Some progressive hair coloring products marketed to men, such as Grecian Formula 16, contain lead acetate Pb(CH3CO2)2. As the coloring solution is rubbed on the hhair, the Pb2+ ions react with the sulfur atoms in hair proteins to give lead(II) sulfide (PbS), which is black. A typical coloring solution contains 0.3 mass% Pb(CH3CO2)2, and about 2 mL of the solution is used per application. (b) Suppose the hair is washed with shampoo and water that has pH = 5.50. How many washings would be required to remove 50% of the black color? Assume that 3 gal of water is used per washing and that the water becomes saturated with PbS. (c) Does the calculated number of washings look reason-able, given that frequent application of the coloring solution is recommended? What process(es) in addition to dissolution might contribute to the loss of color?

Verified step by step guidance

1. insert step 1: Understand the problem by identifying the chemical reactions involved. Lead(II) acetate reacts with sulfur in hair to form lead(II) sulfide (PbS), which is black.
2. insert step 2: Determine the solubility of PbS in water at pH = 5.50. You may need to look up the solubility product constant (Ksp) for PbS and use it to calculate the concentration of Pb2+ ions in solution.
3. insert step 3: Calculate the amount of PbS that can dissolve in 3 gallons of water per washing. Use the solubility information from step 2 to find out how much PbS can be removed per washing.
4. insert step 4: Determine how many washings are needed to remove 50% of the PbS. Calculate the initial amount of PbS formed and use the dissolution rate per washing to find the number of washings required.
5. insert step 5: Consider other processes that might contribute to color loss, such as mechanical abrasion or chemical reactions with shampoo ingredients, and evaluate if the calculated number of washings is reasonable.

Key Concepts

Lead Acetate and Its Reaction

Lead acetate (Pb(CH3CO2)2) is a compound that releases Pb2+ ions in solution. When applied to hair, these ions react with sulfur atoms in hair proteins, forming lead(II) sulfide (PbS), which is responsible for the black color. Understanding this reaction is crucial for analyzing how the color is retained or removed during washing.

Saturation and Solubility

Saturation refers to the point at which a solution can no longer dissolve additional solute. In this context, the water used for washing becomes saturated with PbS, meaning it can only hold a certain amount of lead sulfide before any excess precipitates out. This concept is essential for calculating how much PbS can be removed from the hair during washing.

pH and Its Effect on Solubility

The pH of a solution can significantly influence the solubility of certain compounds. In this case, the pH of 5.50 may affect the dissolution of PbS in water. Understanding how pH impacts solubility helps in predicting how effectively the washing process can remove the black color from the hair.