Predict the products of the following reactions and balance the equations. (a) \(\mathrm{Zn}\) is added to a solution of \(\mathrm{Cr}_{2}\left(\mathrm{SO}_{4}\right)_{3}\) in acid. (b) \(\mathrm{FeCl}_{2}\) is added to a solution containing an excess of \(\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}\) in hydrochloric acid. (c) \(\mathrm{Cr}^{2+}\) is added to \(\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}\) in acid solution. (d) Mn is heated with CrO \(_{3}\). (e) CrO is added to \(2 \mathrm{HNO}_{3}\) in water. (f) \(\mathrm{FeCl}_{3}\) is added to an aqueous solution of \(\mathrm{NaOH}\).

Understanding oxidation states is crucial when predicting and balancing redox reactions. The oxidation state, often referred to as the oxidation number, determines the degree of oxidation of an atom in a chemical compound. An atom's oxidation state is the hypothetical charge it would have if the compound was composed of ions.

Here's a quick guide to determining oxidation states: Begin with known oxidation states, such as those of alkali metals (+1) and alkaline earth metals (+2). Oxygen is usually -2, except in peroxides, and hydrogen is +1 when bound to nonmetals and -1 with metals. For molecules, the sum of oxidation states of all atoms equals the charge on the molecule or ion.

For instance:

• Zn in its elemental form has an oxidation state of 0.
• In Cr2(SO4)3, Cr must have an oxidation state of +3 to balance the -2 from each sulfate ion (SO4 2-).

These oxidation states are pivotal in recognizing the flow of electrons. In a redox reaction, the element that reduces its oxidation state is gaining electrons (reduced), and the element increasing its oxidation state is losing electrons (oxidized).

The half-reactions method is a systematic way of balancing redox equations. This invaluable tool breaks the daunting task into manageable parts by separating the oxidation and reduction processes.

Here are the essential steps of the half-reactions method:

• Identify and write the two half-reactions — one for oxidation, one for reduction.
• Balance atoms, except for oxygen and hydrogen in each half-reaction.
• Balance oxygen atoms by adding H2O, and hydrogen atoms by adding H+ (in acidic solutions) or OH- (in basic solutions).
• Balance the charges by adding electrons to the more positive side.
• Combine the two half-reactions, ensuring the electrons cancel out, to get the balanced overall equation.

By applying this method, students clearly see how electrons are transferred and ensure mass and charge are conserved, which is the cornerstone of any balanced chemical equation. For example, when Zn reduces Cr3+ to Cr2+, two half-reactions detail the electron loss and gain, resulting in a holistic, balanced chemical equation.

The reactivity series is a list of elements organized by their reactivity from most reactive to least reactive. Metals higher in the series have a greater tendency to lose electrons and are better at reducing cations of metals lower down the series.

In the context of redox reactions, the reactivity series helps predict which metals will oxidize and which will reduce. It's critical for Step 2 in the problem-solving process; knowing that zinc is higher up the series compared to chromium allows us to accurately predict that Zn will be oxidized (lose electrons) and Cr3+ will be reduced to Cr2+.

• A more reactive metal can displace a less reactive metal from its compounds.
• This order heavily influences which elements can be oxidized or reduced in aqueous solutions.

Comprehending the reactivity series not only aids predictions in redox reactions but also determines the spontaneity of a reaction. If a metal higher in the series is reacting with the ion of a metal lower in the series, the reaction is typically spontaneous.