An electric current is a flow of electrical charge. When a metal conducts electricity, the charge is carried by electrons moving through the metal. Electrons are subatomic particles with a negative electrical charge. When a solution conducts electricity, the charge is carried by ions moving through the solution. Ions are atoms or small groups of atoms that have an electrical charge. Some ions have a negative charge and some have a positive charge.
Citric acid is a weak organic acid with the molecular formula C6H8O7, which means a molecule of the acid contains six carbon atoms, eight hydrogen atoms, and seven oxygen atoms. When it is dissolved in water, it partially ionizes to yield three H+ ions (hydrogen atoms which are missing their electron) and a C6H5O7(3-) ion (the 3- means that it has three extra electrons.) The resulting solution is called an "electrolyte."
Citric acid is an acid; albeit a weak acid.
However, that means that the crystals would dissociate and have H+(aq) components.
This H+ is a type of ion and ions are conductor, but since it's a weak acid.
It means that there is a LOW concentration of the H+ ion. With the low ion concentration, it would still conduct electricity. It will be a weak electrolyte (conducts electricity weakly)
Citric acid should be soluble in water due to the hydrogenbonds etc. it will also conduct electricity since its a weak acid and will dissociate in water (the protons will contribute the most to the conductivity due to the high transport numbers for protons in water).
Vinegar (acetic acid) when an acid is in aqueous solution (dissolved in water) there are many loose hydrogen ions (and therefore lots of loose anions as well). Ionic solutions are good conductors of electricity. the stronger the acid, the more hydrogen ions in solution (and more anions), the better the conductor. weak acids like vinegar (acetic acid) conduct much less well because there are much fewer ions in