(1) It is well understood that the spectroscopic absorbance of an analyte specie

Question

(1) It is well understood that the spectroscopic absorbance of an analyte species in solution is proportional to its concentration, at least within a certain range of values ("Beer's Law"). For the analysis of Crs in water (a very toxic form of chromium), the absorbance was measured for a series of calibration standards, resulting in the following best fit line when plotting absorbance (A) vs. [Crs ] in mol/L. Included are the estimated uncertainties for each of the terms: (At 14.2%)-(8.106 x 103 ± 0.423 x 103 L/mol)[CP+] + (0.002 ± 36.0%) A sample of an industrial waste stream analyzed spectroscopically for hexavalent chromium (Cr6+) resulted in an absorbance reading - 0.026. (Also, absorbance, by definition as we will find out later, is unitless). Calculate the concentration of Crs in the waste stream in both molarity and ppm, and report both the relative and absolute uncertainties in the final results. Also, be sure to report the final results with the correct number of significant figures, and make sure that the absolute uncertainty has the correct precision. For this problem, determine the number of significant figures of the Crs+ concentration based on the first non-zero digit of the absolute uncertainty. Report you absolute uncertainty with one significant figure, and the % relative uncertainty with two significant figures. (4 points)

Explanation / Answer

given equation can be viewed as y=mx +c

where y= absorbance

x=concentration

putting value of abs= 0.026 in the equation,

0.026 +- 14.2% = (8.106 * 103 +- 0.432 * 103) [C] + 0.002 + 36%

(0.026 +- 14.2%) - (0.002 + 36%) = (8.106 * 103 +- 0.432 * 103) [C]

relative uncertainities are added when u add or substract values

0.024 +- 50.2% = (8.106 * 103 +- 0.432 * 103) [C]

(0.024 +- 50.2%)/(8.106 * 103 +- 0.432 * 103) = [C]

[C]= (0.024 +- 1.21)/  (8.106 * 103 +- 0.432 * 103)

here, i converted relative uncertainity 50.2% to absolute

this is done by multipying the meaurement by relative ( 0.024 * 50.2= 1.21)

[C] = 0.00296 +- 424.21 (relative uncertainities are added when u multiply or divide values)

the number of significant fugure in concentration is 5.

here, 424.21 is absolute uncertainity and expressed in one significant figure will be 0.4 * 103

relative uncertainity = absolute/ measurement

= 424.21/0.00296

= 143.24 * 103

expressed in 2 significant figure relative uncertainity is 1.4 * 105

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