A Complete Guide to Redox Reactions: Disproportionation, Titrations, and Stoichiometry

Definition of Disproportionation: A disproportionation reaction is a type of redox reaction in which a single species simultaneously undergoes oxidation and reduction. For this to occur, the element must be in an intermediate oxidation state, allowing it to move to both a higher and a lower oxidation state.
Disproportionation of Chlorine Oxyanions:
- Hypochlorite ( $ClO^-$ ): Chlorine is in the $+1$ oxidation state. It can disproportionate in basic solution: $3ClO^- \rightarrow 2Cl^- + ClO_3^-$ .
- Chlorite ( $ClO_2^-$ ): Chlorine is in the $+3$ oxidation state (intermediate).
- Chlorate ( $ClO_3^-$ ): Chlorine is in the $+5$ oxidation state (intermediate).
- Perchlorate ( $ClO_4^-$ ): Chlorine is in its highest possible oxidation state ( $+7$ ). Because it cannot be further oxidized, it is thermodynamically stable against disproportionation.
Other Examples of Disproportionation:
- Manganate Ion: $3MnO_4^{2-} + 4H^+ \rightarrow 2MnO_4^- + MnO_2 + 2H_2O$ . Here, $Mn$ goes from $+6$ to $+7$ and $+4$ .
- Hydrogen Peroxide: $2H_2O_2 \rightarrow 2H_2O + O_2$ . Oxygen goes from $-1$ to $-2$ and $0$ .
- Nitrogen Dioxide: $2NO_2 + H_2O \rightarrow HNO_3 + HNO_2$ . Nitrogen goes from $+4$ to $+5$ and $+3$ .
- Copper(I): $2CuBr \rightarrow CuBr_2 + Cu$ . Copper goes from $+1$ to $+2$ and $0$ .
- Bromine Oxyanions: $BrO_4^-$ ( $Br$ is $+7$ ) cannot disproportionate, whereas $BrO^-$ , $BrO_2^-$ , and $BrO_3^-$ can.

Acidic Medium Reactions: Both potassium dichromate ( $K_2Cr_2O_7$ ) and potassium permanganate ( $KMnO_4$ ) act as strong oxidizing agents in acidic media.
Common Transformations:
- Iodide to Iodine: $I^- \rightarrow I_2$
- Sulphide to Sulphur: $S^{2-} \rightarrow S$
- Ferrous to Ferric: $Fe^{2+} \rightarrow Fe^{3+}$
Distinguishing Transformations:
- In acidic medium, both can oxidize $I^-$ to $I_2$ .
- However, in neutral or faintly alkaline solutions, $KMnO_4$ oxidizes $I^-$ to $IO_3^-$ .
${n}$ -factors in Acidic Medium:
- For $KMnO_4$ ( $MnO_4^- \rightarrow Mn^{2+}$ ): Change is $+7$ to $+2$ , so $n = 5$ .
- For $K_2Cr_2O_7$ ( $Cr_2O_7^{2-} \rightarrow 2Cr^{3+}$ ): Change is $+6$ to $+3$ per chromium atom; total change for 2 atoms is $n = 6$ .

Acetate Ion Test: Reaction with neutral ferric chloride produces a brown-red precipitate.
- Formation of complex: $6CH_3COO^- + Fe^{3+} + H_2O \rightarrow [Fe_3(OH)_2(CH_3COO)_6]^+ + 2H^+$ .
- The central metal $Fe^{3+}$ has an electronic configuration of $3d^5 4s^0$ . Therefore, the number of $d$ electrons ( $Y$ ) is $5$ .
Silver Complexes: In the complex $[Ag(NH_3)_2][Ag(CN)_2]$ , it dissociates into $[Ag(NH_3)_2]^+$ and $[Ag(CN)_2]^-$ .
- In $[Ag(NH_3)_2]^+$ : $Ag + 0 \times 2 = +1 \rightarrow Ag = +1$ .
- In $[Ag(CN)_2]^-$ : $Ag + (-1) \times 2 = -1 \rightarrow Ag = +1$ .
- Sum of oxidation states = $1 + 1 = 2$ .
Iron Complexes:
- $Na_4[Fe(CN)_5(NOS)]$ : $Fe$ is in $+2$ state ( $x$ ).
- $Na_4[FeO_4]$ : $Fe$ is in $+4$ state ( $y$ ).
- $[Fe_2(CO)_9]$ : $Fe$ is in $0$ state ( $z$ ).
- Sum ( $x+y+z$ ) = $2 + 4 + 0 = 6$ .

