Which of the following ions will be most effective in coaogulating the \(\mathrm{As}_{2} \mathrm{~S}_{3}\) sol : (1) \(\mathrm{Fe}^{3 *}\) (2) \(\mathrm{Ba}^{2+}\) (3) \(\mathrm{Cl}^{-}\) (4) \(\mathrm{PO}_{4}^{3-}\)

The Hardy-Schulze rule is a fundamental principle in the science of colloidal solutions. It states that the coagulating power of an ion increases with the valence (charge) of the ion. This means that higher-charged ions are more effective at precipitating colloidal particles.
For example, if you have a negatively charged sol, the ions with a higher positive charge will be more effective in coagulating the particles. The reason is that these ions can neutralize the charge on the colloidal particles more efficiently.
In our exercise, we compared different ions such as \(\text{Fe}^{3+}\), \(\text{Ba}^{2+}\), \(\text{Cl}^{-}\), and \(\text{PO}_4^{3-}\). According to the Hardy-Schulze rule, the ion with the highest positive charge (\(\text{Fe}^{3+}\)) is the most effective in coagulating the negatively charged \(\text{As}_2\text{S}_3\) sol.

The coagulation mechanism involves the aggregation of particles in a colloidal solution to form larger particles, which then settle out of the solution. This can be achieved by adding an electrolyte, which contains ions that neutralize the charges on the colloidal particles, allowing them to come together and form bigger aggregates.
Here's how it works:

• A colloidal particle typically carries an electrical charge, making it stable and preventing aggregation.
• When an electrolyte is added, the ions move toward the oppositely charged colloidal particles.
• The ions neutralize the surface charge, reducing the repulsion between particles.
• This reduction in repulsion allows particles to come closer and form aggregates, resulting in precipitation.

In the case of the negatively charged \(\text{As}_2\text{S}_3\) sol, adding positive ions like \(\text{Fe}^{3+}\) disrupts the stability by neutralizing the negative charge.

Ionic charge plays a crucial role in the coagulation process. The efficiency of an ion in causing coagulation directly depends on its charge. Higher the charge, greater is its coagulating power.
This is why in our step-by-step solution, \(\text{Fe}^{3+}\) (which has a +3 charge) is more effective than \(\text{Ba}^{2+}\) (which has a +2 charge). This also aligns with the Hardy-Schulze rule. Positively charged ions (cations) are more efficient at coagulating a negatively charged sol.
In summary, the higher the positive charge on the cation, the more strongly it attracts the negatively charged colloidal particles, leading to faster and more effective coagulation. That’s why \(\text{Fe}^{3+}\) is the most efficient among the ions given in the exercise.