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

step 1 Okay, so for this question, we're trying to calculate delta G, which is free energy, and we want

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

Calculate the free energy change for this reaction at $25^{\circ} \mathrm{C}$ . Is the reaction spontaneous? (Assume that all reactants and products are in their standard states.) $$\begin{array}{c}{\mathrm{C}_{3} \mathrm{H}_{8}(g)+5 \mathrm{O}_{2}(g) \longrightarrow 3 \mathrm{CO}_{2}(g)+4 \mathrm{H}_{2} \mathrm{O}(g)} \\ {\Delta H_{\mathrm{rxn}}^{\circ}=-2217 \mathrm{kJ} ; \Delta S_{\mathrm{rxn}}^{\circ}=101.1 \mathrm{J} / \mathrm{K}}\end{array}$$

Calculate the free energy change for this reaction at $25^{\circ} \mathrm{C}$ . Is the
reaction spontaneous? (Assume that all reactants and products
are in their standard states.)
$$\begin{array}{c}{\mathrm{C}_{3} \mathrm{H}_{8}(g)+5 \mathrm{O}_{2}(g) \longrightarrow 3 \mathrm{CO}_{2}(g)+4 \mathrm{H}_{2} \mathrm{O}(g)} \\ {\Delta H_{\mathrm{rxn}}^{\circ}=-2217 \mathrm{kJ} ; \Delta S_{\mathrm{rxn}}^{\circ}=101.1 \mathrm{J} / \mathrm{K}}\end{array}$$

Key Concepts

Gibbs Free Energy

Gibbs free energy is a thermodynamic state function defined by the equation ?G = ?H - T?S, which combines enthalpy and entropy effects to predict the overall spontaneity of a reaction. A negative ?G indicates that a reaction is spontaneous under constant temperature and pressure, while a positive ?G suggests non-spontaneity.

Enthalpy Change

Enthalpy change, represented by ?H, is a measure of the total heat exchange during a reaction at constant pressure. It indicates whether a reaction releases energy (exothermic) or absorbs energy (endothermic), and it plays a crucial role in determining the free energy change when analyzed in conjunction with entropy change.

Entropy Change

Entropy change, symbolized by ?S, quantifies the change in disorder or randomness in a system during a reaction. An increase in entropy (positive ?S) generally favors spontaneity by reducing the free energy, especially when the temperature is sufficiently high to amplify this effect.

Standard States

Standard states refer to a set of reference conditions (typically 1 bar pressure for gases and 1 M concentration for solutions) under which thermodynamic properties are tabulated. When reactions are stated to have reactants and products in their standard states, the corresponding thermodynamic values, such as ?H and ?S, are considered to be standard values.

Spontaneity

Spontaneity in thermodynamics is determined by the sign of the Gibbs free energy change. A spontaneous reaction has a negative ?G, meaning it proceeds without the need for additional energy input under the given conditions. The balance of enthalpy and entropy contributions, particularly as expressed in ?G = ?H - T?S, is fundamental to assessing whether a reaction is spontaneous.

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