Problem 138 - Chemistry The Molecular Nature of Matter

Question

Lead compounds are often highly colored and are toxic to mold, mildew, and bacteria, properties that in the past were useful for paints used before 1960 . Today we know lead is very hazardous and it is not used in paint; however, old paint is still a problem. If a certain lead-based paint contains \(14.5 \% \mathrm{PbCr}_{2} \mathrm{O}_{7}\) and \(73 \%\) of the paint evaporates as it dries, what mass of lead will be in a paint chip that weighs \(0.15 \mathrm{~g}\) ?

Step-by-Step Solution

Answer

A paint chip weighing 0.15 g contains approximately 0.001586 g of lead.

Step 1: Calculate the Mass of the Solid Paint

First, calculate the mass of the non-evaporated portion of the paint after it dries. Since 73% of the paint evaporates upon drying, the remaining solid portion of the paint is 27%. The mass of the solid paint can be calculated by multiplying the total weight of the wet paint chip by the percentage that does not evaporate: 0.15 g * (27/100) = 0.0405 g.

Step 2: Calculate the Mass of \(\mathrm{PbCr}_{2} \mathrm{O}_{7}\) in the Dried Paint

Calculate the amount of lead chromate in the dried paint chip. Given that the paint contains 14.5% lead chromate by mass, the mass of the lead chromate in the dried paint can be calculated by multiplying the mass of the solid paint by 14.5%. The calculation is 0.0405 g * (14.5/100) = 0.0058725 g of \(\mathrm{PbCr}_{2} \mathrm{O}_{7}\).

Step 3: Calculate the Mass of Lead in the Paint Chip

Using the molar mass of \(\mathrm{PbCr}_{2} \mathrm{O}_{7}\) (323.19 g/mol for Pb and 151.99 g/mol for each \(\mathrm{Cr}_{2}\) plus 16 g/mol for each oxygen atom, totaling to 323.19 + 2*151.99 + 7*16 = 767.17 g/mol), and knowing the molar mass of lead (Pb) is 207.2 g/mol, calculate the mass percentage of lead in lead chromate: (207.2 / 767.17) * 100 \approx 27.00%. Finally, use this percentage to calculate the mass of lead in the paint chip: 0.0058725 g * (27.00/100) = 0.001585575 g of Pb.

Key Concepts

Lead Chromate

Lead chromate, known chemically as PbCrO₄, is a vibrant yellow compound that was historically used in paint due to its rich pigment and durability. The chemistry behind lead chromate involves the lead (Pb) ion and the chromate (CrO₄^2-) ion coming together to form a bright, insoluble substance. This compound is a prime example of ionic bonding, where lead, a metal, donates electrons to the non-metal chromate.

When dissolved in water, chromate can react with lead ions to precipitate lead chromate. The equation representing this reaction is Pb²⁺ + CrO₄^2- → PbCrO₄ (s). For those studying stoichiometry, it is essential to note that the reaction forms a 1:1 molar ratio of lead to chromate ions.

Stoichiometry

Stoichiometry is the branch of chemistry that deals with the quantitative relationships of substances as they undergo chemical reactions. It's based on the law of conservation of mass, which states that in a chemical reaction, matter is neither created nor destroyed. With stoichiometry, we can predict the outcomes of reactions, determining how much of each substance will react and what will be produced.

The stoichiometry of lead chromate forming in an equation is simple: one mole of lead (II) ions reacts with one mole of chromate ions to produce one mole of lead chromate. It's critical for students to understand how to use stoichiometry to calculate the mass of reactants or products in a chemical reaction, as seen in the textbook exercise solution where we calculate the mass of lead in lead chromate within a paint chip.

Hazards of Lead

Despite its historical use, lead is now known to pose significant health risks. Exposure to lead can result in severe health consequences, particularly for children, leading to developmental delays and cognitive deficits. In adults, lead exposure can cause kidney damage and high blood pressure among other issues. Because of these hazards, the use of lead in household paints has been banned in many countries.

Lead-based paint remains a prevalent health issue in older buildings. When paint containing lead deteriorates or is disturbed during renovations, it can release lead dust or chips that are harmful when inhaled or ingested. This danger underlines the importance of safely managing environments where lead-based paint may have been used.

Percentage Composition

Percentage composition in chemistry refers to the percent by mass of each element in a compound. It is an essential concept when determining the formula of a compound or in analyzing its chemical nature. Students use this information to infer the ratio of elements in a compound and can calculate the amount of a particular substance present in a mixture.

In the context of the exercise, we used the percentage of lead chromate in the paint (14.5%) to find the mass of lead chromate in a dried 0.15 g paint chip. Understanding percentage composition is a valuable skill in a variety of real-world applications, such as quality control in manufacturing processes, where it's crucial to know the proportions of different ingredients.