NEET 2020 Chemistry Question 127 Solution

In the forward reaction $$2\text{Cl (g)} \to \text{Cl}_2 \text{ (g)}$$, two isolated chlorine atoms form a stable covalent $$\text{Cl}-\text{Cl}$$ single bond. Because chemical bond formation stabilizes the system by lowering potential energy, heat is evolved into the surroundings (exothermic process): $$\Delta_r H < 0 \text{ (negative)}$$

Entropy ($$S$$) is a measure of molecular randomness or disorder. On the reactant side, there are two independent moles of freely moving gaseous chlorine atoms. On the product side, they are constrained into a single mole of diatomic molecules: $$\Delta n_g = 1 - 2 = -1 < 0$$ Because the number of independent gaseous particles decreases from 2 to 1, the randomness of the system decreases: $$\Delta_r S < 0 \text{ (negative)}$$

According to Gibbs-Helmholtz equation: $$\Delta_r G = \Delta_r H - T \Delta_r S$$ Since both $$\Delta H < 0$$ and $$\Delta S < 0$$, the reaction is spontaneous ($$\Delta G < 0$$) only at low temperatures where the negative $$\Delta H$$ term dominates over the positive $$-T\Delta S$$ term.

Both thermodynamic parameters are strictly less than zero: $$\Delta_r H < 0$$ and $$\Delta_r S < 0$$.