Question

Ethylenediaminetetraacetate (EDTA \(^{4-} )\) is used as a complexing agent in chemical analysis with the structure shown in Fig. \(21.7 .\) Solutions of EDTA \(^{4-}\) are used to treat heavy metal poisoning by removing the heavy metal in the form of a soluble complex ion. The complex ion virtually prevents the heavy metal ions from reacting with biochemical systems. The reaction of EDTA \(^{4-}\) with \(\mathrm{Pb}^{2+}\) is $$\mathrm{Pb}^{2+}(a q)+\mathrm{EDTA}^{4-(a q)} \rightleftharpoons \mathrm{PbEDTA}^{2-}(a q) \\\ \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad K=1.1 \times 10^{18}$$ Consider a solution with 0.010 mol of \(\mathrm{Pb}\left(\mathrm{NO}_{3}\right)_{2}\) added to 1.0 \(\mathrm{L}\) of an aqueous solution buffered at \(\mathrm{pH}=13.00\) and containing 0.050\(M \mathrm{Na}_{4} \mathrm{EDTA} .\) Does \(\mathrm{Pb}(\mathrm{OH})_{2}\) precipitate from this solution? \(\left[K_{\mathrm{sp}} \text { for } \mathrm{Pb}(\mathrm{OH})_{2}=1.2 \times 10^{-15}\right]\)

Short answer

In the given solution, the ion product of \(\mathrm{Pb}(\mathrm{OH})_{2}\) is calculated as \(0\), and it is smaller than the solubility product constant \(\mathrm{K_{sp}} = 1.2 \times 10^{-15}\). Therefore, \(\mathrm{Pb}(\mathrm{OH})_{2}\) does not precipitate from the solution.

Step-by-step solution

Calculate the concentration of \(OH^{-}\)

Since the solution is buffered at pH = 13.00, we can use the relationship between pH, pOH, and the concentrations of \(H^{+}\) and \(OH^{-}\) ions: \(pH + pOH = 14\) \(pOH = 14 - pH = 14 - 13.00 = 1\) Now, we can find the concentration of \(OH^{-}\) ions: \([OH^{-}] = 10^{-pOH} = 10^{-1} = 0.1 \ \mathrm{M}\)

Calculate the initial concentration of \(\mathrm{Pb^{2+}}\)

Initially, 0.010 mol of \(\mathrm{Pb}\left(\mathrm{NO}_{3}\right)_{2}\) is added to 1.0 L of the solution, so the initial concentration of \(\mathrm{Pb^{2+}}\) is: \([\mathrm{Pb^{2+}}]_0 = \frac{0.010 \ \mathrm{mol}}{1.0 \ \mathrm{L}} = 0.010 \ \mathrm{M}\)

Determine the concentration of \(\mathrm{PbEDTA^{2-}}\)

Using the reaction constant \(K = 1.1 \times 10^{18}\) and the initial concentrations, we can write an expression for the equilibrium constant: \(K = \frac{[\mathrm{PbEDTA^{2-}}]}{[\mathrm{Pb^{2+}}][\mathrm{EDTA}^{4-}]}\) In the reaction, \(\mathrm{Pb^{2+}}\) and \(\mathrm{EDTA^{4-}}\) will react to form \(\mathrm{PbEDTA^{2-}}\). Assuming all \(\mathrm{Pb^{2+}}\) reacts, the equilibrium concentrations will be: \([\mathrm{PbEDTA^{2-}}] = 0.010 \ \mathrm{M}\) \([\mathrm{Pb^{2+}}] = 0\) \([\mathrm{EDTA^{4-}}] = 0.050 - 0.010 = 0.040 \ \mathrm{M}\)

Calculate the remaining concentration of \(\mathrm{Pb^{2+}}\)

Since \(K\) is very large, the equilibrium lies far to the right (formation of a complex), and we can assume that the reaction goes to completion. So, the remaining concentration of \(\mathrm{Pb^{2+}}\) is negligible.

