Question

Mercury(I) chloride, \(\mathrm{Hg}_{2} \mathrm{Cl}_{2}\), was formerly administered orally as a purgative. Although we usually think of mercury compounds as highly toxic, the \(K_{\mathrm{sp}}\) of mercury(I) chloride is small enough \(\left(1.3 \times 10^{-18}\right)\) that the amount of mercury that dissolves and enters the bloodstream is tiny. Calculate the concentration of mercury(I) ion present in a saturated solution of \(\mathrm{Hg}_{2} \mathrm{Cl}_{2}\)

Short answer

The concentration of mercury(I) ion in the saturated solution of mercury(I) chloride is approximately \(1.02 \times 10^{-6}\, \mathrm{M}\).

Step-by-step solution

Write the dissolution reaction of \(\mathrm{Hg}_{2}\mathrm{Cl}_{2}\)

Let's write the dissolution chemical reaction of mercury(I) chloride: \(\mathrm{Hg}_{2}\mathrm{Cl}_{2} \, \rightleftharpoons \, 2\mathrm{Hg}_{\mathrm{I}}^{+} + 2\mathrm{Cl}^{-}\) - Mercury(I) chloride dissociates into 2 mercury(I) ions and 2 chloride ions in an equilibrium reaction.

Write the \(K_{\mathrm{sp}}\) expression

The solubility product constant, \(K_{\mathrm{sp}}\), is the product of the concentrations of the ions raised to their stoichiometric coefficients. In our case, for the equilibrium reaction, the expression is: \(K_{\mathrm{sp}} = [\mathrm{Hg}_{\mathrm{I}}^{+}]^{2} [\mathrm{Cl}^{-}]^{2}\) Here, \([\mathrm{Hg}_{\mathrm{I}}^{+}]\) and \([\mathrm{Cl}^{-}]\) are the concentrations of mercury(I) and chloride ions, respectively.

Determine the concentrations at equilibrium

Let's assume that the concentration of mercury(I) ions at equilibrium is \(x \, \mathrm{M}\). Since there are 2 chloride ions released for each dissociation of \(\mathrm{Hg}_{2}\mathrm{Cl}_{2}\), the concentration of chloride ions at equilibrium will be \(2x \, \mathrm{M}\). Now we can rewrite the expression for \(K_{\mathrm{sp}}\) in terms of \(x\): \(K_{\mathrm{sp}} = (x)^{2}(2x)^{2}\)

Solve for the mercury(I) ion concentration \(x\)

We are given the value of the solubility product constant, \(K_{\mathrm{sp}} = 1.3 \times 10^{-18}\). We substitute this into the expression and solve for \(x\): \(1.3 \times 10^{-18} = (x)^{2}(2x)^{2}\) After solving for \(x\), we get: \(x \approx 1.02 \times 10^{-6} \, \mathrm{M}\) The concentration of mercury(I) ion in the saturated solution of mercury(I) chloride is approximately \(1.02 \times 10^{-6}\, \mathrm{M}\).

Key concepts

Chemical Equilibrium

Chemical equilibrium is a fascinating concept in chemistry that describes the state of a reaction where the rates of the forward and reverse reactions are equal. At this point, the concentrations of the reactants and products remain constant over time. This doesn't mean the reactions stop; rather, they continue to occur at the same rate, balancing each other out.

• During equilibrium, the reaction appears static but is dynamic at the molecular level.
• It's important to note that equilibrium can be achieved from either direction, starting with reactants or products.

Chemical equilibrium is crucial for understanding many natural processes, such as how gases in our atmosphere balance or how buffers maintain pH in biological systems. It's a core concept that helps students understand the dynamic nature of chemical reactions that seem static but are continuously happening.

Dissolution Reaction

Dissolution reactions are processes where a solid substance dissolves in a solvent to form a solution. In the case of mercury(I) chloride, the dissolution reaction involves the solid compound dissociating into its constituent ions in water. The dissolution can be represented by the equation:
\[\mathrm{Hg}_{2}\mathrm{Cl}_{2} \rightleftharpoons 2\mathrm{Hg}_{\mathrm{I}}^{+} + 2\mathrm{Cl}^{-}\]

• The double arrow indicates that the reaction reaches an equilibrium state.
• As mercury(I) chloride dissolves, it forms two mercury ions and two chloride ions.
• The extent to which it dissolves is characterized by its solubility product constant, \(K_{\mathrm{sp}}\).

Understanding dissolution reactions is key to comprehending how substances like salts dissolve in water and how their ionic concentrations affect the solution's properties.

Mercury Compounds

Mercury compounds, such as mercury(I) chloride, are well-known for their toxic properties. However, the toxicity often depends on how much of the compound can dissolve in water and enter the body. The solubility product constant \(K_{\mathrm{sp}}\) of mercury(I) chloride is very low \((1.3 \times 10^{-18})\), indicating that only a tiny amount can dissolve, making it less harmful in low concentrations.

• Mercury-related substances can be dangerous, but not all forms are equally toxic.
• The low solubility means less mercury is available to interact with biological systems.
• Handling mercury compounds requires care, understanding the specific risks related to each form.

By analyzing the solubility and equilibrium of mercury compounds, scientists can predict how they behave in the environment and manage their safe use in various applications.