Chlorine dioxide (ClO2), which is produced by the reaction 2...

Chlorine dioxide $\left(\mathrm{ClO}_{2}\right)$, which is produced by the reaction $$ 2 \mathrm{NaClO}_{2}(a q)+\mathrm{Cl}_{2}(g) \longrightarrow 2 \mathrm{ClO}_{2}(g)+2 \mathrm{NaCl}(a q) $$ has been tested as a disinfectant for municipal water treatment. Using data from Table $17.1$, calculate $\mathscr{E}^{\circ}$ and $\Delta G^{\circ}$ at $25^{\circ} \mathrm{C}$ for the production of $\mathrm{ClO}_{2}$.

Chlorine dioxide $\left(\mathrm{ClO}_{2}\right)$, which is produced by the reaction
$$
2 \mathrm{NaClO}_{2}(a q)+\mathrm{Cl}_{2}(g) \longrightarrow 2 \mathrm{ClO}_{2}(g)+2 \mathrm{NaCl}(a q)
$$
has been tested as a disinfectant for municipal water treatment. Using data from Table $17.1$, calculate $\mathscr{E}^{\circ}$ and $\Delta G^{\circ}$ at $25^{\circ} \mathrm{C}$ for the production of $\mathrm{ClO}_{2}$.

Key Concepts

Relationship Between ?G° and Cell Potential

The change in Gibbs free energy (?G°) for a redox reaction is directly related to the cell potential by the equation ?G° = -nFE°. In this equation, n represents the number of moles of electrons transferred in the reaction, and F is Faraday's constant. This relationship is fundamental in connecting electrochemical measurements to the thermodynamic favorability and the energy output or input of the reaction.

Standard Reduction Potentials

Standard reduction potentials are numerical values that indicate the tendency of a chemical species to gain electrons under standard conditions. They provide a basis for predicting the direction of redox reactions. These potentials are measured relative to a standard hydrogen electrode, and comparing them allows one to identify which half-reaction will occur as oxidation and which as reduction in a galvanic cell.

Overall Cell Potential Calculation

The overall cell potential (E°cell) of an electrochemical reaction is determined by combining the standard reduction potentials of the two half-reactions. This is done by subtracting the standard potential of the oxidation half-reaction (when written as a reduction reaction) from that of the reduction half-reaction. A positive E°cell indicates that the reaction can proceed spontaneously under standard conditions.

Redox Reaction Stoichiometry

Redox reaction stoichiometry involves balancing chemical equations in terms of both mass and charge, reflecting the number of electrons transferred between the reactants. Determining the correct number of electrons exchanged in the reaction is crucial when applying the ?G° = -nFE° equation, as it ensures that the thermodynamic calculations accurately represent the reaction's electron flow.

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