Entropy is simply a measure of the amount of molecular disorder within a system. A system that has all its atoms arranged in some perfectly ordered manner has an entropy value of zero. This is the substance of the third law of thermodynamics. Entropy is a measure of the amount of molecular disorder within a system. Entropy can only be produced within a system.

The change in entropy is denoted by the formula,

$\Delta$$S = S_{f} - S_{i}$.

In thermodynamic definition, the expression for entropy is given below.

dS = $\frac{dq_{rev}}{T}$

$\Delta$$S_{o}$ = $\Delta$$S_{products}$ - $\Delta$$S_{reactant}$

$\Delta$$S_{V}$ = $\frac{\Delta H_{V}}{T_{b}}$.

Some of the solved problems based on entropy formula is given below:

Question 1: Ethanol boils at 78.4oC, the enthalpy of vaporization of ethanol is 42.4KJ mol-1. Calculate the entropy of vaporization of ethane.
Solution:
$\Delta$SV = $\frac{\Delta H_{V}}{T_{b}}$

Given $\Delta$HV = 42.4 $\times$ 103 J mol-1

Tb = 78.4o = 351.4 K

$\Delta$SV = $\frac{42.4 \times 10^{3}}{351.4}$ = 120.66 JK-1mol-1

Question 2: Calculate the standard entropy change associated with the following reaction at 298K.

P4(s) + 5O2(g) $\rightarrow$ P4O10(s)

At 298K for P4 = 41.1 JK-1mol-1, O2 = 205.0 JK-1 and P4O10 = 231.0 JK-1 mol-1
Solution:
$\Delta$So = $\Delta$Sproducts - $\Delta$Sreactant

$\Delta$So = [$\Delta$S P4O10 - ($\Delta$S P4 + 5$\Delta$S O2)]

= 231 - (41.1 + 5 $\times$ 205.0)

= 231 - 1066.1 = - 835.1 JK-1 mol-1