Determine the ion product of \(\mathrm{Pb}(\mathrm{OH})_{2}\)

Calculate the ion product of \(\mathrm{Pb}(\mathrm{OH})_{2}\) with the remaining concentration of \(\mathrm{Pb^{2+}}\) ions and the concentration of \(OH^{-}\) ions: Ion product \(= [\mathrm{Pb^{2+}}][OH^{-}]^2 \approx 0 \cdot (0.1)^2 = 0\)

Compare the ion product with \(\mathrm{K_{sp}}\)

The solubility product constant for \(\mathrm{Pb}(\mathrm{OH})_{2}\), \(\mathrm{K_{sp}} = 1.2 \times 10^{-15}\). Now, compare the ion product with \(\mathrm{K_{sp}}\): Ion product \( = 0 \ < \ \mathrm{K_{sp}} = 1.2 \times 10^{-15}\) Since the ion product is smaller than the solubility product constant, \(\mathrm{Pb}(\mathrm{OH})_{2}\) does not precipitate from the solution.

Key concepts

EDTA

Ethylenediaminetetraacetate, or EDTA, is a powerful chelating agent widely used in complexation chemistry. A chelating agent is a molecule that can bind to metal ions, effectively "grabbing" them out of solution.
This action is particularly useful in both industrial and medical applications, including treatments for heavy metal poisoning.

• EDTA works by forming a stable complex with metal ions such as lead ( Pb^{2+}), which prevents these ions from interacting with other compounds in the body.
• The negatively charged EDTA molecule wraps around the positively charged metal ion, similar to a claw, creating a complex ion.
• This complex is usually more soluble in aqueous solutions than the free metal ion, making it easier for the body to excrete it.

In essence, EDTA's role in complexation chemistry is to ensure that unwanted metal ions are deactivated and made harmless by keeping them bound and soluble. Its effectiveness in such tasks is demonstrated by the large equilibrium constant for its reaction with metals, indicating a highly stable complex.

Heavy Metal Poisoning

Heavy metal poisoning occurs when heavy metals, such as lead, mercury, or cadmium, accumulate in the body, potentially leading to serious health effects.

• These metals can interfere with the normal biological processes because they tend to bind with proteins and enzymes in the body, disrupting their function.
• Symptoms of heavy metal poisoning can include abdominal pain, fatigue, neurological problems, and more.
• For instance, lead poisoning is especially concerning because it can impact brain development in children.

To combat heavy metal poisoning, agents like EDTA are administered to form non-reactive complexes with the metals. By doing so, these agents prevent the metals from interacting with the body's biochemical systems and facilitate their removal through excretion.
This method of treatment is known as chelation therapy, and it's a practical approach to reduce metal toxicity efficiently.

Solubility Product

The solubility product ( K_{sp}) is an equilibrium constant that applies to the dissolution of a sparingly soluble salt. In the context of complexation chemistry, it's crucial to know whether a salt will precipitate out of a solution or not.

• The constant value represents the product of the concentrations of the ions of the salt when the solution is saturated.
• For Pb(OH)_{2}, the K_{sp} is given as 1.2 × 10^{-15}, which indicates very low solubility in water.
• Comparing the ion product of a dissolved substance to the K_{sp} helps determine if precipitation will occur. If the ion product is less than K_{sp}, precipitation does not occur.

In the case of the solution with EDTA and lead, the ion product was found to be zero, which was much less than the K_{sp} for Pb(OH)_{2}. This comparison confirmed that lead hydroxide would not precipitate, as the presence of EDTA kept the lead ions in solution.

Equilibrium Constant

The equilibrium constant ( K) is a fundamental concept for understanding how far a chemical reaction proceeds. In complexation reactions, such as those involving EDTA and metal ions, K helps predict the concentration of each species at equilibrium.

• K is calculated as the ratio of the concentrations of products to reactants, each raised to their respective stoichiometric coefficients.
• The exceptionally high value of 1.1 × 10^{18} for the reaction between lead and EDTA indicates that the reaction strongly favors the formation of the PbEDTA^{2-} complex.
• This means once lead ions are added to the solution with EDTA, they are almost entirely converted into the complex, leaving nearly no free Pb^{2+} ions.

Understanding K is essential because it quantifies the extent of the reaction and the stability of the complex formed, which in this situation, means a safe and effective removal of heavy metal ions from the solution.