In a research laboratory, an aqueous stock solution of an organic chromophore has an unknown concentration. To determine that concentration, a chemist performs the following steps.
1. Exactly 10.00mL of the stock solution is transferred to a 100.0mL volumetric flask and diluted to the mark with distilled water.
2. The diluted solution is placed in a 1.00cm cuvette and its absorbance at λmax is recorded as 0.415±0.005.
3. On the same instrument and with the same cuvette, a reference solution that is 2.00×10−4M in the same chromophore gives an absorbance of 0.356±0.005.
(a) Determine the molar concentration of the diluted solution prepared in step 1. Show all calculations.
(b) Calculate the molar concentration of the original stock solution. Report your answer to the correct number of significant figures.
(c) Using the absorbance uncertainties provided (±0.005 for each reading), estimate the absolute uncertainty in the calculated concentration of the stock solution. Clearly state any assumptions made in your propagation of uncertainty.
(d) The bottle label on the stock solution claims a concentration of 2.0×10−3M. Based on your result and its uncertainty from parts (b) and (c), assess whether the label is accurate. Justify your answer quantitatively.