Both sucrose and lactose posses the same molecular formula, but sucrose is a non-conducting sugar and lactose is a reducing agent sugar. Why ?
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In sucrose, hemiacetal hydroxyl groups of glucose are fructose are involved in the glycosidic linkage. Hence sucrose is a non-reducing sugar. In lactose, hemiacetal hydroxy groups of galactose involved in the glycosidic but of glucose not involved in glycosidic linkage. Hence lactose is a reducing sugar.
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A simple sugar, called a monosaccharide, is chemically a poly-hydroxy aldehyde or ketone. The aldehyde or ketone in the molecule will react as a reducing agent and be oxidized to an acid. Many of those reactions involve color changes so the reaction process is easy to observe in the lab, and makes a good chemical test for the presence of the aldehyde or ketone groups.
All simple sugars, monosaccharides, are reducing sugars. This included glucose, fructose, galactose, ribose and many others.
When two simple sugars are fused together, a disaccharide is formed. There are several ways that the fusing is possible. If the bond between them connects both of their aldehyde and ketone groups, but that bond can still open and close, the sugar will still be a reducing sugar. Thus, maltose, lactose, and other disaccharides are still reducing sugars.
However, if the bond joining the two sugars cannot open and close, the aldehyde or ketone groups are chemically “protected” from oxidation, and will not behave as a reducing sugar. Sucrose fits this description. It is not a reducing sugar.
Another factor that differentiates disaccharides is the orientation of the bonds joining them together. That orientation can be up or down from the perspective of a particular carbon in the sugar (the one with the aldehyde or ketone on it). These two orientations are referred to by biochemists as alpha and beta. The alpha orientation ones are almost all able to be broken apart by the same enzyme. The beta ones need different enzymes.
In humans, the one beta oriented disaccharide that we can usually break up and digest is the bond in lactose. It is broken by the enzyme lactase. Some adults lack sufficient lactase to digest lactose before it reaches the large intestine, where bacteria digest it releasing lots of gas molecules, causing pain and bloating. Such individuals are called lactose-intollerant.
Polysaccharides are chains of simple sugars, most often just glucose molecules. In some of these all the linking bonds are alpha and humans can break them up for energy. These are the starches.
In others, all the linking bonds are beta and no animals can break them apart without help from bacteria. These are cellulose, also called insoluble fiber, molecules. Soil bacteria and certain gut bacteria in rhuminant animals like cows, sheep, goats, camels and others, can break the beta bonds, enabling the host animal to then digest the glucose molecules that have been freed up.
While these polysaccharides are technically reducing sugars, their reactions are hard to observe without breaking them up first, which invalidates the results. This is because these molecules may have thousands to hundreds of thousands of glucose or other simple sugar molecules in a single starch or cellulose molecule with a single aldehyde or ketone group that can act as a reducing agent. There are so few molecules changing, that it's hard to design a test that makes it easy to see the results.
There are many more interesting facets to our body's use of simple and complex carbohydrates, that also effect our nutrition.