- Sodium carbonate, also called "washing soda," can be made...

- Sodium carbonate, also called "washing soda," can be made by heating sodium hydrogen carbonate: $$ \begin{gathered} 2 \mathrm{NaHCO}_3(s) \longrightarrow \mathrm{Na}_2 \mathrm{CO}_3(\mathrm{~s})+\mathrm{CO}_2(\mathrm{~g})+\mathrm{H}_2 \mathrm{O}(l) \\ \Delta H^{\circ}=+135.6 \mathrm{kj} \Delta G^{\circ}=+34.6 \mathrm{~kJ} \text { at } 25^{\circ} \mathrm{C} \end{gathered} $$ (a) Calculate $\Delta S^{\circ}$ for this reaction. Is the sign reasonable? (b) Calculate $\Delta G^{\circ}$ at 0 K ; at 1000 K .

- Sodium carbonate, also called "washing soda," can be made by heating sodium hydrogen carbonate:

$$
\begin{gathered}
2 \mathrm{NaHCO}_3(s) \longrightarrow \mathrm{Na}_2 \mathrm{CO}_3(\mathrm{~s})+\mathrm{CO}_2(\mathrm{~g})+\mathrm{H}_2 \mathrm{O}(l) \\
\Delta H^{\circ}=+135.6 \mathrm{kj} \Delta G^{\circ}=+34.6 \mathrm{~kJ} \text { at } 25^{\circ} \mathrm{C}
\end{gathered}
$$

(a) Calculate $\Delta S^{\circ}$ for this reaction. Is the sign reasonable?
(b) Calculate $\Delta G^{\circ}$ at 0 K ; at 1000 K .

Key Concepts

Gibbs Free Energy Temperature Dependence

Gibbs free energy is temperature-dependent, as shown by the equation ?G = ?H - T?S. This dependence means that the thermodynamic favorability (spontaneity) of a reaction can change with temperature, serving as a key consideration in reaction and process design across different thermal conditions.

Reaction Spontaneity

The sign of Gibbs free energy (?G°) indicates whether a reaction is spontaneous under given conditions. A negative ?G° denotes a spontaneous process, while a positive value implies non-spontaneity. Evaluating ?G° at various temperatures helps predict whether a reaction will proceed as written under those conditions.

Entropy Change Calculation

Entropy, a measure of system disorder, can be derived from the relationship ?G° = ?H° - T?S°. Rearranging the equation allows computation of ?S° when ?G° and ?H° are known. This calculation is crucial when reactions involve phase changes or the production of gases, which generally increase entropy.

Standard-State Thermodynamic Quantities

This concept encompasses the definitions and roles of ?H° (enthalpy change), ?G° (Gibbs free energy change), and ?S° (entropy change) under standard conditions. These quantities are fundamental in understanding reaction energetics, indicating whether a reaction absorbs or releases heat, creates or reduces disorder, and is spontaneous.

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