For a number of years it was not clear whether mercury(I)...

For a number of years it was not clear whether mercury(I) ions existed in solution as $\mathrm{Hg}^{+}$ or as $\mathrm{Hg}_{2}^{2+}$. To distinguish between these two possibilities, we could set up the following system: $$ \operatorname{Hg}(l)|\operatorname{soln} \mathrm{A} \| \operatorname{soln} \mathrm{B}| \operatorname{Hg}(l) $$ where soln A contained $0.263$ g mercury(I) nitrate per liter and soln $\mathrm{B}$ contained $2.63 \mathrm{~g}$ mercury $(\mathrm{I})$ nitrate per liter. If the measured emf of such a cell is $0.0289 \mathrm{~V}$ at $18^{\circ} \mathrm{C}$, what can you deduce about the nature of the mercury(I) ions?

For a number of years it was not clear whether mercury(I) ions existed in solution as $\mathrm{Hg}^{+}$ or as $\mathrm{Hg}_{2}^{2+}$. To distinguish between these two possibilities, we could set up the following system:
$$
\operatorname{Hg}(l)|\operatorname{soln} \mathrm{A} \| \operatorname{soln} \mathrm{B}| \operatorname{Hg}(l)
$$
where soln A contained $0.263$ g mercury(I) nitrate per liter and soln $\mathrm{B}$ contained $2.63 \mathrm{~g}$ mercury $(\mathrm{I})$ nitrate per liter. If the measured emf of such a cell is $0.0289 \mathrm{~V}$ at $18^{\circ} \mathrm{C}$, what can you deduce about the nature of the mercury(I) ions?

Key Concepts

Electrochemical Cells

Electrochemical cells are devices that convert chemical energy into electrical energy through redox reactions occurring at two electrodes. By constructing a cell from two half-cells and measuring the electromotive force (emf), one can derive information about the chemical processes, reaction equilibria, and the nature of the species involved in the redox processes.

Concentration Cells

A concentration cell is a type of electrochemical cell where both electrodes are made of the same material but are exposed to solutions of different concentrations. The potential difference generated arises solely from the concentration gradient of the active species in each half-cell, making it a powerful tool to study the role of ion concentration and reaction stoichiometry in redox processes.

Nernst Equation

The Nernst equation relates the cell potential to the concentrations (or activities) of the reactants and products involved in the electrode reactions. It provides a quantitative method to determine how changes in concentration can affect the emf of a cell. In this context, correctly applying the Nernst equation helps deduce which redox species are involved based on the measured cell potential and the stoichiometry of the electron transfer.

Dimeric Nature of Mercury(I) Ions

Mercury(I) ions are known to exist predominantly as a dimeric species, Hg?²?, rather than as monomeric Hg?. This dimerization is energetically favored and affects the stoichiometry and corresponding Nernst equation of the redox reaction. The experimental emf and concentration differences in the cell provide evidence supporting the dimeric nature, which plays a crucial role in understanding its chemical behavior in solution.

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