`=>` Two methods are used to balance chemical equations for redox processes.
•One of these methods is based on the change in the oxidation number of reducing agent and the oxidising agent
•The other method is based on splitting the redox reaction into two half reactions — one involving oxidation and the other involving reduction.

Both these methods are in use and the choice of their use rests with the individual using them.

(a) `color{green}("Oxidation Number Method:")` In writing equations for oxidation-reduction reactions, just as for other reactions, the compositions and formulas must be known for the substances that react and for the products that are formed. The oxidation number method is now best illustrated in the following steps:

Step 1: Write the correct formula for each reactant and product.

Step 2: Identify atoms which undergo change in oxidation number in the reaction by assigning the oxidation number to all elements in the reaction.

Step 3: Calculate the increase or decrease in the oxidation number per atom and for the entire molecule/ion in which it occurs. If these are not equal then multiply by suitable number so that these become equal. (If you realise that two substances are reduced and nothing is oxidised or vice-versa, something is wrong. Either the formulas of reactants or products are wrong or the oxidation numbers have not been assigned properly).

Step 4: Ascertain the involvement of ions if the reaction is taking place in water, add `color{red}(H^+)` or `color{red}(OH^–)` ions to the expression on the appropriate side so that the total ionic charges of reactants and products are equal. If the reaction is carried out in acidic solution, use `color{red}(H^+)` ions in the equation; if in basic solution, use `color{red}(OH^–)` ions.

Step 5 : Make the numbers of hydrogen atoms in the expression on the two sides equal by adding water `color{red}(H_2O)` molecules to the reactants or products. Now, also check the number of oxygen atoms. If there are the same number of oxygen atoms in the reactants and products, the equation then represents the balanced redox reaction.

`color{green}("Let us now explain the steps involved in the method with the help of a few problems given below:")`


(b) `color{green}("Half Reaction Method:")` In this method, the two half equations are balanced separately and then added together to give balanced equation. Suppose we are to balance the equation showing the oxidation of `color{red}(Fe^(2+))` ions to `color{red}(Fe^(3+))` ions by dichromate ions `color{red}((Cr_2O_7)^(2–))` in acidic medium, wherein, `color{red}(Cr_2O_7^(2–))` ions are reduced to `color{red}(Cr^(3+))` ions. The following steps are involved in this task.


Step 1:`color{green}("Produce unbalanced equation for the reaction in ionic form :")`

`color{red}(Fe^(2+)(aq) + Cr_2O_7^(2–) (aq) → Fe^(3+) (aq) + Cr^(3+)(aq))` ............(8.50)

Step 2: `color{green}("Separate the equation into halfreactions :")`

`color{green}("Oxidation half :")` `color{red}(overset(+2)(Fe^(2+))(aq) → overset(+3)(Fe^(3+))(aq))` .................(8.51)

`color{green}("Reduction half :")` `color{red}(overset(+6)(Cr_2 ) overset(-2)(O_7^(2-)) (aq) → overset(+3)(Cr^(3+)) (aq)) ` .............(8.52)

Step 3: Balance the atoms other than `color{red}(O)` and `color{red}(H)` in each half reaction individually. Here the oxidation half reaction is already balanced with respect to `color{red}(Fe)` atoms. For the reduction half reaction, we multiply the `color{red}(Cr^(3+))` by 2 to balance `color{red}(Cr)` atoms.

`color{red}(Cr_2O_7^(2-)(aq) → 2Cr^(3+)(aq))` .......................(8.53)

Step 4: For reactions occurring in acidic medium, add `color{red}(H_2O)` to balance `color{red}(O)` atoms and `color{red}(H^+)` to balance `color{red}(H)` atoms.

`color{green}("Thus, we get :")`

`color{red}(Cr_2O_7^(2-)(aq) +14H^(+)(aq) → 2Cr^(3+)(aq) +7H_2O(l))` .................(8.54)

Step 5: Add electrons to one side of the half reaction to balance the charges. If need be, make the number of electrons equal in the two half reactions by multiplying one or both half reactions by appropriate number.

