## Thursday, April 25, 2013

### The entropy increases when things fall apart

The translational entropy dominates when bonds are broken
An entropy change has four contributions$$\Delta S^\circ=\Delta S^{Molecular}+\Delta S^{\circ,Translation}+\Delta S^{Rotation}+\Delta S^{Vibration}$$For reactions where bonds are broken $S^{\circ,Translation}$ usually dominates.

For example for the reaction $H_2 \rightarrow 2H$ the entropy changes at 25 $^\circ$C are:$$\Delta S^\circ = 11.6+100.1-12.8-0.0=98.9 \text{ J/molK}$$For breaking the hydrogen bond between two water molecules, $H_2O\cdot \cdot \cdot HOH\rightarrow 2H_2O$, the free energy energy contributions are$$\Delta S^\circ =0.0+136.2+9.3-66.0=79.4 \text{ J/molK}$$In both cases $\Delta S^\circ$ is positive because two particles have more entropy than one.

In many cases $\Delta S^\circ \approx \Delta S^{\circ,Translation}$ is a reasonable approximation.

Test: What happens to the standard entropy for this process