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 hair, 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. (a) Assuming that 30% of the Pb(CH₃CO₂)₂ is converted to PbS, how many milligrams of PbS are formed per application of the coloring solution?

Verified step by step guidance

1. Calculate the mass of Pb(CH_3CO_2)_2 in the 2 mL solution: First, find the mass of the solution using its density (assuming it's similar to water, 1 g/mL), then calculate the mass of Pb(CH_3CO_2)_2 using the given mass percentage.
2. Determine the moles of Pb(CH_3CO_2)_2: Use the molar mass of Pb(CH_3CO_2)_2 to convert the mass from the previous step to moles.
3. Calculate the moles of PbS formed: Since 30% of Pb(CH_3CO_2)_2 is converted to PbS, multiply the moles of Pb(CH_3CO_2)_2 by 0.30 to find the moles of PbS.
4. Convert moles of PbS to mass: Use the molar mass of PbS to convert the moles of PbS to mass in grams.
5. Convert the mass of PbS to milligrams: Since 1 gram is 1000 milligrams, multiply the mass in grams by 1000 to get the mass in milligrams.

Key Concepts

Stoichiometry

Stoichiometry is the calculation of reactants and products in chemical reactions. It involves using balanced chemical equations to determine the relationships between the amounts of substances consumed and produced. In this context, stoichiometry will help calculate how much lead(II) sulfide (PbS) is formed from the lead acetate (Pb(CH3CO2)2) based on the given mass percentage and the reaction's conversion efficiency.

Mass Percent Concentration

Mass percent concentration is a way to express the concentration of a solute in a solution, defined as the mass of the solute divided by the total mass of the solution, multiplied by 100. In this problem, the 0.3 mass% of Pb(CH3CO2)2 indicates that there are 0.3 grams of lead acetate in every 100 grams of the solution, which is crucial for determining the amount of lead available for conversion to PbS.

Chemical Reaction and Product Formation

In a chemical reaction, reactants are transformed into products through the breaking and forming of bonds. The specific reaction in this case involves lead(II) ions reacting with sulfur atoms in hair proteins to form lead(II) sulfide (PbS). Understanding this reaction is essential for calculating the amount of PbS produced from the lead acetate in the hair coloring solution, especially considering the stated conversion efficiency.