Problem 97 - Chemistry The Central Science

Question

Lead(II) carbonate, PbCO \(_{3},\) is one of the components of the passivating layer that forms inside lead pipes.(a) If the \(K_{s p}\) for \(\mathrm{PbCO}_{3}\) is \(7.4 \times 10^{-14}\) what is the molarity of \(\mathrm{Pb}^{2+}\) in a saturated solution of lead(II) carbonate? (b) What is the concentration in ppb of \(\mathrm{Pb}^{2+}\) ions in a saturated solution? (c) Will the solubility of \(\mathrm{PbCO}_{3}\) increase or decrease as the \(\mathrm{pH}\) is lowered? \((\boldsymbol{d} )\)The EPA threshold for acceptable levels of lead ions in water is 15 ppb. Does a saturated solution of lead(II) carbonate produce a solution that exceeds the EPA limit?

Step-by-Step Solution

Answer

The molarity of Pb2+ in a saturated solution of PbCO3 is \(2.72 \times 10^{-7} \textrm{ M}\), and the concentration of Pb2+ ions is 272 ppb. The solubility of PbCO3 will increase as the pH is lowered. The concentration of Pb2+ in a saturated solution of PbCO3 exceeds the EPA limit of 15 ppb.

Step 1: Write the solubility equilibrium

Write the solubility equilibrium for the dissolution of PbCO3: \[PbCO_3(s) \rightleftharpoons Pb^{2+}(aq) + CO_3^{2-}(aq)\]

Step 2: Express Ksp in terms of molar solubility

From the equilibrium, let the molar solubility of PbCO3 be x mol/L. Therefore, in a saturated solution, \[ [Pb^{2+}] = x \textrm{ M}\] \[ [CO_3^{2-}] = x \textrm{ M}\] The solubility product constant (Ksp) is given by: \[K_{sp} = [Pb^{2+}][CO_3^{2-}] = x^2\]

Step 3: Calculate molar solubility

We are given the value of Ksp for PbCO3 = \(7.4 \times 10^{-14}\) Use this to solve for the molar solubility: \[x^2 = 7.4 \times 10^{-14}\] Solve for x: \[x = \sqrt{7.4 \times 10^{-14}}\] \[x = 2.72 \times 10^{-7} \textrm{ M}\] The molarity of Pb2+ in a saturated solution of PbCO3 is \(2.72 \times 10^{-7} \textrm{ M}\).

Step 4: Convert molarity to ppb

To convert to ppb, we'll use the following conversion factor: 1 M = 1000 ppm = 1000,000 ppb \({[Pb^{2+}]}_{ppb} = {2.72 \times 10^{-7}} M \times {10^9} \,ppb/M\) \({[Pb^{2+}]}_{ppb} = 272 \,ppb\) The concentration of Pb2+ ions in a saturated solution of PbCO3 is 272 ppb.

Step 5: Solubility versus pH

Lowering the pH means increasing the concentration of H+ ions in the solution. Since CO32- ions can combine with H+ ions to form HCO3- ions, the equilibrium will shift to the left, according to Le Chatelier's principle. Hence, the solubility of PbCO3 will increase as the pH is lowered.

Step 6: Compare with EPA limit

We found that the concentration of Pb2+ ions in a saturated solution of PbCO3 is 272 ppb. The EPA threshold for acceptable levels of lead ions in water is 15 ppb. Thus, a saturated solution of PbCO3 exceeds the EPA limit.

Key Concepts

Molar Solubility

Molar solubility is a term that describes the maximum amount of a substance that can dissolve in a liter of solvent to form a saturated solution. It is denoted in moles per liter (mol/L or M). For substances like lead(II) carbonate (PbCO₃), this value is crucial to understand as it tells us how much of the compound can be present in water before solids start to precipitate. This concept is particularly important when considering the safety of drinking water, as certain ions, such as lead ions, can be toxic.

When given the solubility product constant (K_sp), one can calculate the molar solubility of a compound using the equilibrium expression for its dissolution. In the case of lead(II) carbonate, how to convert this value into more practical units like parts per billion (ppb) is often necessary to compare with standards like those set by the Environmental Protection Agency (EPA) for safe drinking water. Solubility will vary depending on the conditions such as temperature and pH, which can be understood through the principles of chemical equilibrium.

Lead(II) Carbonate

Lead(II) carbonate is a chemical compound with the formula PbCO₃. It is poorly soluble in water, which is an essential property when studying its effects and behavior in the environment, especially in water systems. Lead(II) carbonate can form a passivating layer inside lead pipes, which is often a context where its solubility becomes a significant concern.

In a saturated solution, where no more solute can dissolve, we can determine the concentration of lead ions by understanding the solubility product constant. Knowing the molar solubility helps us assess the risks associated with lead in water. The calculation of how much Pb²⁺ is released into water from lead(II) carbonate is necessary for understanding whether water is safe to consume and for taking measures to prevent lead poisoning.

EPA Lead Level Threshold

The Environmental Protection Agency (EPA) has set a threshold for lead levels in drinking water to protect public health. The EPA threshold, defined as the 'action level,' is currently 15 parts per billion (ppb). If lead concentrations in water exceed this limit, it indicates a significant risk of lead exposure, which can have severe health consequences, notably for children.

When we talk about the safety levels of lead in water, it's crucial to be able to convert between units such as molarity (M) and ppb. This conversion allows us to measure if the concentration of Pb²⁺ ions from a compound like lead(II) carbonate surpasses the safe drinking water standard. Understanding and applying these regulatory limits is key for water quality monitoring and for ensuring that measures are taken to mitigate lead contamination.

Le Chatelier's Principle

Adjustment of Equilibrium

When a chemical system at equilibrium experiences a change in concentration, pressure, volume, or temperature, Le Chatelier's principle predicts that the system will respond to counteract the change and restore equilibrium. For example, when the pH of a solution containing lead(II) carbonate decreases, which means the concentration of H⁺ ions increases, the equilibrium will shift to reduce the stress. This happens by consuming H⁺ ions and precipitating out less PbCO₃, thus increasing the solubility of lead(II) carbonate.

Importance in Solubility Contexts

In context to solubility, Le Chatelier's principle helps us understand why solubility can change with pH. Lowering pH in a solution of PbCO₃ will result in more dissolution to form hydronium and bicarbonate ions. This is central to predicting and controlling the behavior of potentially harmful substances in water treatment and environmental protection.