How are complete ionic and net ionic equations written for chemical reactions in aqueous solutions

Explanation:

Balanced Chemical equation:

HClO₂(aq) + NaOH(aq) → H₂O(l) + NaClO₂ (aq)

Ionic equation:

H⁺(aq) + ClO₂⁻(aq) + Na⁺(aq) + OH⁻(aq) → H₂O(l) + Na⁺(aq) + ClO₂⁻ (aq)

Net ionic equation:

H⁺(aq) + OH⁻(aq) → H₂O(l)  

The ClO₂⁻(aq) and Na⁺ (aq) are spectator ions that's why these are not written in net ionic equation. The water can not be splitted into ions because it is present in liquid form.

Spectator ions:

These ions are same in both side of chemical reaction. These ions are cancel out. Their presence can not effect the equilibrium of reaction that's why these ions are omitted in net ionic equation.  

Chemical equation:

NaCl(aq) + KBr(aq)  → NaBr(aq) + KCl(aq)

Ionic equation:

Na⁺(aq)  + Cl⁻(aq) + K⁺(aq)  + Br⁻(aq)  → Na⁺(aq) + Br⁻(aq) + K⁺(aq)  + Cl⁻(aq)

Net ionic equation can not be written for this reaction because nothing is changed on both side. There is no solid, liquid and gaseous product. All are aqueous and cancel each other.

in the analysis of systems that involve fluid flow, we frequently encounter the combination of properties u and pv.