Question

EDTA is used as a complexing agent in chemical analysis. Solutions of EDTA, usually containing the disodium salt \(\mathrm{Na}_{2} \mathrm{H}_{2} \mathrm{EDTA}\), are also used to treat heavy metal poisoning. The equilibrium constant for the following reaction is \(1.0 \times 10^{23}\) : Calculate \(\left[\mathrm{Pb}^{2+}\right]\) at equilibrium in a solution originally \(0.0010 \mathrm{M}\) in \(\mathrm{Pb}^{2+}, 0.050 \mathrm{M}\) in \(\mathrm{H}_{2} \mathrm{EDTA}^{2-}\), and buffered at \(\mathrm{pH}=6.00\).

Short answer

The equilibrium concentration of \(\mathrm{Pb^{2+}}\) is approximately \(5.0 \times 10^{-5} \mathrm{M}\).

Step-by-step solution

Write the balanced chemical equation

The complex formation between \(\mathrm{Pb^{2+}}\) and \(\mathrm{H}_{2}\mathrm{EDTA}^{2-}\) can be represented by the following balanced chemical equation: \[\mathrm{Pb^{2+}} + \mathrm{H}_{2}\mathrm{EDTA}^{2-} \rightleftharpoons \mathrm{Pb} \mathrm{H}_{2}\mathrm{EDTA}\]

Write the equilibrium expression

For the balanced chemical equation given above, the equilibrium constant expression can be written as: \[K = \dfrac{[\mathrm{Pb}\mathrm{H}_{2}\mathrm{EDTA}]}{[\mathrm{Pb^{2+}}][\mathrm{H}_{2}\mathrm{EDTA}^{2-}]}\] Given that the equilibrium constant, \(K\), for this reaction is \(1.0 \times 10^{23}\).

Set up and solve expressions for the equilibrium concentrations

Let the change in concentration for \(\mathrm{Pb}^{2+}\) be \(-x\) and for \(\mathrm{H}_{2}\mathrm{EDTA}^{2-}\) also be \(-x\). The change in concentration for \(\mathrm{PbH}_{2}\mathrm{EDTA}\) will be \(+x\). The table for the equilibrium concentrations is as follows: | Species | Initial | Change | Equilibrium | |--------|--------|-------|-------------| | \(\mathrm{Pb^{2+}}\) | \(0.0010\) | \(-x\) | \(0.0010-x\) | | \(\mathrm{H_{2}EDTA^{2-}}\) | \(0.050\) | \(-x\) | \(0.050-x\) | | \(\mathrm{PbH_{2}EDTA}\) | \(0\) | \(+x\) | \(x\) | We can now substitute these equilibrium concentrations back into the equilibrium constant expression: \[K = \dfrac{[\mathrm{Pb}\mathrm{H}_{2}\mathrm{EDTA}]}{[\mathrm{Pb^{2+}}][\mathrm{H}_{2}\mathrm{EDTA}^{2-}]} = \dfrac{x}{(0.0010-x)(0.050-x)}\] We are solving for \(x\) (i.e., the concentration of \(\mathrm{Pb^{2+}}\) at equilibrium) with \(K = 1.0 \times 10^{23}\): \[1.0 \times 10^{23} = \dfrac{x}{(0.0010-x)(0.050-x)}\]

Solve for the equilibrium concentration of \(\mathrm{Pb^{2+}}\)

As the value of \(K\) is very large, we can assume that the concentrations of \(\mathrm{Pb^{2+}}\) and \(\mathrm{H_{2}EDTA^{2-}}\) will decrease by a negligible amount. Therefore, \(x \approx 0.0010\) and \(x \ll 0.050\). Using these approximations, the simplified expression for \(K\) becomes: \[1.0 \times 10^{23} = \dfrac{x}{(0.0010)(0.050)}\] Now, we can solve for \(x\): \[x = (0.0010)(0.050)(1.0 \times 10^{23})\] \[x = 5.0 \times 10^{-5}\] Thus, the equilibrium concentration of \(\mathrm{Pb^{2+}}\) is approximately \(5.0 \times 10^{-5} \mathrm{M}\).

Key concepts

EDTA Complexing Agent

Ethylenediaminetetraacetic acid, commonly known as EDTA, is a powerful chelating agent. This means it has the ability to bind to metal ions, forming stable complexes.

In chemistry and clinical laboratories, EDTA's chelating properties are harnessed in complexometric titrations to determine the concentration of metal ions in a solution. Its applications are broad, and one of the interesting uses of EDTA is in the field of medicine, particularly for treating heavy metal poisoning.

Understanding Chelation

Chelation involves the formation of two or more separate coordinate bonds between a polydentate (multiple-bonding) ligand and a single central atom. The EDTA molecule wraps around metal ions like lead, forming a stable complex. This process is reversible, which is why we refer to the equilibrium constant when describing these reactions.

Equilibrium Constant Calculation

In chemical equilibrium, the concentration of reactants and products reach a state where they do not change over time. The equilibrium constant, denoted as K, is a ratio that quantifies the position of the system at equilibrium.

For the reaction between a metal ion, such as lead (Pb²⁺), and EDTA, the equilibrium constant is given as a large number (\(1.0 \times 10^{23}\)), indicating the formation of a very stable complex.

Calculation Steps Simplified

To calculate the equilibrium constant, we consider the concentration of each species at equilibrium. With very large or small values of K, we can make approximations to simplify the calculation process. These approximations stem from the understanding that if K is large, the reaction proceeds almost to completion, and if K is small, the reaction barely proceeds.

Heavy Metal Poisoning Treatment

Heavy metal poisoning can have serious health implications. It often results from the accumulation of metals like lead, mercury, or arsenic in the body, affecting various bodily functions.

EDTA has proven effective in the treatment of such poisoning due to its ability to form complexes with the heavy metal ions, reducing their toxic effects. The metal-EDTA complexes are more soluble and less toxic than the free metal ions, allowing the body to safely excrete these metals.

EDTA in Clinical Use

The administration of EDTA for heavy metal detoxification is known as chelation therapy. This therapy must be closely monitored, as the complexing agent can also bind to essential minerals in the body, leading them to be excreted along with toxic metals. Therefore, the application of chelation therapy is carried out under strict medical supervision and involves careful dosage and timing to minimize potential side effects.