This question is a little confusing. According to my teacher, the entropy should decrease, but I think that sugar is crystalline first and later it dissolves, so the randomness increases and so the entropy should also increase. What is the correct answer?
While it may seem that randomness always increases when a crystal is dissolved into a liquid phase, it does not have to be that way.
Concerning sugar, the molecule has a large number of hydroxyl groups and is generally rather large when compared with the water molecule around it — much larger than your average sodium or chloride ions. Every hydroxyl will act as both a hydrogen bond donor and an acceptor, likely to two different water molecules, creating a cage of water that is rather ordered and large again when comparing to the sodium or chloride ion’s solvation cell. This will decrease the disorder (and hence entropy) of the free water so much, that it counteracts the increase in entropy of the crystal dissolving. (The effect is more pronounced with sucrose when compared to glucose due to the molecule’s size and the number of hydroxyls.)
On the other hand, the molecules in a sugar crystal are likely less ordered than the ions of a salt crystal. They will form extensive hydrogen-bonding networks, yes; but overall if you shift one row of molecules relative to its neighbour you won’t necessarily break the crystal as you won’t suddenly have ions of the same charge next to each other. And finally, the single salt crystal will break down into much smaller fragments than the sugar molecules.
So summed up, the effects are:
large solvation cells
crystal breaks down into larger (less disordered) fragments upon solvation
sugar crystals themselves are less ordered than salt crystals
Meaning that there is a lot less entropy to be gained.
The second law of thermodynamics states that a process in an isolated system will be spontaneous only if the entropy of the system increases as a result of the said process. Since sugar spontaneously dissolves in water, the total entropy of water and sugar has to increase when sugar dissolves.
You're the correct one here.
Entropy will go up when a solid becomes aqueous (or dissolved at all) or when liquids mix. This is because there are an increased number of microstates that are indistinguishable from each other when a solid is dissolved or when liquids mix.
(However, do note that if you dissolve a gas, entropy goes down)