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.

Step by step solution

01

Create the calibration curve

Plot the absorbance (y-axis) against the known concentrations (\(K^{+}\) mmol L\(^{-1}\)) (x-axis). Connecting the points will create the calibration curve.

02

Find the concentration corresponding to the absorbance of the test solution

Locate the absorbance value of 0.429 (from the test solution) on the y-axis of the calibration curve, and draw a horizontal line that intersects with the calibration curve. From this intersection point, draw a vertical line down to the x-axis. The x-coordinate of this point is the concentration of the potassium ions in the test solution.

03

Computations to adjust the concentration

The concentration value obtained from the calibration curve is the concentration in the entire 25 mL of solution (from Step 2). To express this in mmol \(K^{+}\) (g sample) \(^{-1}\), divide this concentration by the mass of the sample, which is 0.482 g.

04

Rounding to 3 significant figures

The concentration value from Step 3 will be rounded to 3 significant figures. This is the final value for the concentration of \(K^{+}\) ions in the test sample.

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