The maximum allowable concentration of \(\mathrm{Pb}^{2+}\) ions in drinking water is \(0.05 \mathrm{ppm}\) (that is, \(0.05 \mathrm{~g}\) of \(\mathrm{Pb}^{2+}\) in 1 million \(\mathrm{g}\) of water \() .\) Is this guideline exceeded if an underground water supply is at equilibrium with the mineral anglesite, \(\mathrm{PbSO}_{4}\left(K_{\mathrm{sp}}\right.\) \(\left.=1.6 \times 10^{-8}\right) ?\)

The safety of drinking water is a crucial public health matter, and one aspect of this is controlling the concentration of contaminants such as lead ions (\textnormal{\texttt{Pb}}^{2+}). Lead is a toxic metal, and its presence in drinking water can have severe health consequences, particularly for young children and pregnant women.

Regulatory bodies like the Environmental Protection Agency (EPA) in the United States set guidelines for the maximum allowable concentration of lead ions in drinking water. These regulations often stipulate a maximum level in parts per million (ppm), which is a way to express very dilute concentrations. For instance, \(0.05 \mathrm{ppm}\) refers to \(0.05 \mathrm{g}\) of \(\mathrm{Pb}^{2+}\) ions in one million grams of water, which is equivalent to \(0.05 \mathrm{mg/L}\).

Measuring and ensuring that the lead concentration does not exceed this threshold is key to maintaining water safety. The calculation involves understanding the solubility of lead compounds in water and their potential to release lead ions to reach levels that may surpass the regulatory guidelines.

The Ksp, or solubility product constant, is an equilibrium constant that pertains to the solubility of sparingly soluble salts. It represents the extent to which a compound can dissolve in water and is calculated by multiplying the concentrations of the ions in the solution at equilibrium.

In the case of anglesite (\(\mathrm{PbSO}_{4}\)), its solubility is depicted by the equilibrium: \(\mathrm{PbSO}_{4}(s) \rightleftharpoons \mathrm{Pb^{2+}}(aq)\) + \(\mathrm{SO_{4}^{2-}}(aq)\). The Ksp can be expressed as \(K_{sp} = [\mathrm{Pb^{2+}}][\mathrm{SO_{4}^{2-}}]\). If anglesite disassociates into equal molar amounts of \(\mathrm{Pb^{2+}}\) and \(\mathrm{SO_{4}^{2-}}\), the Ksp simplifies to \(K_{sp} = x^2\), where \(x\) indicates the molarity of \(\mathrm{Pb^{2+}}\) ions in the solution. This allows for the calculation of lead concentration in water samples in contact with anglesite and verification against safety regulations.

Understanding the principles of equilibrium in solubility is essential for analyzing the dissolution of compounds like anglesite in water. The equilibrium constant represents the ratio of the concentration of products to reactants at equilibrium. In solubility equilibria, the constant is specific to the slightly soluble compound and is given by their respective solubility product constant (Ksp).

For a salt like anglesite (\(\mathrm{PbSO}_{4}\)), the equilibrium equation \(K_{sp} = [\mathrm{Pb^{2+}}][\mathrm{SO_{4}^{2-}}]\) captures the ratio of the product concentrations. It's instrumental in determining if a water supply in equilibrium with anglesite will exceed the lead concentration guidelines set for drinking water. When these guidelines are approached or surpassed, it indicates a potential health risk, and the source may require treatment to reduce the lead concentration to an acceptable level.

Chemists often need to convert molarity, or moles per liter (M), into parts per million (ppm) for reporting concentrations in a more tangible form. This conversion is particularly useful in environmental chemistry, such as assessing the purity of drinking water.

\textnormal{\texttt{Molarity (M)}} is a measure of the number of moles of a substance per liter of solution, while ppm quantifies the mass of a substance per million parts of the total solution. To convert molarity to ppm for a solution with a known density, one can use the conversion factor: \(1 M = 1 \mathrm{g/L} = 1000 \mathrm{mg/L}\).

Therefore, by multiplying the molarity by 1000, we can convert moles per liter to milligrams per liter, which is equivalent to ppm since \(1 \mathrm{mg/L} = 1 \mathrm{ppm}\). This straightforward calculation provides a clear way to compare the concentration of a solution to regulatory thresholds such as the acceptable levels of lead ions in drinking water.