Balance the following ionic equations for reactions in...

Balance the following ionic equations for reactions in acidic solution. $\mathrm{H}^{+}$ or $\mathrm{H}_{2} \mathrm{O}$ (but $\left.\mathrm{not} \mathrm{OH}^{-}\right)$ may be added as necessary. (a) $\mathrm{P}_{4}(\mathrm{~s})+\mathrm{NO}_{3}^{-}(\mathrm{aq}) \longrightarrow \mathrm{H}_{3} \mathrm{PO}_{4}(\mathrm{aq})+\mathrm{NO}(\mathrm{g})$ (b) $\mathrm{H}_{2} \mathrm{O}_{2}(\mathrm{aq})+\mathrm{MnO}_{4}^{-}(\mathrm{aq}) \longrightarrow \mathrm{Mn}^{2+}(\mathrm{aq})+\mathrm{O}_{2}(\mathrm{~g})$ (c) $\mathrm{HgS}(\mathrm{s})+\mathrm{Cl}^{-}(\mathrm{aq})+\mathrm{NO}_{3}^{-}(\mathrm{aq}) \longrightarrow$ $\mathrm{HgCl}_{4}^{2-}(\mathrm{aq})+\mathrm{NO}_{2}(\mathrm{~g})+\mathrm{S}(\mathrm{s})$ (d) $\mathrm{HBrO}(\mathrm{aq}) \longrightarrow \mathrm{Br}^{-}(\mathrm{aq})+\mathrm{O}_{2}(\mathrm{~g})$

Balance the following ionic equations for reactions in acidic solution. $\mathrm{H}^{+}$ or $\mathrm{H}_{2} \mathrm{O}$ (but $\left.\mathrm{not} \mathrm{OH}^{-}\right)$ may be added as necessary.
(a) $\mathrm{P}_{4}(\mathrm{~s})+\mathrm{NO}_{3}^{-}(\mathrm{aq}) \longrightarrow \mathrm{H}_{3} \mathrm{PO}_{4}(\mathrm{aq})+\mathrm{NO}(\mathrm{g})$
(b) $\mathrm{H}_{2} \mathrm{O}_{2}(\mathrm{aq})+\mathrm{MnO}_{4}^{-}(\mathrm{aq}) \longrightarrow \mathrm{Mn}^{2+}(\mathrm{aq})+\mathrm{O}_{2}(\mathrm{~g})$
(c) $\mathrm{HgS}(\mathrm{s})+\mathrm{Cl}^{-}(\mathrm{aq})+\mathrm{NO}_{3}^{-}(\mathrm{aq}) \longrightarrow$
$\mathrm{HgCl}_{4}^{2-}(\mathrm{aq})+\mathrm{NO}_{2}(\mathrm{~g})+\mathrm{S}(\mathrm{s})$
(d) $\mathrm{HBrO}(\mathrm{aq}) \longrightarrow \mathrm{Br}^{-}(\mathrm{aq})+\mathrm{O}_{2}(\mathrm{~g})$

Key Concepts

Redox Reactions

Redox reactions involve the transfer of electrons between species, resulting in changes in the oxidation states of atoms. They are characterized by one species undergoing oxidation (loss of electrons) while another undergoes reduction (gain of electrons), and understanding this concept is fundamental to balancing such reactions.

Half-Reaction Method

The half-reaction method is a systematic approach used to balance redox equations. In this method, the oxidation and reduction processes are separated into individual equations. Each half-reaction is balanced for mass and charge independently before the electrons lost in the oxidation half are equated to the electrons gained in the reduction half, and then the two are recombined.

Oxidation States

Oxidation states indicate the degree of oxidation of an atom in a compound and are used to identify which species are oxidized and which are reduced. Assigning oxidation numbers helps to track the electron flow during a reaction, which is critical for formulating the appropriate half-reactions.

Balancing in Acidic Solutions

When balancing ionic redox reactions under acidic conditions, additional species like H+ and H2O are used to balance hydrogen and oxygen atoms. This technique leverages the properties of the solution—namely the presence of H+—to ensure that both mass and charge are conserved in the overall reaction.

Conservation of Mass and Charge

The principle of conservation of mass and charge is fundamental in all chemical reactions; it requires that the number of atoms of each element and the total charge be the same on both sides of a balanced chemical equation. This concept underpins the process of balancing chemical equations and ensures that the derived equations obey the laws of physics and chemistry.