Question

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 g of water). Is this guideline exceeded if an underground water supply is at equilibrium with the mineral anglesite, \(\mathrm{PbSO}_{4}\left(K_{\mathrm{sp}}=1.6 \times 10^{-8}\right) ?\)

Short answer

The equilibrium concentration of \( Pb^{2+} \) from the dissolution of anglesite in water is \( 1.26 \times 10^{-4} M \), which is less than the acceptable concentration of \( 2.41 \times 10^{-4} M \) as per guidelines. Hence, the guideline is not exceeded.

Step-by-step solution

Conversion of Mass Ratio to Molar Concentration

First, convert the acceptable concentration of Pb^2+ ions from ppm to the appropriate molar units – moles per litre (M). Given 0.05 g of Pb^2+ in 1 million g of water, this translates to 0.05 g in 1 million mL of water (since the density of water can roughly approximated as 1 g/mL). In other words, this is 0.05 g/L. Then, convert to moles per litre by dividing by the molar mass of Pb^2+ (\( 207.2 \, g/mol \)). Hence, the acceptable concentration is \( \frac{0.05 \, g/L}{207.2 \, g/mol} = 2.41 \times 10^{-4} M \).

Calculate the Concentration of Pb^2+ at Equilibrium

In the dissolution of \( PbSO_{4} \), the concentrations of \( Pb^{2+} \) and \( SO_{4}^{-2} \) ions are equal. Hence, the \( K_{sp} = [Pb^{2+}][SO_{4}^{-2}] \) simplifies to \( [Pb^{2+}] = \sqrt{K_{sp}} \). Substituting the given value of \( K_{sp} = 1.6 \times 10^{-8} \), the equilibrium concentration of \( Pb^{2+} \) is \( \sqrt{1.6 \times 10^{-8} M} = 1.26 \times 10^{-4} M \).

Compare the Equilibrium Concentration with the Acceptable Concentration

Now one needs to compare the equilibrium concentration of \( Pb^{2+} \) with the acceptable concentration. If the former is less than or equal to the latter, the guideline is not exceeded.

Key concepts

Maximum Allowable Concentration

When discussing the quality of drinking water, the term 'maximum allowable concentration' (MAC) refers to the highest level of a contaminant, such as lead (Pb^2+), that is considered safe for human consumption. Authorities establish these limits after thorough health-based evaluations. The MAC for lead in drinking water has been set at a very low threshold of 0.05 ppm to minimize any potential health risks.

To determine if the MAC is exceeded, scientists translate ppm values to molar concentrations because this unit, moles per liter (M), allows for easier comparison with solubility products and other concentration measures used in chemical calculations. It's crucial to know whether certain minerals in water, when dissolved, may release contaminants exceeding these allowable levels.

Ksp (Solubility Product Constant)

The Ksp, or solubility product constant, is an essential tool in environmental chemistry. It provides a quantitative measure of a compound's solubility in water. Specifically, it is the equilibrium constant for the dissolution of a salt into its constituent ions. For example, the mineral anglesite, PbSO4, will dissolve in water to give Pb^2+ and SO4^2- ions in a specific ratio that is governed by its Ksp value.

In our exercise, we have a Ksp value of 1.6 x 10^-8 for PbSO4. This small number indicates that anglesite has a low solubility in water, which corresponds to low concentrations of lead and sulfate ions at equilibrium. By calculating and comparing the Pb^2+ ion concentration to the MAC, we can assess compliance with safety guidelines.

Molar Concentration Calculations

Molar concentration calculations are central to understanding chemical reactions in solution, including those that define chemical equilibria. By converting grams per liter to moles per liter, we standardize concentrations regardless of the substance's molecular weight. This simplification is vital for comparing different substances and for adhering to regulations, like water quality standards.

To illustrate, in the exercise, we converted the maximum allowable concentration of Pb^2+ ions from ppm to molar concentration, which involved dividing the given mass (0.05 g/L) by the atomic mass of lead to obtain a molar concentration of 2.41 x 10^-4 M. This molar concentration then allows for a direct comparison with equilibrium concentrations derived from the Ksp.

Dissolution of Minerals in Water

The dissolution of minerals in water is a process that governs the concentration of various ions and compounds in natural waters. This process is influenced by factors such as mineral composition, temperature, pressure, and the presence of other ions that can shift equilibrium.

In environmental chemistry scenarios, like the dissolution of anglesite in the exercise, understanding the dissolution process helps to predict concentrations of potential pollutants, such as Pb^2+ ions. The Ksp plays a critical role here, as it can be used to calculate the equilibrium concentration of dissolved ions, which in this case would be lead, posing a potential health risk.

Environmental Chemistry

Environmental chemistry is an interdisciplinary field that explores the chemical processes occurring in the environment, including the distribution and effects of chemical species in the air, soil, and water. The ultimate goal is to understand and mitigate the potential impacts of chemicals on ecosystems and human health.

Applying the principles of environmental chemistry, as shown in the anglesite dissolution exercise, involves using scientific methods and calculations to assess the risks of chemical contaminants. By evaluating these risks against established guidelines, like the maximum allowable concentration, environmental chemists play a crucial role in safeguarding the quality of our drinking water and the health of our ecosystems.