Which Of The Following Reactions Will Occur Spontaneously As Written

Determining Spontaneous Reactions: A Gibbs Free Energy Guide

Understanding which chemical reactions occur spontaneously is fundamental to predicting the direction of natural processes, from the rusting of iron to the complex biochemistry within our cells. It does not imply the reaction happens quickly—kinetics governs speed—but rather that it is thermodynamically favorable. The definitive tool for this prediction is the Gibbs free energy change (ΔG), a thermodynamic potential that combines a system's enthalpy (heat) and entropy (disorder) changes. Because of that, a spontaneous reaction is one that proceeds without requiring continuous external energy input under a given set of conditions. The rule is absolute: if ΔG < 0, the reaction is spontaneous as written; if ΔG > 0, it is non-spontaneous; and if ΔG = 0, the system is at equilibrium. This principle allows us to evaluate any reaction by calculating or interpreting its ΔG Surprisingly effective..

The Gibbs Free Energy Equation: The Heart of Spontaneity

The relationship is defined by the equation: ΔG = ΔH – TΔS

Where:

• ΔG is the change in Gibbs free energy (in kJ/mol). And a negative ΔH (exothermic) generally favors spontaneity. * T is the absolute temperature in Kelvin (K). In practice, * ΔS is the change in entropy. * ΔH is the change in enthalpy (heat content). A positive ΔS (increase in disorder) generally favors spontaneity.

This equation reveals the delicate balance. On top of that, a reaction can be driven by a large negative ΔH (exothermic), a large positive ΔS (increased disorder), or a combination of both. Crucially, temperature (T) acts as a weighting factor for the entropy term. This means the spontaneity of some reactions can reverse with a change in temperature. Take this: a reaction with a positive ΔH and a positive ΔS might be non-spontaneous at low temperatures but become spontaneous at high temperatures because the TΔS term eventually outweighs the unfavorable ΔH.

Evaluating Common Reaction Scenarios

To make this concrete, let's analyze several representative reactions. For each, we will consider the signs of ΔH and ΔS and predict spontaneity at standard conditions (298 K, 1 atm) and discuss temperature dependence.

1. The Classic Exothermic, Entropy-Increasing Reaction

Reaction: 2H₂(g) + O₂(g) → 2H₂O(l)

• ΔH: Highly negative (~-572 kJ). Forming strong O-H bonds from H-H and O=O bonds releases immense energy.
• ΔS: Negative. We go from 3 moles of gaseous reactants (high disorder) to 2 moles of liquid product (low disorder). Gases are vastly more disordered than liquids.
• Analysis: The large, negative ΔH strongly favors spontaneity. The negative ΔS opposes it. At room temperature, the exothermic term (ΔH) dominates the -TΔS term (which becomes positive because ΔS is negative, making -TΔS positive). So, ΔG is negative, and the reaction is spontaneous. This is the thermite-like combustion of hydrogen, which occurs explosively once initiated. While increasing temperature makes the -TΔS term more positive (less favorable), the massive negative ΔH means this reaction remains spontaneous at all reasonable temperatures.

2. The Endothermic, Entropy-Increasing Reaction

Reaction: 2HgO(s) → 2Hg(l) + O₂(g) (Decomposition of mercury(II) oxide)

• ΔH: Positive (endothermic). Breaking the solid lattice requires energy.
• ΔS: Highly positive. We go from 2 moles of solid to 2 moles of liquid and 1 mole of gas. The creation of a gas molecule causes a massive increase in disorder.
• Analysis: The positive ΔH opposes spontaneity, while the large positive ΔS strongly favors it. The key is the temperature. At low temperatures, the TΔS term is small, so ΔG ≈ ΔH (positive), and the reaction is non-spontaneous. As temperature increases, the TΔS term grows and eventually becomes larger than the positive ΔH. At the temperature where ΔH = TΔS, ΔG = 0. Above this temperature, ΔG becomes negative. This reaction is non-spontaneous at room temperature but becomes spontaneous at sufficiently high temperatures. This is why heating is required to decompose many stable solid compounds.

3. The Exothermic, Entropy-Decreasing Reaction

Reaction: N₂(g) + 3H₂(g) → 2NH₃(g) (Haber Process, at standard conditions)

• ΔH: Negative (exothermic). Forming the strong N-H bond releases heat.
• ΔS: Negative. We go from 4 moles of gas to 2 moles of gas. A decrease in the number of gas molecules means a decrease in disorder.
• Analysis: The negative ΔH favors spontaneity, but the negative ΔS opposes it (making -TΔS positive). At room temperature, the exothermic ΔH is large enough to overcome the unfavorable entropy term, so ΔG is negative, and the reaction is spontaneous. Still, because ΔS is negative, increasing temperature makes the -TΔS term more positive, working against the negative ΔH. There is a temperature where the two terms balance (ΔG=0). Above that temperature, the reaction becomes non-spontaneous. This is why the industrial Haber process uses a compromise temperature (around 450°C)—high enough for a reasonable rate (kinetics) but low enough to keep ΔG negative (thermodynamics).

4. The Endothermic, Entropy-Decreasing Reaction