Entropy is the measure of disorder in a substance. Entropy is important when discussing the formation of solutions because when you form a solution, the solute becomes more disordered.
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The definition of entropy is the measure of disorder in a substance. When two (or more) substances mix to form a solution, there is an increase in randomness. For example with NaCl mixed with water, entropy is what causes the Na and the Cl to break apart and dissolve. When you dissolve NaCl, the ions wander around and put themselves into a highly entropic situation. This increase in entropy (from the low entropy in sodium chloride to the higher entropy of salt water) is what allows the NaCl to dissolve.