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Entropy Formula

"Entropy is the measure of randomness or disorderness of the system". The absolute value of entropy cannot be determined as it depends on the initial and final state of the system. To determine the change in entropy the change between initial and final state is considered.

In the case of an irreversible process, the change in entropy between two equilibrium states is calculated by finding a reversible path between the two states and calculating the entropy change for that path. When the products of a reaction are less complex and more disordered than the reactants, the reaction is said to proceed with a gain in entropy.

In all natural processes, the entropy of the universe increases. Living organisms consist of collections of molecules much more highly organized than the surrounding materials from which they are constructed, and organisms maintain and produce order, seemingly oblivious to the second law of thermodynamics.

Change in Entropy Formula is given by

The thermodynamic definition of entropy is based on the change in entropy (dS) that occurs during physical or chemical changes, which is expressed as

For a measurable change between the initial and final state, this expression integrated to

The units of entropy is calories per degree or cal deg-1. The molar entropy is expressed in joules per kelvin per mole (JK-1mol-1)

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Entropy Problems

Solved problems based on entropy are given below.

Solved Examples

Question 1: Calculate $\Delta$S for the synthesis of ammonia at 25oC.

N2 + 3H2 $\rightarrow$ 2NH3   $\Delta$H = -92.6kJmol-1
Solution:

Here we use the formula

$\Delta$S = 2(NH3) - [S(N2) + 3S(H2)]

$\Delta$S = (2)(192.5 JK-1mol-1) - [191.6JK-1mol-1 + (3)(130.6 JK-1mol-1)]

$\Delta$S = -198.4 JK-1mol-1

Question 2: Calculate the entropy change per mole when ice melts at 0oC. Remember that the enthalpy change equals the heat added to the system at constant pressure.

Solution:

The equation is

H2O(s) $\rightarrow$ H2O(l)

$\Delta$H (fusion) = +6.01KJmol-1

So we use the equation

$\Delta$S = $\frac{6010Jmol-1}{273K}$

= +22.0JK-1mol-1

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