Final answer:
The atoms in a molecule of a substance that does not conduct electricity when dissolved in water are held together by covalent bonds, indicating that the substance is a nonelectrolyte and behaves as an insulator.
Step-by-step explanation:
When a soft substance is dissolved in water and the resulting solution does not conduct electricity, this indicates that the solution does not contain freely mobile, charged species. Since the solution is non-conductive, the atoms in a molecule of this substance are held together by covalent bonds. These molecules do not break apart into ions when dissolved in water, and therefore, the solution remains an insulator, similar to pure water or dry table salt. In contrast, electrolytes, which can be strong or weak, dissolve in water to give a solution that conducts electricity due to the presence of ions.