Calculate the free energy change for this reaction at 25^∘ C. Is the reaction spontaneous? C3 H

step 1 In this question, we've been given a reaction in which C3H8 reacts with 5 moles of O2 to produce

Calculate the free energy change for this reaction at 25^∘...

Calculate the free energy change for this reaction at $25^{\circ} \mathrm{C}$. Is the reaction spontaneous? $$ \begin{gathered} \mathrm{C}_{3} \mathrm{H}_{8}(g)+5 \mathrm{O}_{2}(g) \longrightarrow 3 \mathrm{CO}_{2}(g)+4 \mathrm{H}_{2} \mathrm{O}(g) \\ \Delta H_{\mathrm{rxn}}^{\circ}=-2217 \mathrm{~kJ} ; \Delta S_{\mathrm{rxn}}^{\circ}=101.1 \mathrm{~J} / \mathrm{K} \end{gathered} $$

Calculate the free energy change for this reaction at $25^{\circ} \mathrm{C}$. Is the reaction spontaneous?
$$
\begin{gathered}
\mathrm{C}_{3} \mathrm{H}_{8}(g)+5 \mathrm{O}_{2}(g) \longrightarrow 3 \mathrm{CO}_{2}(g)+4 \mathrm{H}_{2} \mathrm{O}(g) \\
\Delta H_{\mathrm{rxn}}^{\circ}=-2217 \mathrm{~kJ} ; \Delta S_{\mathrm{rxn}}^{\circ}=101.1 \mathrm{~J} / \mathrm{K}
\end{gathered}
$$

Key Concepts

Gibbs Free Energy

Gibbs free energy is a thermodynamic potential that combines enthalpy and entropy to predict whether a process will occur spontaneously at a constant temperature and pressure. The change in Gibbs free energy (?G) is calculated using the equation ?G = ?H - T?S, and the sign of ?G indicates whether the reaction is spontaneous (negative ?G), non-spontaneous (positive ?G), or at equilibrium (?G = 0).

Enthalpy Change (?H)

Enthalpy change represents the heat absorbed or released during a reaction at constant pressure. A negative ?H indicates an exothermic reaction, meaning that heat is released, which can favor the spontaneity of the reaction.

Entropy Change (?S)

Entropy change quantifies the change in disorder or randomness of a system during a reaction. An increase in entropy (positive ?S) tends to favor the spontaneity of a reaction, especially at higher temperatures, because it contributes to a decrease in Gibbs free energy.

Temperature's Role in Free Energy

Temperature is a critical factor in determining the spontaneity of a reaction because it affects the T?S term in the Gibbs free energy equation. Even if a reaction is exothermic (negative ?H), the temperature can influence whether the entropy change is sufficiently large to make ?G negative, thereby favoring spontaneity.

Reaction Spontaneity

Spontaneity is determined by the sign of the Gibbs free energy change. A negative ?G indicates that a reaction is spontaneous under the given conditions, while a positive ?G indicates non-spontaneity. Analyzing ?G helps predict the direction in which a chemical reaction will proceed naturally.

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