When permanganate ions in aqueous solution react with cobalt...

When permanganate ions in aqueous solution react with cobalt metal in strong acid, the equation for the reaction that takes place is $2 \mathrm{MnO}_{4}^{-}(a q)+16 \mathrm{H}^{+}(a q)+5 \mathrm{Co}(s) \longrightarrow$ (a) Calculate $\Delta S^{\circ}$ for the reaction at $25^{\circ} \mathrm{C}$. (b) Calculate $S^{\circ}$ for $\mathrm{Co}^{2+}$, given $S^{\circ}$ for $\mathrm{Co}$ is $30.04 \mathrm{~J} / \mathrm{mol} \cdot \mathrm{K}$.

When permanganate ions in aqueous solution react with cobalt metal in strong acid, the equation for the reaction that takes place is
$2 \mathrm{MnO}_{4}^{-}(a q)+16 \mathrm{H}^{+}(a q)+5 \mathrm{Co}(s) \longrightarrow$
(a) Calculate $\Delta S^{\circ}$ for the reaction at $25^{\circ} \mathrm{C}$.
(b) Calculate $S^{\circ}$ for $\mathrm{Co}^{2+}$, given $S^{\circ}$ for $\mathrm{Co}$ is $30.04 \mathrm{~J} / \mathrm{mol} \cdot \mathrm{K}$.

Key Concepts

Standard Molar Entropy

Standard molar entropy is an intensive property that quantifies the absolute entropy per mole of a substance under standard conditions (usually 25 °C, 1 atm, and 1 M concentration for solutions). It is used as a baseline measure to compare the degree of disorder or randomness present in substances and is essential for calculating the overall change in entropy when a chemical reaction occurs.

Reaction Entropy Change Calculation

The entropy change for a reaction (?S°) is determined by taking the sum of the standard molar entropies of the products, each multiplied by their stoichiometric coefficients, and subtracting the corresponding sum for the reactants. This provides insight into whether the overall reaction leads to an increase or decrease in disorder, which is a key factor in predicting reaction spontaneity and understanding the thermodynamic behavior of the system.

Thermodynamic Standard Conditions

Thermodynamic standard conditions refer to a set of agreed-upon conditions (typically 25 °C, 1 atm pressure, and 1 M concentration for solutions) under which standard thermodynamic data such as Gibbs free energy, enthalpy, and entropy are reported. These conditions provide a common framework that enables consistent evaluation and comparison of thermodynamic properties across different reactions and substances.

Standard Entropy of Aqueous Ions

The standard molar entropy values for aqueous ions are critical in thermodynamic calculations involving reactions in solution. These values consider the solvation effects and the distribution of energy levels of ions in a solvent. Accurate determination or calculation of an ion’s standard entropy, such as that for a metal ion produced in a redox reaction, is essential for understanding the overall entropy change and for making predictions about reaction spontaneity.

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