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Suppose you are given these substances:

$\ce{NaOH(aq)}$

$\ce{HCl(aq) }$

$\ce{C6H12O6(aq) }$

$\ce{NH3(l)}$

Are there rules to figure out how conductive each compound is? Is it based on intermolecular forces or polarity?

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A lot of work was done in the 19th and 20th century on determining the conductivity of aqueous solutions. It was a huge field called conductometry (check Wikipedia). You experimentally measure the resistance of a solution by placing the desired liquid between two inert electrodes and pass high frequency alternating current to prevent electrolysis. In solutions, electrical current is carried by ions. If your solution has ions or if it is ionizable, it will conduct electricity. Now you can determine which solution has ions based on ionization, e.g. you can write $\ce{HCl (aq) -> H+ + Cl-}$ and can predict that it must be a conductive solution. In fact, the aqueous $\ce{H+}$ has the highest conductivity known in water. $\ce{OH-}$ is next.

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    $\begingroup$ But how did you come to that conclusion? I understand it is based on the ions but oh is o2+ + H-, why is that less than HCl? $\endgroup$ – Vikram Kaushik Feb 22 at 21:20
  • $\begingroup$ It is actually a circular argument, people first measured conductivities of various solutions and then they classified that certain substances are good conductors (like NaCl solutions) and some of them are poor conductors (high resistance like acetic acid solutions). OH is not O2+H(-), it is a unit made of oxygen and hydrogen atoms. Check your textbook for electrolytes. $\endgroup$ – M. Farooq Feb 22 at 21:25

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