Which of the following reactions (equations unbalanced)...

Which of the following reactions (equations unbalanced) would be expected to be spontaneous at $25^{\circ} \mathrm{C}$ and $1 \mathrm{~atm}$ ? (a) $\mathrm{PbO}(s)+\mathrm{NH}_{3}(g) \longrightarrow \mathrm{Pb}(s)+\mathrm{N}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(g)$ (b) $\mathrm{NaOH}(s)+\mathrm{HCl}(g) \longrightarrow \mathrm{NaCl}(s)+\mathrm{H}_{2} \mathrm{O}(l)$ (c) $\mathrm{Al}_{2} \mathrm{O}_{3}(s)+\mathrm{Fe}(s) \longrightarrow \mathrm{Fe}_{2} \mathrm{O}_{3}(s)+\mathrm{Al}(s)$ (d) $2 \mathrm{CH}_{4}(g) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{6}(g)+\mathrm{H}_{2}(g)$

Which of the following reactions (equations unbalanced) would be expected to be spontaneous at $25^{\circ} \mathrm{C}$ and $1 \mathrm{~atm}$ ?
(a) $\mathrm{PbO}(s)+\mathrm{NH}_{3}(g) \longrightarrow \mathrm{Pb}(s)+\mathrm{N}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(g)$
(b) $\mathrm{NaOH}(s)+\mathrm{HCl}(g) \longrightarrow \mathrm{NaCl}(s)+\mathrm{H}_{2} \mathrm{O}(l)$
(c) $\mathrm{Al}_{2} \mathrm{O}_{3}(s)+\mathrm{Fe}(s) \longrightarrow \mathrm{Fe}_{2} \mathrm{O}_{3}(s)+\mathrm{Al}(s)$
(d) $2 \mathrm{CH}_{4}(g) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{6}(g)+\mathrm{H}_{2}(g)$

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Key Concepts

Standard State Conditions

Standard state conditions, typically 25°C and 1 atm pressure, provide a common reference that allows the comparison of different reactions’ spontaneity through standard thermodynamic data. These conditions ensure that the calculated free energy changes are consistent and comparable when determining if a reaction is spontaneous under normal laboratory conditions.

Gibbs Free Energy

Gibbs free energy (?G) is the primary thermodynamic quantity used to determine whether a reaction is spontaneous under constant temperature and pressure. A reaction where ?G is negative is considered thermodynamically favorable and will proceed without external input, making this concept central in evaluating reaction spontaneity.

Enthalpy and Entropy

Enthalpy (?H) and entropy (?S) are key thermodynamic parameters that influence the sign and magnitude of the Gibbs free energy change, as defined by the equation ?G = ?H - T?S. A reaction can be spontaneous if it releases heat (negative ?H) and/or leads to an increase in disorder (positive ?S), with temperature playing a crucial role in balancing these factors.

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