Question

For the reaction

$\mathbf{2}\mathit{O}\left(\mathit{g}\right)\mathbf{\to }{\mathit{O}}_{\mathbf{2}}\left(\mathit{g}\right)$

a. predict the signs of $\mathbf{∆}\mathbf{H}\mathbf{}\mathbf{and}\mathbf{}\mathbf{∆}\mathbf{S}$.

b. would the reaction be more spontaneous at high or low temperatures?

Short answer

1. The signs are predicted as $∆\mathrm{H}$is negative and$\mathbf{∆}\mathbf{S}$is negative.
2. The reaction be more spontaneous at low temperatures

Step-by-step solution

Step 1: Introduction to the Concept

Entropy (S) is a metric for a system's degree of disorder or unpredictability. Entropy increases as a substance transitions from solid to liquid to gaseous. The entropy change $\mathbf{∆}\mathbf{S}$ is positive for a reaction that proceeds with an increase in the number of moles of gaseous products and vice versa.

Enthalpy (H) is a measure of a system's heat content. The enthalpy change $\mathbf{∆}\mathbf{H}$ is negative for exothermic events in which heat is released but positive for endothermic reactions in which energy is absorbed.

Step 2: Determination of sign of  ∆H and  ∆S

From the given reaction,

$2O\left(g\right)\to O_2\left(g\right)$

In this reaction, 2O atoms come together to produce a O₂ molecule, forming new bonds. $\mathbf{∆}\mathbf{H}$is negative because bond creation is an exothermic process.

$\mathbf{∆}\mathbf{S}$is negative because the number of moles of gaseous constituents decreases as the reaction progresses(i.e., 2 moles of reactants and 1 mole of gaseous product).

Step 3: Determination of more spontaneous given reactions

b)

For the reaction in question:

$\mathbf{∆}\mathbf{H}$and$\mathbf{∆}\mathbf{S}$are negative numbers.

According to Gibbs free energy equation,

$\mathit{\Delta }\mathit{G}\mathbf{=}\mathit{\Delta }\mathit{H}\mathbf{-}\mathit{T}\mathit{\Delta }\mathit{S}$

$\mathbf{∆}\mathbf{G}$must be negative for a reaction to be spontaneous. This is conceivable when the temperature is low, and the reaction is dominated by$\mathbf{∆}\mathbf{H}$, depending on the signs of $\mathbf{∆}\mathbf{H}$and$\mathbf{∆}\mathbf{S}$.