Solution:
$\text{Hint: Entropy decreases when liquid is converted into solid}$
$\text{Step 1: Understand what entropy is and when it increases or decreases}$
$\text{Entropy is a measure of the disorder or randomness in a system. Generally, entropy increases when:}$
$\text{• A solid changes to a liquid or a liquid changes to a gas (phase transitions toward more disorder)}$
$\text{• A reaction produces more gaseous molecules than it consumes}$
$\text{• Temperature increases}$
$\text{• Volume increases}$
$\text{Conversely, entropy decreases when:}$
$\text{• A gas changes to a liquid or a liquid changes to a solid (phase transitions toward more order)}$
$\text{• A reaction produces fewer gaseous molecules than it consumes}$
$\text{• Temperature decreases}$
$\text{• Volume decreases}$
$\text{Step 2: Analyze each option}$
$\text{Option 1: Crystallization of sucrose from solution}$
$\text{In this process, dissolved sucrose molecules in solution (where they have considerable freedom of movement) arrange themselves into a highly ordered crystalline solid structure. This transition from a disordered state (solution) to an ordered state (crystal) results in a significant decrease in entropy. The randomness decreases as the molecules become fixed in position in the crystal lattice.}$
$\text{Option 2: Rusting of iron}$
$\text{Rusting is an oxidation process where iron reacts with oxygen and water to form iron oxide (rust). The chemical reaction can be represented as:}$
$3\text{Fe(s)} + 4\text{H}_2\text{O(l)} \rightarrow \text{Fe}_3\text{O}_4\text{(s)} + 4\text{H}_2\text{(g)}$
$\text{In this reaction, solid iron and liquid water produce solid iron oxide and hydrogen gas. Because gaseous hydrogen is produced, there is an increase in disorder. Gas molecules have much more freedom of movement than solids or liquids. Therefore, entropy increases during rusting.}$
$\text{Option 3: Melting of ice}$
$\text{When ice melts, it transitions from a solid (where water molecules are arranged in a rigid, crystalline structure) to a liquid (where molecules can move more freely). This increase in molecular motion and disorder means that entropy increases during melting.}$
$\text{Option 4: Vaporization of camphor}$
$\text{During vaporization, solid camphor is converted directly into the vapor phase (sublimation). In the solid state, camphor molecules are relatively fixed in position, while in the vapor state, they have much greater freedom of movement and occupy a much larger volume. This substantial increase in disorder means that entropy increases significantly during vaporization.}$
$\text{Step 3: Identify the process where entropy decreases}$
$\text{Based on the analysis above, only crystallization of sucrose from solution (Option 1) involves a decrease in entropy, as it is a process where a disordered system (solution) becomes more ordered (crystal).}$
$\text{The correct answer is option 1: Crystallization of sucrose from solution.}$