Complete and balance the following equations. If no reaction occurs, so state. (a) \(\operatorname{TiCl}_{4}(\mathrm{g})+\mathrm{Na}(1) \stackrel{\Delta}{\longrightarrow}\) (b) \(\mathrm{Cr}_{2} \mathrm{O}_{3}(\mathrm{s})+\mathrm{Al}(\mathrm{s}) \stackrel{\Delta}{\longrightarrow}\) (c) \(\mathrm{Ag}(\mathrm{s})+\mathrm{HCl}(\mathrm{aq}) \longrightarrow\) (d) \(\mathrm{K}_{2} \mathrm{Cr}_{2} \mathrm{O}_{7}(\mathrm{aq})+\mathrm{KOH}(\mathrm{aq}) \longrightarrow\) (e) \(\mathrm{MnO}_{2}(\mathrm{s})+\mathrm{C}(\mathrm{s}) \stackrel{\Delta}{\longrightarrow}\)

Understanding the reactivity series is crucial when predicting the outcomes of chemical reactions. The reactivity series is a list of elements organized by their ability to displace others in a compound. More reactive elements can displace less reactive elements from their compounds during a chemical reaction.

For example, in the exercise, aluminum (Al) is above chromium (Cr) in the reactivity series. This is why aluminum is capable of reducing chromium(III) oxide (Cr2O3) to chromium (Cr) in an oxidation-reduction reaction. The reaction can be represented by the equation \( \text{Cr2O3(s)} + 2\text{Al(s)} \rightarrow \text{Al2O3(s)} + 2\text{Cr(s)} \). Here, aluminum acts as a reducing agent, and chromium(III) oxide is reduced.

Oxidation-reduction reactions, commonly known as redox reactions, are processes that involve the transfer of electrons between elements. When an element gains electrons, it is reduced, and when an element loses electrons, it is oxidized.

In step 1 of the exercise solution, the equation \( \text{TiCl4(g)} + 4\text{Na(l)} \rightarrow \text{Ti(s)} + 4\text{NaCl(s)} \) involves sodium (Na) being oxidized as it loses electrons to form NaCl, whereas titanium tetrachloride (TiCl4) is reduced to titanium (Ti). The ability to correctly balance redox equations is essential in predicting the stoichiometry of the products formed in a reaction.

Chemical reactions can be classified into several types, including synthesis, decomposition, single displacement, double displacement, and combustion. This classification helps in understanding the reaction mechanisms and predicting the products.

For instance, the reaction given in step 5, \( \text{MnO2(s) + C(s)} \rightarrow \text{Mn(s) + CO2(g)} \), is a type of redox reaction where manganese dioxide (MnO2) is reduced to manganese (Mn), and carbon (C) is oxidized to carbon dioxide (CO2). This particular reaction is also a decomposition reaction because a single compound (MnO2) breaks down into simpler substances (Mn and CO2). Noting the type of reaction helps in formulating and balancing the chemical equation.