Question

Which of the following electrolytes will have maximum coagulating value for \(\mathrm{Agl} / \mathrm{Ag}^{+}\)sol? (a) \(\mathrm{Na}_{3} \mathrm{PO}_{4}\) (b) \(\mathrm{Na}_{2} \mathrm{SO}_{4}\) (c) \(\mathrm{NaCl}\) (d) \(\mathrm{Na}_{2} \mathrm{~S}\)

Short answer

NaCl has the maximum coagulating value due to the lowest charge on Cl⁻.

Step-by-step solution

Understanding Coagulating Value

Coagulating value refers to the amount of an electrolyte needed to coagulate a dispersion. The smaller the amount required, the higher the coagulating power, and thus, the smaller the coagulating value.

Identify Charge on the Coagulating Ion

To determine which electrolyte will have the maximum coagulating value, we need to consider the charge of the ion it provides because the coagulating power of an electrolyte is proportional to the sixth power of the charge of its ion. For the given options, identify the cations: Na⁺ in each, and more importantly consider the anions: PO₄³⁻, SO₄²⁻, Cl⁻, and S²⁻.

Applying Hardy-Schulze Rule

According to the Hardy-Schulze rule, the effectiveness of an electrolyte in coagulating a given sol is directly proportional to the charge on the ion responsible for coagulation. The higher the charge on the coagulating ion, the greater its ability to coagulate a sol. Here, coagulation would be primarily by the anion.

Analyze the Charge on Anions

The anions for the electrolytes are: PO₄³⁻, SO₄²⁻, Cl⁻, and S²⁻. Therefore, the coagulating value decreases as we go from Cl⁻ (1-), SO₄²⁻ (2-), S²⁻ (2-), to PO₄³⁻ (3-). Hence, \( ext{NaCl} \) with Cl⁻ would have the maximum coagulating value (lowest coagulating power) since the charge on Cl⁻ is the lowest among the given options.

Key concepts

Hardy-Schulze Rule

The Hardy-Schulze rule is a crucial principle in colloid chemistry that helps predict the coagulating ability of ions in a colloidal solution. It states that the coagulating power of an electrolyte is directly correlated to the charge of the ion that causes coagulation. So, the higher the charge on the ion, the more efficient the coagulation process.

This rule explains why different electrolytes exhibit varying abilities to coagulate colloids, even at similar concentrations. In practical terms, if you have multiple electrolytes and need to coagulate a given colloidal sol, the one with the ion holding the highest charge will be most effective. As applied in the exercise, understanding this rule allows us to predict how different anions like \( \text{PO}_4^{3-}\) or \( \text{Cl}^-\), with differing charges, will behave in coagulating an \( \text{AgI} / \text{Ag}^+\) sol.

Electrolyte Coagulation

Electrolyte coagulation refers to the process through which ions introduced to a colloidal sol aggregate the suspended particles, causing them to fall out of suspension. This process is largely influenced by the charge and concentration of the ions available for coagulation.

When considering an electrolyte, Coulomb’s law plays a pivotal role. The force between charged ions becomes a deciding factor in how effectively these ions neutralize or compress the electrical double layer around colloidal particles. As a result, reducing the repulsive forces and encouraging coagulation.

In the exercise, electrolytes like \( \text{Na}_3 \text{PO}_4\) and \( \text{NaCl}\) are compared for their coagulating values. Here, the effectiveness depends on how their ions interact with the charged surface of the colloidal particles, highlighting their potential to cause coagulation through neutralizing surface charges.

Anion Charge Impact

The charge on an anion is a significant factor that determines how well an electrolyte can coagulate a colloidal system. Higher valency anions typically demonstrate greater coagulating power due to their ability to exert stronger electrostatic forces on the colloidal particles.

For example, \( \text{PO}_4^{3-}\) has a greater charge compared to \( \text{Cl}^-\), making it more efficient at compressing the electrical double layer around particles. This leads to better aggregation and ultimately, effective coagulation.

In the given exercise scenario, analyzing the charges of \( \text{PO}_4^{3-}\), \( \text{SO}_4^{2-}\), and \( \text{Cl}^-\) helps determine their relative coagulating values. The greater the charge, the lower the coagulating value needed, meaning less of the electrolyte is required to achieve effective coagulation. Understanding these charge impacts is key to predicting the behavior of electrolytes in specific colloidal applications.