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Chapter 30: Problem 2

Determine unknowns from a calibration curve. The following data are for a set of calibration standards of \(\mathrm{Zn}\), measured by atomic absorption spectroscopy. Absorbance measurements for a series of standard solutions containing different amounts of zinc: $$ \begin{array}{cc} \text { Zinc concentration }\left(\mu \mathrm{g} \mathrm{mL}^{-1}\right) & \text { Absorbance } \\ 0 & 0.000 \\ 1 & 0.082 \\ 2 & 0.174 \\ 3 & 0.257 \\ 4 & 0.340 \\ 5 & 0.408 \\ 6 & 0.463 \\ 7 & 0.511 \\ 8 & 0.543 \\ 9 & 0.561 \\ 10 & 0.575 \\ \hline \end{array} $$ Draw a calibration curve by hand using graph paper and estimate the concentration of zinc in the following water samples: (a) an undiluted sample, giving an absorbance of \(0.157 ;\) (b) a 20 -fold dilution, giving an absorbance of \(0.304\) (c) a five-fold dilution, giving an absorbance of \(0.550\) Give your answer to three significant figures in each case.

Short Answer

Expert verified
The estimated concentrations of zinc are dependent on the specific calibration curve created. However, for an undiluted sample with an absorbance of 0.157, the concentration should lie between 1 and 2 \(\mu \mathrm{g/mL}\). For a 20-fold diluted sample with an absorbance of 0.304, the concentration should be around 40 \(\mu \mathrm{g/mL}\) (after multiplying the estimate for 2-3 \(\mu \mathrm{g/mL}\) by 20). And for a five-fold diluted sample with an absorbance of 0.550, the concentration should be about 25 \(\mu \mathrm{g/mL}\) (after multiplying the estimate for 5 \(\mu \mathrm{g/mL}\) by 5).

Step by step solution

01

Create Calibration Curve

To create a calibration curve, plot the given zinc concentrations against corresponding absorbance measurements. The graph will start at the origin (0,0), since zero concentration of Zinc gives zero absorbance. The x-axis can be labeled as 'Zinc concentration \(\mu \mathrm{g/mL}\) ' and the y-axis as 'Absorbance'. Join the plotted points to create a curve.
02

Estimate Undiluted Sample

To find the zinc concentration of an undiluted sample that gives an absorbance of 0.157, locate this value on the y-axis of the calibration curve and trace a line to the curve. Then, drop a line from this intersection point to the x-axis. The corresponding x-axis value is the concentration of zinc in the sample. In case of calculations, use linear approximation for simplicity unless the calibration curve is decidedly non-linear.
03

Estimate Concentration in a 20-Fold Dilution

Repeat the process described in step 2 for a sample that gives an absorbance of 0.304. However, this sample has been diluted 20-fold, so the determined zinc concentration must be multiplied by 20 to obtain the original concentration of zinc.
04

Estimate Concentration in a Five-Fold Dilution

Similarly, for a five-fold diluted sample giving an absorbance of 0.550, find the corresponding zinc concentration from the calibration curve and multiply it by 5 to find the original zinc concentration.

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Most popular questions from this chapter

Determine the concentration of metal ions based on atomic spectroscopy of test and standard solutions. The following data represent a set of calibration standards for \(\mathrm{K}^{+}\)in aqueous solution, measured by flame photometry: Absorbance of standard solutions containing \(\mathrm{K}^{+}\)at up to \(0.5 \mathrm{mmol} \mathrm{L}^{-1}\) $$ \begin{array}{cc} \mathrm{K}^{+} \text {concentration }\left(\mathrm{mmol} \mathrm{L}^{-1}\right) & \text { Absorbance } \\ 0 & 0.000 \\ 0.1 & 0.155 \\ 0.2 & 0.279 \\ 0.3 & 0.391 \\ 0.4 & 0.537 \\ 0.5 & 0.683 \\ \hline \hline \end{array} $$ Draw a calibration curve using the above data and use this to estimate the amount of \(\mathrm{K}^{+}\)in a test sample prepared by digestion of \(0.482 \mathrm{~g}\) of sample in a final volume of \(25 \mathrm{ml}\) of solution, giving an absorbance of \(0.429\) when measured at the same time as the standards shown above. Express your answer in mmol \(\mathrm{K}^{+}\)(g sample) \(^{-1}\), to 3 significant figures.
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