Lead(II) chromate \(\left(\mathrm{PbCrO}_{4}\right)\) is used as the yellow pigment for marking traffic lanes but is banned from house paint because of the risk of lead poisoning. It is produced from chromite \(\left(\mathrm{FeCr}_{2} \mathrm{O}_{4}\right),\) an ore of chromium: $$ \begin{array}{r} 4 \mathrm{FeCr}_{2} \mathrm{O}_{4}(s)+8 \mathrm{~K}_{2} \mathrm{CO}_{3}(a q)+7 \mathrm{O}_{2}(g) \longrightarrow \\ 2 \mathrm{Fe}_{2} \mathrm{O}_{3}(s)+8 \mathrm{~K}_{2} \mathrm{CrO}_{4}(a q)+8 \mathrm{CO}_{2}(g) \end{array} $$ Lead(II) ion then replaces the \(\mathrm{K}^{+}\) ion. If a yellow paint is to have \(0.511 \% \mathrm{PbCrO}_{4}\) by mass, how many grams of chromite are needed per kilogram of paint?

Molar mass calculation is a fundamental concept in chemistry. It involves finding the mass of one mole of a substance, which is expressed in grams per mole (g/mol). To calculate the molar mass of a compound, sum the molar masses of its individual elements.
For instance, take the compound Lead(II) chromate \(\text{PbCrO}_4\).
The molar mass is calculated as:

• Lead (Pb): 207.2 g/mol
• Chromium (Cr): 51.996 g/mol
• Oxygen (O - four atoms): 4 \( \times \) 16 g/mol = 64 g/mol

Adding these together gives us:
\(207.2 + 51.996 + 64 = 323.2\) g/mol.
This means one mole of Lead(II) chromate weighs 323.2 grams. Such calculations help us relate masses of substances to their molar quantities in chemical reactions.

Chemical reactions describe the process where reactants transform into products. Understanding the stoichiometry of a reaction is key. For the given exercise, the reaction involves chromite \( \text{FeCr}_2 \text{O}_4\):

The balanced chemical reaction is:

\(4 \text{FeCr}_2 \text{O}_4(s) + 8 \text{K}_2 \text{CO}_3(aq) + 7 \text{O}_2(g) \longrightarrow 2 \text{Fe}_2 \text{O}_3(s) + 8 \text{K}_2 \text{CrO}_4(aq) + 8 \text{CO}_2(g)\)

This equation shows how reactants combine in fixed ratios to form products. Here, 4 moles of chromite react with 8 moles of potassium carbonate and 7 moles of oxygen to produce potassium chromate among other products.
Conversions using stoichiometry (like moles to grams) rely on balanced equations to ensure mass and atoms are conserved. This balance is crucial for solving problems like determining required reactants for a certain product amount.

Mass percentage conversion helps in quantifying the composition of a mixture. To convert a mass percentage to an absolute mass, use the formula:
\( \text{Mass of Compound} = \text{Percentage by Mass} \times \text{Total Mass}\)
In the exercise, the yellow paint is 0.511% by mass of \( \text{PbCrO}_4 \). If we have 1 kg (1000 g) of paint:

• Convert the percentage: \(\frac{0.511}{100} = 0.00511\)
• Multiply by total mass: \(0.00511 \times 1000 = 5.11 \) grams of \( \text{PbCrO}_4\)

This means there are 5.11 grams of Lead(II) chromate in 1 kg of paint. Such conversions are essential in preparing solutions and mixtures in precise concentrations.

Lead poisoning is a serious health hazard, particularly from prolonged exposure. Lead ions, when introduced into the body, can impair neurological functions, cause anemia, and damage organs. Due to these risks, compounds containing lead, like Lead(II) chromate \( \text{PbCrO}_4 \), are restricted in applications like household paints. The regulations aim to minimize exposure, especially in children, who are more vulnerable to lead's toxic effects.
In the context of the problem, although Lead(II) chromate is useful for marking traffic lanes due to its vibrant color, its potential for harmful exposure means it must be handled with caution and restricted to non-residential applications.

Chromite \( \text{FeCr}_2 \text{O}_4 \) is an important mineral and the primary source of chromium. Chromium is used in various industrial applications, including the production of stainless steel, dyes, and pigments. Chromite ore is processed to extract potassium chromate, which can be converted to Lead(II) chromate:

In the exercise:
\(4 \text{FeCr}_2 \text{O}_4 + 8 \text{K}_2 \text{CO}_3 + 7 \text{O}_2 \rightarrow 2 \text{Fe}_2 \text{O}_3 + 8 \text{K}_2 \text{CrO}_4 + 8 \text{CO}_2 \)

This shows the transformation of chromite into useful products through chemical reactions. Understanding these processes is essential for efficient resource utilization and minimizing environmental impact.