Step-by-step explanation:
To balance half equations of a redox reaction is important to not only balance the mass (ammount of atoms of each element in both sides of the equation), but also balance the charges (ion's charges and electrons).
For example:
The reaction:
![Fe^(+2) + MnO_4^- \longrightarrow Fe^(+3) + Mn^(+2)](https://img.qammunity.org/2021/formulas/chemistry/high-school/mnma4y6fnx40e3jt0hcai8fgvjt8ocotbh.png)
First step is to identify the element oxidized (loses electrons/valence increases) and the element reduced (gains electrons/valence decreases)
- Fe is oxidized (valence from +2 to +3)
- Mn is reduced (valence from +7 to +2)
So we have to half equations:
Oxidation equation
![Fe^(+2) \longrightarrow Fe^(+3)](https://img.qammunity.org/2021/formulas/chemistry/high-school/8zojon8ql65yu0igh5qcjc3a9anoms8fbq.png)
Here the mass is balanced, but the charges aren't. Balancing:
![Fe^(+2) \longrightarrow Fe^(+3)+ e^-](https://img.qammunity.org/2021/formulas/chemistry/high-school/v6n3h4q6qkercag7a27m2svr6soidjhdxj.png)
Reduction equation
![MnO_4^- \longrightarrow Mn^(+2)](https://img.qammunity.org/2021/formulas/chemistry/high-school/6brdgs36md7xe1maz47zzr1wf146ytylsv.png)
Balancing the mass with H2O and H+ (assuming acid medium)
![MnO_4^- \longrightarrow Mn^(+2) + 4 H_2O](https://img.qammunity.org/2021/formulas/chemistry/high-school/4nu0kftjpm4i89xkqqx3mvfqx1j986facx.png)
![MnO_4^- + 8 H^+ \longrightarrow Mn^(+2) + 4 H_2O](https://img.qammunity.org/2021/formulas/chemistry/high-school/2f4u97u11mg3dplna8x43ip4s1w9ez3zhy.png)
Balancing charges
![MnO_4^- + 8 H^+ + 5e^- \longrightarrow Mn^(+2) + 4 H_2O](https://img.qammunity.org/2021/formulas/chemistry/high-school/2aymu26lw448h7ocbknqjstp0xeckgk6ea.png)
Global balance
![5 Fe^(+2) + MnO_4^- + 8 H^+\longrightarrow 5 Fe^(+3) + Mn^(+2) + 4 H_2O](https://img.qammunity.org/2021/formulas/chemistry/high-school/yq6yav2m8nxlxgrtb8sqe5jbjq2rzzkz5r.png)