Balance each of the following unbalanced equations; then...

Balance each of the following unbalanced equations; then calculate the standard potential, $E^{\circ}$ and decide whether each is product-favored at equilibrium as written. (All reactions are carried out in acid solution. (a) $\mathrm{I}_{2}(\mathrm{s})+\mathrm{Br}^{-}(\mathrm{aq}) \rightarrow \mathrm{I}^{-}(\mathrm{aq})+\mathrm{Br}_{2}(\ell)$ (b) $\mathrm{Fe}^{2+}(\mathrm{aq})+\mathrm{Cu}^{2+}(\mathrm{aq}) \rightarrow \mathrm{Cu}(\mathrm{s})+\mathrm{Fe}^{3+}(\mathrm{aq})$ (c) $\mathrm{Fe}^{2+}(\mathrm{aq})+\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}(\mathrm{aq}) \rightarrow$ $\mathrm{Fe}^{3+}(\mathrm{aq})+\mathrm{Cr}^{3+}(\mathrm{aq})$ (d) $\mathrm{MnO}_{4}-(\mathrm{aq})+\mathrm{HNO}_{2}(\mathrm{aq}) \rightarrow$ $\mathrm{Mn}^{2+}(\mathrm{aq})+\mathrm{NO}_{3}^{-}(\mathrm{aq})$

Balance each of the following unbalanced equations; then calculate the standard potential, $E^{\circ}$ and decide whether each is product-favored at equilibrium as written. (All reactions are carried out in acid solution.
(a) $\mathrm{I}_{2}(\mathrm{s})+\mathrm{Br}^{-}(\mathrm{aq}) \rightarrow \mathrm{I}^{-}(\mathrm{aq})+\mathrm{Br}_{2}(\ell)$
(b) $\mathrm{Fe}^{2+}(\mathrm{aq})+\mathrm{Cu}^{2+}(\mathrm{aq}) \rightarrow \mathrm{Cu}(\mathrm{s})+\mathrm{Fe}^{3+}(\mathrm{aq})$
(c) $\mathrm{Fe}^{2+}(\mathrm{aq})+\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}(\mathrm{aq}) \rightarrow$
$\mathrm{Fe}^{3+}(\mathrm{aq})+\mathrm{Cr}^{3+}(\mathrm{aq})$
(d) $\mathrm{MnO}_{4}-(\mathrm{aq})+\mathrm{HNO}_{2}(\mathrm{aq}) \rightarrow$
$\mathrm{Mn}^{2+}(\mathrm{aq})+\mathrm{NO}_{3}^{-}(\mathrm{aq})$

Key Concepts

Redox Reactions

Redox reactions, or oxidation-reduction reactions, involve the transfer of electrons between chemical species. One species undergoes oxidation (loss of electrons) while another undergoes reduction (gain of electrons). Understanding the electron transfer mechanisms in these reactions is fundamental to predicting the behavior and outcome of redox processes in various chemical environments.

Half-Reaction Method

The half-reaction method is a systematic approach to balance redox equations by separately balancing the oxidation and reduction reactions. In each half-reaction, atoms and charge are balanced by adding water, hydrogen ions, and electrons. Once both half-reactions are balanced, they are combined to give the overall balanced redox equation. This method is particularly useful in acidic or basic solutions where additional species such as H+ or OH– play a role in maintaining charge balance.

Standard Reduction Potential

Standard reduction potentials are measures of the tendency of a chemical species to acquire electrons and be reduced under standard conditions. These values, typically given in volts, help predict the direction of electron flow in an electrochemical cell. A higher reduction potential indicates a greater likelihood of reduction, which is crucial in determining the spontaneity of a redox reaction.

Electrochemical Cell and Standard Potential Calculation

In an electrochemical cell, the overall standard cell potential is obtained by combining the standard reduction potentials of the half-reactions. This involves reversing the oxidation reaction (which inverts the sign of its potential) before adding it to the reduction potential of the reduction half-reaction. The resulting standard potential is used to assess whether the reaction is spontaneous under standard conditions.

Reaction Spontaneity and Equilibrium

The spontaneity of a redox reaction at standard conditions is determined by the sign and magnitude of the overall cell potential (E°). A positive cell potential indicates that the reaction is product-favored and proceeds spontaneously as written. Conversely, a negative cell potential suggests that the forward reaction is non-spontaneous under standard conditions. This concept links electrochemistry with chemical equilibrium, bridging thermodynamics and reaction kinetics.

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