Entropy

[FREAK]

This is a simple question about entropy (which is very important concept in understanding life)
I have learned that when molecules split and mole number increases the entropy of the system also increases. It is explained by saying that - when a molecule is splited to smaller molecules it decreases order in the system (they used the example of gas enclosed in a cylinder and their random motion). I don't know what is the measure of disorder, it seems a bit abstract to me. Though I understand that molecules are like packets of atoms; the larger the molecule the greater the orderliness. But it doesn't seem measurable.
But we know that entropy is a measurable physical quantity- which is measured using the equation S=Q/T
Can you explain the increase in entropy in the mentioned case using the equation provided?

[Darby]

There is ordered energy holding a molecule together - separate the molecule into bits, and that energy (if not partially captured and used) just becomes random heat, and the disorder in the system increases in either case.

[adichemadi]

Entropy is not disorderliness. It is the measure of how thermal energy can spread or shared into available microstates of the system. It shows in how many ways the thermal energy can be spreaded in the system. It means dilution of thermal energy.

[mith]

change in S is Q/T, there is no actual S for any one particle, it's a group phenomenon which makes sense because it's a measure of different configurations available to a system.