Some progressive hair dyes marketed to men, such as GrecianFormula 16, contain lead acetate, Pb(CH3CO2)2. As the dye solutionis rubbed on the hair, the Pb2+ ions react with the sulfur atoms inhair proteins to give lead(II) sulfide (PbS), which is black. Atypical dye solution contains 0.3 mass % Pb(CH3CO2)2, and about 2mL of dye solution is used per application.
(a) Assuming that 30% of the Pb(CH3CO2)2 isconverted to PbS, how many milligrams of PbS are formed perapplication of the dye?
(b) Suppose the hair is washed with shampoo andwater that has pH = 5.50. How many washings would be required toremove 50% of the black color? Assume that 3 gal of water is usedper washing and that the water becomes saturated with PbS.
(c) Does the calculated number of washings lookreasonable, given that frequent application of the dye isrecommended? What process(es) in addition to dissolution might contribute to the loss of color?