Titanium dioxide, the most widely used white pigment, occurs...

Titanium dioxide, the most widely used white pigment, occurs naturally but is often colored by the presence of impurities. The chloride process is often used in purifying rutile, a mineral form of titanium dioxide. a. Show that the unit cell for rutile, shown below, conforms to the formula $\mathrm{TiO}_{2}$. (Hint: Recall the discussion in Sections $10.4$ and $10.7 .$ ) b. The reactions for the chloride process are $$\begin{array}{l}2 \mathrm{TiO}_{2}(s)+3 \mathrm{C}(s)+4 \mathrm{Cl}_{2}(g) \\\quad \stackrel{950^{\circ} \mathrm{C}}{\longrightarrow} 2 \mathrm{TiCl}_{4}(g)+\mathrm{CO}_{2}(g)+2 \mathrm{CO}(g) \\ \mathrm{TiCl}_{4}(g)+\mathrm{O}_{2}(g) \stackrel{1000-1400^{\circ} \mathrm{C}}{\longrightarrow} \mathrm{TiO}_{2}(s)+2 \mathrm{Cl}_{2}(g) \end{array}$$ Assign oxidation states to the elements in both reactions. Which elements are being reduced, and which are being oxidized? Identify the oxidizing agent and the reducing agent in each reaction.

Titanium dioxide, the most widely used white pigment, occurs naturally but is often colored by the presence of impurities. The chloride process is often used in purifying rutile, a mineral form of titanium dioxide.
a. Show that the unit cell for rutile, shown below, conforms to the formula $\mathrm{TiO}_{2}$. (Hint: Recall the discussion in Sections $10.4$ and $10.7 .$ )
b. The reactions for the chloride process are
$$\begin{array}{l}2 \mathrm{TiO}_{2}(s)+3 \mathrm{C}(s)+4 \mathrm{Cl}_{2}(g) \\\quad \stackrel{950^{\circ} \mathrm{C}}{\longrightarrow} 2 \mathrm{TiCl}_{4}(g)+\mathrm{CO}_{2}(g)+2 \mathrm{CO}(g) \\
\mathrm{TiCl}_{4}(g)+\mathrm{O}_{2}(g) \stackrel{1000-1400^{\circ} \mathrm{C}}{\longrightarrow} \mathrm{TiO}_{2}(s)+2 \mathrm{Cl}_{2}(g)
\end{array}$$
Assign oxidation states to the elements in both reactions. Which elements are being reduced, and which are being oxidized? Identify the oxidizing agent and the reducing agent in each reaction.

Key Concepts

Oxidizing and Reducing Agents

Within redox processes, the oxidizing agent is the substance that accepts electrons (is reduced) while the reducing agent donates electrons (is oxidized). Correct identification of these agents is fundamental in analyzing electron flow and reaction mechanisms in chemical transformations.

Unit Cell Analysis

This concept involves understanding that the entire crystal structure can be described by a repeating unit cell which contains atoms arranged in a specific geometry. By determining the number and fraction of atoms per unit cell (using, for example, contributions from corners, faces, and internal positions), the overall composition formula of the material can be deduced.

Fractional Atomic Contributions

In crystallography, atoms located on corners, faces, edges, or within the body of a unit cell contribute a fraction of an atom to the unit cell count. This fractional accounting is essential to deduce the empirical formula from the unit cell, as it sums the total number of each type of atom present in the repeating unit.

Oxidation State Assignment

This key concept involves assigning oxidation numbers to elements in compounds based on their bonding environment and electronegativity differences. It is a bookkeeping tool used to track electron transfer in reactions, and it is critical for understanding how elements change oxidation states in redox reactions.

Redox Reactions

Redox reactions are chemical processes that involve the transfer of electrons between species. In these reactions, one species is oxidized (loses electrons) and another is reduced (gains electrons). Understanding redox allows chemists to balance complex chemical reactions and predict the outcomes based on changes in oxidation states.

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