Question:
$\text{Select the correct option based on statements below:}$
$\text{Assertion (A): A liquid crystallizes into a solid and is accompanied by a decrease in entropy.}$
$\text{Reason (R): In crystals, molecules organize in an ordered manner.}$
Solution:
$\text{Hint: A liquid crystallises into a solid and is accompanied by a decrease in entropy.}$
$\text{Step 1: Analyze the assertion (A)}$
$\text{The assertion states that when a liquid crystallizes to form a solid, there is a decrease in entropy. This is a fundamental concept in thermodynamics. Entropy is a measure of the disorder or randomness in a system. In a liquid, molecules have considerable freedom of movement and are arranged randomly, resulting in higher entropy. When the liquid crystallizes to form a solid, the molecules become fixed in position in a regular pattern, restricting their movement and reducing the disorder. This leads to a decrease in entropy. Therefore, assertion (A) is true.}$
$\text{Step 2: Analyze the reason (R)}$
$\text{The reason states that in crystals, molecules organize in an ordered manner. This is also correct. In a crystalline solid, the molecules or atoms are arranged in a fixed, repeating three-dimensional pattern or lattice. This ordered arrangement is what defines a crystal and distinguishes it from amorphous solids where the arrangement is random. The molecules in a crystal have specific positions and orientations, creating a highly organized structure. Therefore, reason (R) is true.}$
$\text{Step 3: Determine if the reason (R) explains the assertion (A)}$
$\text{Now we need to determine if the ordered arrangement of molecules in crystals (R) explains why entropy decreases during crystallization (A).}$
$\text{The decrease in entropy during crystallization is directly due to the molecules becoming more ordered. When molecules transition from the relatively disordered arrangement in a liquid to the highly ordered arrangement in a crystal, there is a reduction in the number of possible microscopic states (positions and energies) available to the system. This reduction in possible states is what causes the decrease in entropy, as entropy is proportional to the logarithm of the number of possible microscopic states.}$
$\text{Therefore, the ordered arrangement of molecules in crystals (R) directly explains why entropy decreases during crystallization (A). The reason (R) provides the correct explanation for the assertion (A).}$
$\text{Step 4: Select the correct option}$
$\text{Since both the assertion (A) and the reason (R) are true, and the reason correctly explains the assertion, option 1 is the correct answer: Both (A) and (R) are True and (R) is the correct explanation of (A).}$