Lead was determined in a brass sample by atomic absorption and the method of standard additions. The original sample was dissolved and diluted to 50.0 mL. This solution was introduced into an AA spectrometer and an absorbance of 0.42 was obtained. To the original solution, 20.0 mL of a Pb standard that contained 10.0 mg/ml Pb was added. The absorbance of this second solution was 0.58.

(a) Determine the mass of Pb in the original sample in mg.

(b) What assumption has been made to use this single addition method?

(c) What could be done to check the assumption made in part (b)?