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Weak acids are substances that do not fully dissociate into ions when dissolved in water. Instead of separating completely into ions, weak acids establish an equilibrium between the dissolved ions and the undissociated molecules. This means that at any given time in the solution, a large fraction of the acid molecules remain intact.
To illustrate this, consider acetic acid (\( CH_3COOH \)). When dissolved in water, only a small fraction of acetic acid molecules dissociate to form hydrogen ions (\( H^+ \)) and acetate ions (\( CH_3COO^- \)). Most of the acetic acid molecules remain as \( CH_3COOH \).
This limited ionization of weak acids results in a lower concentration of ions. And lower ion concentration typically means poor electrical conductivity. Because fewer ions are available to move and carry charge, weak acid solutions don't conduct electricity as well as strong acids, which dissociate completely.

Similar to weak acids, weak bases also partially ionize in solution. A weak base is a substance that reacts with water to produce hydroxide ions (\( OH^- \)), but this reaction does not go to completion. This implies that not all the molecules of a weak base will convert into ions when dissolved in water.
For example, ammonia (\( NH_3 \)) is a common weak base. When added to water, it partially ionizes to form a small number of \( OH^- \) ions and ammonium ions (\( NH_4^+ \)). However, a significant portion remains as unreacted \( NH_3 \) molecules.
As a result, the concentration of ions is fairly low in a solution of weak bases, just like in weak acids. Accordingly, the electrical conductivity is also lower compared to strong bases. Strong bases would completely dissociate and thus provide a high ion concentration, making them better conductors.

Ion concentration is a critical factor in determining the electrical conductivity of a solution. Conductivity measures how well a solution can carry an electrical current, and this is directly linked to the presence of moving charged particles—ions.
Solutions with a high ion concentration will usually have better electrical conductivity. This is because more ions allow for more charge carriers to move throughout the solution, facilitating the flow of electricity.
For both weak acids and weak bases, the partial ionization leads to a lower ion concentration. Consequently, their ability to conduct electricity is diminished when compared to solutions of strong acids or bases, which fully dissociate into their component ions. In essence, more complete ionization means stronger conductivity due to the increased availability of charge carriers.