Q.Match the following parameters with description for spontaneity. The parameters are ΔrH°, ΔrS° and ΔrG° (in that order).
Parameters

Concept: Entropy Change Prediction

Spontaneity is governed by the Gibbs equation $\Delta_r G° = \Delta_r H° - T\Delta_r S°$. A process is spontaneous when $\Delta_r G° < 0$, non-spontaneous when $\Delta_r G° > 0$, and at equilibrium when $\Delta_r G° = 0$.

(i) $\Delta_r H° = +$, $\Delta_r S° = -$, $\Delta_r G° = +$

Both terms in $\Delta_r G° = \Delta_r H° - T\Delta_r S°$ are positive (the enthalpy term is positive, and $-T\Delta_r S°$ is also positive because $\Delta_r S°$ is negative). At any temperature, $\Delta_r G°$ remains positive.

Match: (c) Non-spontaneous at all temperatures.

(ii) $\Delta_r H° = -$, $\Delta_r S° = -$, $\Delta_r G° = +$ at high $T$ …

The Gibbs free energy change $\Delta_r G°$ is the ultimate arbiter of spontaneity at constant temperature and pressure. A reaction proceeds spontaneously when $\Delta_r G° < 0$, is at equilibrium when $\Delta_r G° = 0$, and is non-spontaneous when $\Delta_r G° > 0$.

The relationship between enthalpy, entropy, and free energy is captured in the fundamental equation:

This tells us that spontaneity depends on the interplay between the enthalpy change (energy released or absorbed) and the entropy change (disorder created or destroyed), weighted by temperature. The temperature acts as a lever: at high $T$, the entropy term dominates; at low $T$, the enthalpy term dominates.

Let's analyze each parameter set systematically.

Analysis of each case

1. Case (i): $\Delta_r H° = +$, $\Delta_r S° = -$, $\Delta_r G° = +$

The reaction is endothermic (absorbs heat, positive $\Delta_r H°$) and decreases disorder (negative $\Delta_r S°$). Substituting into the Gibbs equation:

Both terms are positive. The enthalpy term is positive, and subtracting a negative entropy contribution (which means adding a positive term) makes $\Delta_r G°$ even more positive. At any temperature, $\Delta_r G° > 0$.

This reaction is non-spontaneous at all temperatures. It fights both thermodynamic driving forces: it requires energy input and decreases disorder.

Match: (i) → (c)

2. Case (ii): $\Delta_r H° = -$, $\Delta_r S° = -$, $\Delta_r G° = +$ at high $T$

The reaction is exothermic (releases heat, negative $\Delta_r H°$) but decreases disorder (negative $\Delta_r S°$). The Gibbs equation becomes:

At low temperatures, the enthalpy term (negative, favorable) dominates, so $\Delta_r G° < 0$ and the reaction is spontaneous. As temperature increases, the positive term $T|\Delta_r S°|$ grows larger. Eventually, at high enough temperature, this positive contribution overwhelms the negative enthalpy term, making $\Delta_r G° > 0$.

The problem states that $\Delta_r G° = +$ at high $T$, confirming the reaction becomes non-spontaneous at high temperature.

Match: (ii) → (a)

3. Case (iii): $\Delta_r H° = -$, $\Delta_r S° = +$, $\Delta_r G° = -$ …