In which of the following processes entropy increases?

A. A liquid evaporates to vapour.

B. Temperature of a crystalline solid lowered from 130 K to 0 K.

C. 2NaHCO_3(s) → Na2CO_3(s) + CO_2(g) + H₂O_(g)

D. Cl_2(g) → 2Cl_(g)

Choose the correct answer from the options given below:

To determine in which of the given processes entropy increases, let us first understand what entropy ($S$) represents. Entropy is a thermodynamic measure of the molecular randomness, disorder, or the number of microstates available to a system. A process results in an increase in entropy ($\Delta S>0$) if the product state is more disordered or has more freedom of motion than the initial state.

Let us analyze each statement individually:

A. A liquid evaporates to vapour:
In a liquid state, molecules are relatively close to each other with restricted movement. When a liquid evaporates to form a vapour (gas), the molecules gain significant freedom of movement and occupy a much larger volume. Since the gaseous state is highly disordered compared to the liquid state, this process leads to an increase in entropy. Thus, entropy increases in process A.

B. Temperature of a crystalline solid lowered from 130 K to 0 K:
Lowering the temperature of a substance decreases the thermal motion of its constituent particles. As the temperature of a crystalline solid is lowered towards absolute zero (0 K), the molecules or atoms settle into their lowest energy states and become highly ordered. According to the Third Law of Thermodynamics, the entropy of a perfectly crystalline solid approaches zero as the temperature approaches 0 K. Thus, cooling the solid decreases its entropy. Therefore, entropy does not increase in process B.

C. $2{\mathrm{NaHCO}}_{3_{\left(s\right)}}\to {\mathrm{Na}}_2{\mathrm{CO}}_{3_{\left(s\right)}}+{\mathrm{CO}}_{2_{\left(g\right)}}+H_2{O}_{\left(g\right)}$:
Here, we start with 2 moles of a solid reactant and produce 1 mole of a solid product along with 2 moles of gaseous products (${\mathrm{CO}}_2$ and $H_{2}O$). Gaseous molecules have much higher entropy than solid reactants. Since there is a net generation of gas phase molecules from solid reactants, the disorder of the system increases significantly. Thus, entropy increases in process C.

D. ${\mathrm{Cl}}_{2_{\left(g\right)}}\to 2{\mathrm{Cl}}_{\left(g\right)}$:
In this chemical reaction, 1 mole of diatomic chlorine gas molecules dissociates to produce 2 moles of individual, monoatomic chlorine gas atoms. An increase in the number of gaseous particles increases the number of microstates and the degree of freedom, thereby increasing the randomness of the system. Thus, entropy increases in process D.

Therefore, the processes in which entropy increases are A, C, and D.