Oxalic Acid vs. $KMnO_4$ Titration:
- Temperature Requirement: The solution must be heated to approximately $60^\circ C$ ( $333 - 343\,K$ ) to initiate the reaction because it is slow at room temperature.
- Autocatalysis: Once Manganese(II) ions ( $Mn^{2+}$ ) are formed, they act as a catalyst, making the reaction proceed faster and faster.
- Equation: $2MnO_4^- + 5(COO)_2^{2-} + 16H^+ \rightarrow 10CO_2 + 2Mn^{2+} + 8H_2O$ .
Ferrous Ammonium Sulphate (FAS) vs. $KMnO_4$ Titration:
- No heating is required. Heating would cause the atmospheric oxidation of $Fe^{2+}$ to $Fe^{3+}$ , leading to titration errors.
Iodometry and Starch Indicator:
- Reaction: $I^- + H_2O_2 \rightarrow I_2 + H_2O$ .
- Indicator: Starch forms a deep blue complex with Iodine ( $A = I_2$ ).
Indicator Properties:
- Phenolphthalein: A weak acid ( $HPh$ ). It is colorless in acidic media and pink in basic media ( $pH$ dependent). It dissociates in base: $HPh \rightleftharpoons H^+ + Ph^-$ (Pink).
- Methyl Orange: Exists in a quinonoid form at the end point of base-versus-acid titrations.
- Redox Indicators: These are sensitive to changes in oxidation potential, whereas acid-base indicators are sensitive to changes in $pH$ .
Limitations of $KMnO_4$ Titration: Permanganate titrations are not performed in the presence of $HCl$ because $MnO_4^-$ oxidizes $Cl^-$ to chlorine gas ( $Cl_2$ ), interfering with the result.

Kjeldahl-like Nitrogen Estimation:
- Calculation: Mass percentage of Nitrogen = $\frac{\text{Millimoles of } NH_3}{\text{Sample Weight}} \times 14 \times 10^{-3} \times 100$ .
- Example: For a $0.166\,g$ sample with $7.5\,mmol$ of $NH_3$ , result is $\approx 63\%$ .
Neutralization Formula: $N_1V_1 = N_2V_2$ or $(M_1 \times V_1 \times n_1) = (M_2 \times V_2 \times n_2)$ .
Freezing Point Depression ( $\Delta T_f$ ):
- Equation: $\Delta T_f = i \times K_f \times m$ .
- For $KCl$ , $i = 2$ (assuming $100\%$ ionization). For a solution with molality $0.85\,mol/kg$ and $K_f = 2.0\,K\,kg/mol$ , $\Delta T_f = 2 \times 2 \times 0.85 = 3.4 \approx 3\,K$ .
Gas Stoichiometry ( $CO_2$ and $Ca(OH)_2$ ):
- Conditions: $STP = 273\,K, 1\,atm$ . Molar volume of gas = $22.4\,L = 22400\,cm^3$ .
Dilution Equation: $M_1V_1 = M_2V_2$ .
- To prepare $500\,mL$ of $0.1\,M$ $NaOH$ from a stock solution (made of $5\,g$ $NaOH$ in $450\,mL$ ), use $M_{stock} = \frac{5}{40} \times \frac{1000}{450}$ . Resulting volume required is $180\,mL$ .

Strongest Agents (Redox Potentials):
- Higher (more positive) reduction potential ( $E^\circ$ ) indicates a stronger oxidizing agent. Example: $S_2O_8^{2-}$ ( $E^\circ = 2.05\,V$ ) is a stronger oxidizer than $Au^{3+}$ ( $1.4\,V$ ) or $O_2$ ( $1.23\,V$ ).
- Higher oxidation potential indicates stronger reducing power. Order: $Ca > Mg > Zn > Ni$ .
Lanthanoid Agents:
- Strong oxidizing agent: $Ce^{4+}$ (tries to reach stable $+3$ state).
- Strong reducing agent: $Eu^{2+}$ (tries to reach stable $+3$ state).
Hydrogen Isotopes:
- Isotopes of hydrogen (Protium, Deuterium, Tritium) have different physical properties (boiling point, density) due to the large relative mass difference between them.
Cathodic Protection: Magnesium blocks are fixed to the bottom of ships to provide sacrificial protection (cathodic protection), preventing the corrosion of the steel hull by water and salt.
Superoxides and Peroxides: In Potassium oxides: $K_2O$ (oxide), $K_2O_2$ (peroxide), and $KO_2$ (superoxide), the oxidation state of Potassium is consistently $+1$ .