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.