Complex ion formation has been used to extract gold, which exists in nature in the uncombined state. To separate it from other solid impurities, the ore is treated with a sodium cyanide (NaCN) solution in the presence of air to dissolve the gold by forming the soluble complex ion \(\left[\mathrm{Au}(\mathrm{CN})_{2}\right]^{-}\). (a) Balance the following equation: $$\mathrm{Au}+\mathrm{CN}^{-}+\mathrm{O}_{2}+\mathrm{H}_{2} \mathrm{O} \longrightarrow\left[\mathrm{Au}(\mathrm{CN})_{2}\right]^{-}+\mathrm{OH}^{-}$$ (b) The gold is obtained by reducing the complex ion with zinc metal. Write a balanced ionic equation for this process. (c) What is the geometry and coordination number of the \(\left[\mathrm{Au}(\mathrm{CN})_{2}\right]^{-}\) ion?

Understanding how to balance a chemical equation is crucial when studying chemical reactions. Balancing ensures that the same number of atoms for each element is present on both sides of the equation, following the law of conservation of mass. Take the complex ion formation involving gold and cyanide: initially, the unbalanced equation is given by \[ \mathrm{Au} + \mathrm{CN}^{-} + \mathrm{O}_{2} + \mathrm{H}_{2} \mathrm{O} \longrightarrow \left[\mathrm{Au}(\mathrm{CN})_{2}\right]^{-} + \mathrm{OH}^{-} \].
To balance this equation, one must account for all gold (Au), cyanide (CN⁻), oxygen (O₂), and water molecules (H₂O) on the reactant side and ensure they are equally represented on the product side. The balanced equation is \[ 4\mathrm{Au} + 8\mathrm{CN}^{-} + \mathrm{O}_{2} + 2\mathrm{H}_{2}\mathrm{O} \rightarrow 4\left[\mathrm{Au}(\mathrm{CN})_{2}\right]^{-} + 4\mathrm{OH}^{-} \].
The balance is achieved by adjusting the coefficients – the numbers placed before compounds – to get an equal number of each type of atom on both sides. Practice with various equations aids in developing a more intuitive sense of how to balance reactions efficiently.

Writing an ionic equation involves expressing a chemical reaction with ions as they are present in solution for reactions involving ionic compounds. It's a way to focus on the substances that actually change during the reaction, as opposed to molecular equations that list compounds in their complete form. When gold is extracted using a cyanide solution, and the complex ion \([\mathrm{Au}(\mathrm{CN})_{2}]^{-}\)
is reduced by zinc, the balanced ionic equation is essential to represent what’s really happening. The zinc displaces gold from its complex ion, resulting in \[\mathrm{Zn} + 2\left[\mathrm{Au}(\mathrm{CN})_{2}\right]^{-} \rightarrow \mathrm{Au} + \left[\mathrm{Zn}(\mathrm{CN})_{4}\right]^{2-}\].
When balancing, the number of electrons lost by the zinc must equal the number of electrons gained by the gold ions. Often net ionic equations are also written to show only the species that undergo a change, excluding spectator ions. This deepens the understanding of the underlying stoichiometry and redox processes.

The coordination number of a central atom in a complex is the total number of ligand (donor atom) connections it has. In the gold cyanide example, \([\mathrm{Au}(\mathrm{CN})_{2}]^{-}\)
the gold atom (Au) is connected to two cyanide (CN⁻) ions, which means its coordination number is 2. Furthermore, the geometry of a complex ion pertains to the spatial arrangement of the ligands connected to the central atom. For \([\mathrm{Au}(\mathrm{CN})_{2}]^{-}\),
the geometry is linear because the two cyanide ions are positioned at opposite sides of the gold atom. The concept of coordination geometry is important as it influences the chemical reactivity and properties of the compound, like color and magnetism. Understanding both the coordination number and geometry offers insight into the behavior of complex ions in different chemical reactions and is foundational for comprehending more advanced topics in coordination chemistry.