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First of all, solid sucrose (pure sugar) is not a conductor. It is an insulator just as many other materials. But, the question is most often posed when it is combined with water and one finds that dissolved sucrose and dissolved salt create solutions with very different electrical properties. The difference derives from the fact that salts dissolve in the form of ions and sucrose dissolves in the form of molecules that do not have charge.

Conductivity in solutions is different than conductivity in a wire or other metal object. In metals, electrons move when a voltage is applied and only electrons.

In water, the application of a voltage results in the movement of charge, but the charges are not nearly-free electrons but rather ions (charged atoms or molecules). In pure water, the ions that are moving are the protons in the form of H3O+ and hydroxide ions, OH-. In other ionic solutions it is the dissolved ions themselves, for instance in salt water, sodium chloride dissociated into the ions Na+ and Cl-.

Sucrose and water form a "non-ionic solution." Sucrose and other materials can dissolve in water and not be broken into charged pieces the way salts are. (If the solute is broken into charged pieces, then it forms an "ionic solution.") If the molecules in solution remain in tact and are not charged then they are not affected by the electric field (force equals charge times the strength of the field) that is created in the solution when the voltage is applied.

It should be said that pure water has a very small conductivity, so small that it is sometimes said that pure water does not conduct electricity. The ionic movement in pure water is just very small, but impurities, such as present in tap water, or salt increases the conductivity a great deal.

Caveat: This brief explanation covers the essential phenomena that one learns in a beginning chemistry class, but eventually one can encounter more complex situations with conducting liquids, e.g. molten salt conducts via ions and Mercury conducts via electrons. You are pretty safe with the simple explanation when it comes to things dissolved in water.

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