In Why Things Dissolve you saw salt fall apart into ions while sugar stayed as whole molecules, and Strong and Weak Acids showed that some acids ionize completely and others barely. Both ideas meet in one question: does a dissolved substance make ions, and how many?
Key idea
A strong electrolyte is present in solution almost entirely as ions: soluble ionic compounds, strong acids and strong bases. A weak electrolyte forms only a few ions: weak acids such as $\mathrm{CH_3COOH}$ and weak bases such as $\mathrm{NH_3}$. A nonelectrolyte forms none: molecular compounds such as sugar, ethanol and urea. Ions keep their own formulas: $$\mathrm{CaCl_2(s)} \to \mathrm{Ca^{2+}(aq)} + 2\,\mathrm{Cl^-(aq)}, \qquad \mathrm{Na_2SO_4(s)} \to 2\,\mathrm{Na^+(aq)} + \mathrm{SO_4^{2-}(aq)}.$$
Why it works
An ionic solid is already made of ions; water molecules surround and pull them apart, so every formula unit that dissolves becomes ions. A molecular substance is held together by covalent bonds that water doesn't break, so it dissolves as whole molecules. Acids are the exception among molecules: they react with water, giving away $\mathrm{H^+}$ to make $\mathrm{H_3O^+}$, completely for strong acids and only a little for weak ones. A solution conducts electricity because its ions move, so more ions means a brighter conductivity bulb.
Worked example: Classify
Classify each as a strong, weak or nonelectrolyte: $\mathrm{KNO_3}$, $\mathrm{HF}$, $\mathrm{C_2H_5OH}$ (ethanol), $\mathrm{HNO_3}$.
- $\mathrm{KNO_3}$: a soluble ionic compound: strong.
- $\mathrm{HF}$: a weak acid: weak.
- Ethanol: molecular and not an acid: nonelectrolyte.
- $\mathrm{HNO_3}$: a strong acid: strong.
Answer: Strong, weak, non, strong.
Worked example: Counting ions
How many moles of ions form when $0.10\ \text{mol}$ of $\mathrm{Al_2(SO_4)_3}$ dissolves?
- $\mathrm{Al_2(SO_4)_3} \to 2\,\mathrm{Al^{3+}} + 3\,\mathrm{SO_4^{2-}}$: 5 ions per formula unit. Sulfate stays together as one ion.
- $0.10 \times 5 = 0.50\ \text{mol}$ of ions.
Answer: $0.50\ \text{mol}$
Common mistake
Two errors. First, thinking "soluble" means "strong electrolyte": sugar and ethanol dissolve very well and make no ions at all. Second, splitting a formula into atoms instead of ions, as in "$\mathrm{CaCl_2} \to \mathrm{Ca^{2+}} + \mathrm{Cl_2^{2-}}$". The subscript 2 means two separate chloride ions, each $-1$. Check: the charges on the right must add to zero, and each ion must be a real ion ($\mathrm{Cl^-}$, $\mathrm{NO_3^-}$, $\mathrm{SO_4^{2-}}$).