mathrm{C}}=\frac{R_{1}+R_{3}+R_{5}+R_{7}}{4}-\frac{R_{2}+R_{4}+R_{6}+R_{8}}{4}=-0.05 \\ & E_{\mathrm{D}}=\frac{R_{1}+R_{2}+R_{7}+R_{8}}{4}-\frac{R_{3}+R_{4}+R_{5}+R_{6}}{4}=1.30 \\ & E_{\mathrm{E}}=\frac{R_{1}+R_{3}+R_{6}+R_{8}}{4}-\frac{R_{2}+R_{4}+R_{5}+R_{7}}{4}=-0.10 \\ & E_{\mathrm{F}}=\frac{R_{1}+R_{4}+R_{5}+R_{8}}{4}-\frac{R_{2}+R_{3}+R_{6}+R_{7}}{4}=0.05 \\ & E_{\mathrm{G}}=\frac{R_{1}+R_{4}+R_{6}+R_{7}}{4}-\frac{R_{2}+R_{3}+R_{5}+R_{8}}{4}=0.00 \end{aligned}
Ordering the factors by their absolute values
\begin{array}{lr}\text { Factor D } & 1.30 \\ \text { Factor A } & 0.35 \\ \text { Factor E } & -0.10 \\ \text { Factor B } & 0.05 \\ \text { Factor C } & -0.05 \\ \text { Factor F } & 0.05 \\ \text { Factor G } & 0.00\end{array}
shows that the concentration of acid (factor D) has a substantial effect on the response, with a concentration of 0.05~ \mathrm{M} providing a much lower percent recovery. The extraction time (factor A) also appears to be significant, but its effect is not as important as that for the acid’s concentration. All other factors appear to be insignificant.
The method’s estimated standard deviation is
which, for an average recovery of 98.1 \% gives a relative standard deviation of approximately 0.7 \%. If the acid’s concentration is controlled such that its effect approaches that for factors \mathrm{B}, \mathrm{C}, and \mathrm{F}, then the relative standard deviation becomes 0.18 , or approximately 0.2 \%.