Q20.5P - Chemistry: Molecular Nature Of Matter And Change

Question

Why is $∆{\text{S}}_{\text{vap}}$of a substance always larger than $∆{\text{S}}_{\text{fus}}$.

Step-by-Step Solution

Answer

The energy gain from heat and the volume expansion, which is characteristic of entropy rise, characterise vaporisation. Fusion, on the other hand, entails volume contraction: when the substance solidifies, the entire volume shrinks.

As a result, the vaporisation entropy exceeds the fusion entropy

Step 1: Concept Introduction

The mechanism through which the state of a liquid converts into the condition of a vapour is known as vaporisation. As the temperature rises, the kinetic energy of the molecules rises as well.

When two light atoms combine to form a heavier one, this is called fusion. The new atom's total mass is less than the two that generated it; the "missing" mass is released as energy.

Step 2: Equations for vaporization and fusion

Upon vaporization, the substance changes its physical state from liquid to gas, for example water –

${\text{H}}_{\text{2}}\text{O(l)}\to {\text{H}}_{\text{2}}\text{O(g)}$

The entropy of vaporization can be represented as –

$∆{\text{S}}_{\text{vaporization}}{\text{ = S}}_{\text{gas}}{\text{ - S}}_{\text{liquid}}$

Similarly, upon fusion the substance changes its physical state from liquid to solid, for example water –

${\text{H}}_{\text{2}}\text{O(l)}\to {\text{H}}_{\text{2}}\text{O(s)}$

The entropy of fusion can be represented as –

$∆{\text{S}}_{\text{fusion}}\text{ = } {\text{S}}_{\text{liquid}}{\text{ - S}}_{\text{solid}}$

Step 3: Entropy of vaporization is greater than fusion

The difference in entropy is –

$\begin{array}{rcl}∆\mathrm{S}& =& ∆{\mathrm{S}}_{\mathrm{vaporization}}-∆{\mathrm{S}}_{\mathrm{fusion}}\\ & =& {\text{(S}}_{\text{gas}}{\text{ - S}}_{\text{liquid}}{\text{) - (S}}_{\text{liquid}}{\text{ - S}}_{\text{solid}}\text{)}\\ & =& {\text{S}}_{\text{gas}}{\text{ + S}}_{\text{solid}}\end{array}$

The vaporization is characterized by the energy gain from heat and the volume expansion, characteristic to entropy increase. Whereas fusion involves volume contraction - as the substance is solidified, so the total volume is reduced.

 

Therefore, the vaporization entropy is larger than the fusion entropy.