`color{green}("The oxidation half reaction is thus rewritten to balance the charge:")`


`color{red}(Fe^(2+)(aq) → Fe^(3+)(aq) + e^(-))` ...........................(8.55)

Now in the reduction half reaction there are net twelve positive charges on the left hand side and only six positive charges on the right hand side. Therefore, we add six electrons on the left side

`color{red}(Cr_2O_7^(2-)(aq) +14H^(+)(aq) +6e^(-) → 2Cr^(3+)(aq) + 7H_2O(l)) ` ....................(8.56)

`color{green}("To equalise the number of electrons in both the half reactions, we multiply the oxidation half reaction by 6 and write as :")`

`color{red}(6Fe^(2+) (aq) → 6Fe^(3+)(aq) +6e^(-))` ...........................(8.57)

Step 6: We add the two half reactions to achieve the overall reaction and cancel the electrons on each side. This gives the net ionic
equation as :

`color{red}(6Fe^(2+) (aq) +Cr_2O_7^(2-)(aq) +14H^(+) (aq) → 6Fe^(3+)(aq) +2Cr^(3+)(aq) +7H_2O(l)) ` ...............(8.58)

Step 7: Verify that the equation contains the same type and number of atoms and the same charges on both sides of the equation. This last check reveals that the equation is fully balanced with respect to number of atoms and the charges.

For the reaction in a basic medium, first balance the atoms as is done in acidic medium. Then for each `color{red}(H^+)` ion, add an equal number of `color{red}(OH^–)` ions to both sides of the equation. Where `color{red}(H^+)` and `color{red}(OH^–)` appear on the same side of the equation, combine these to give `color{red}(H_2O).`

`=>` In acid-base systems we come across with a titration method for finding out the strength of one solution against the other using a pH sensitive indicator.

`=>` Similarly, in redox systems, the titration method can be adopted to determine the strength of a reductant/oxidant using a redox sensitive indicator.

`=>` `color{red}("The usage of indicators in redox titration is illustrated below:")`

(i) In one situation, the reagent itself is intensely coloured, e.g., permanganate ion, `color{red}(MnO_4^(–))` . Here `color{red}(MnO_4^(–))` acts as the self indicator. The visible end point in this case is achieved after the last of the reductant (`color{red}(Fe^(2+))` or `color{red}(C_2O_4^(2–))`) is oxidised and the first lasting tinge of pink colour appears at `color{red}(MnO_4^(–))` concentration as low as `color{red}(10^(–6) mol dm^(–3))` (`color{red}(10^(–6) mol L^(–1))`). This ensures a minimal ‘overshoot’ in colour beyond the equivalence point, the point where the reductant and the oxidant are equal in terms of their mole stoichiometry.

(ii) If there is no dramatic auto-colour change (as with `color{red}(MnO_4 ^(–))` titration), there are indicators which are oxidised immediately af ter the last bit of the reactant is consumed, producing a dramatic colour change. The best example is afforded by `color{red}(Cr_2O_7^(2–))`, which is not a self-indicator, but oxidises the indicator substance diphenylamine just after the equivalence point to produce an intense blue colour, thus signalling the end point.

(iii) There is yet another method which is interesting and quite common. Its use is restricted to those reagents which are able to oxidise I– ions, say, for example, `color{red}(Cu(II))`:

`color{red}(2Cu^(2+)(aq) +4I^(-)(aq) → Cu_2I_2(s) +I_2(aq))` ...................................................(8.59)

This method relies on the facts that iodine itself gives an intense blue colour with starch and has a very specific reaction with thiosulphate ions (`color{red}(S_2O_3^(2–))`), which too is a redox reaction.

`color{red}(I_2(aq) +2S_2O_3^(2-)(aq) → 2I^(-) (aq) +S_4O_6^(2-)(aq))` ..................... (8.60)

`color{red}(I_2)`, though insoluble in water, remains in solution containing `color{red}(KI)` as `color{red}(KI_3).`

On addition of starch after the liberation of iodine from the reaction of `color{red}(Cu^(2+))` ions on iodide ions, an intense blue colour appears. This colour disappears as soon as the iodine is consumed by the thiosulphate ions. Thus, the end-point can easily be tracked and the rest is the stoichiometric calculation only.