Problem 50 - Chemistry: An Atoms-Focused Approach

Question

Lead Compounds as Pigments Ancient Egyptians used lead compounds, including \(\mathrm{PbS}, \mathrm{PbCO}_{3},\) and \(\mathrm{Pb}_{2} \mathrm{Cl}_{2} \mathrm{CO}_{3}\) as pigments in cosmetics, and many people suffered from chronic lead poisoning as a result. Calculate the percentage of lead in each of the compounds.

Step-by-Step Solution

Answer

Answer: The mass percentage of lead in each compound is approximately: PbS: 86.59%, PbCO3: 77.55%, Pb2Cl2CO3: 75.87%.

Step 1: Find the molar mass of each compound

To find the molar mass of each compound, we need to multiply the molar mass of each element in the compound by the number of atoms of that element and then add up these products. Keep in mind that the molar mass of Pb = 207.2 g/mol, S = 32.07 g/mol, C = 12.01 g/mol, O = 16.00 g/mol, and Cl = 35.45 g/mol. For \(\mathrm{PbS}\): Molar mass of \(\mathrm{PbS}\) = (1 × 207.2 g/mol) + (1 × 32.07 g/mol) = 239.27 g/mol For \(\mathrm{PbCO}_{3}\): Molar mass of \(\mathrm{PbCO}_{3}\) = (1 × 207.2 g/mol) + (1 × 12.01 g/mol) + (3 × 16.00 g/mol) = 207.2 g/mol + 12.01 g/mol + 48.00 g/mol = 267.21 g/mol For \(\mathrm{Pb}_{2}\mathrm{Cl}_{2}\mathrm{CO}_{3}\): Molar mass of \(\mathrm{Pb}_{2}\mathrm{Cl}_{2}\mathrm{CO}_{3}\) = (2 × 207.2 g/mol) + (2 × 35.45 g/mol) + (1 × 12.01 g/mol) + (3 × 16.00 g/mol) = 414.4 g/mol + 70.9 g/mol + 12.01 g/mol + 48.00 g/mol = 545.31 g/mol

Step 2: Calculate the mass percentage of lead in each compound

Now, we can find the mass percentage of lead (Pb) in each compound by dividing the molar mass of Pb in the compound by the molar mass of the entire compound and then multiplying by 100. For \(\mathrm{PbS}\): Percentage of Pb = \(\frac{(1 × 207.2 g/mol)}{(239.27 g/mol)} × 100\% ≈ 86.59\%\) For \(\mathrm{PbCO}_{3}\): Percentage of Pb = \(\frac{(1 × 207.2 g/mol)}{(267.21 g/mol)} × 100\% ≈ 77.55\%\) For \(\mathrm{Pb}_{2}\mathrm{Cl}_{2}\mathrm{CO}_{3}\): Percentage of Pb = \(\frac{(2 × 207.2 g/mol)}{(545.31 g/mol)} × 100\% ≈ 75.87\%\) The percentage of lead in each compound is approximately: \(\mathrm{PbS}: 86.59\%, \quad \mathrm{PbCO}_{3}: 77.55\%, \quad \mathrm{Pb}_{2}\mathrm{Cl}_{2}\mathrm{CO}_{3}: 75.87\%\)

Key Concepts

Lead Compounds as Pigments

Lead compounds like

• Lead Sulfide (\( \text{PbS} \))
• Lead Carbonate (\( \text{PbCO}_3 \))
• Lead Chlorocarbonate (\( \text{Pb}_2\text{Cl}_2\text{CO}_3 \))

were widely used in ancient times, especially for pigments. These compounds gave vibrant colors used in cosmetics by ancient civilizations.
However, the use came with a serious health risk: lead poisoning. Lead is a heavy metal that, when absorbed into the body, can cause severe health problems over time. Ancient Egyptians were often unaware of these dangers when using lead in their makeup.
Understanding the chemical composition of these compounds is crucial to grasp why they were chosen and why they posed such a risk.

Understanding Mass Percentage

The mass percentage of an element in a compound tells us how much of that element is present compared to the whole compound.
It's calculated using the formula:\[\text{Mass percentage of element} = \left( \frac{\text{mass of the element in the compound}}{\text{molar mass of the compound}} \right) \times 100\%\]For our lead compound examples, the mass percentage helps us know how much lead (\( \text{Pb} \)) is in each pigment. This is important for assessing the potential lead exposure from using these pigments.
High percentages of lead, as seen in \( \text{PbS} \) with 86.59%, indicate a greater risk of lead poisoning.
These calculations help in understanding the significance of lead content in historical contexts and its associated health risks.

Exploring Chemical Formulas

Chemical formulas tell us exactly which elements and how many atoms of each are in a compound. For ancient pigments:

• \( \text{PbS} \): Composed of one lead atom and one sulfur atom.
• \( \text{PbCO}_3 \): Contains one lead atom, one carbon atom, and three oxygen atoms.
• \( \text{Pb}_2\text{Cl}_2\text{CO}_3 \): Made up of two lead atoms, two chlorine atoms, one carbon atom, and three oxygen atoms.

Chemical formulas provide the blueprint of a compound. They let us calculate the molar mass, which is the combined mass of all the atoms in the formula.
Understanding these formulas is key to calculating mass percentages, as they show where each element, like lead, fits into the structure of the compound.

The Role of Ancient Pigments

Ancient pigments were essential for art and cosmetics, providing vivid colors for murals, pottery, and makeup. Pigments like those derived from lead compounds had both aesthetic and cultural significance.
However, their historical use often came with unintended health consequences due to lead content.
These pigments were used without knowledge of their risks, affecting many people's health over time. Studying these compounds helps us appreciate ancient artistry while learning important lessons about chemical safety.
The analysis and understanding of these pigments not only inform us about ancient practices but also highlight the importance of safer alternatives today.