Coagulation of a Gold Sol

Introduction:
When an electrolyte is added to a gold sol, it causes the gold particles to come together and form larger aggregates, resulting in the coagulation or precipitation of the sol. The rate and extent of coagulation depend on the nature and concentration of the electrolyte.

Comparison of Electrolytes:
To determine which electrolyte will bring about the coagulation of a gold sol quickest and in the least concentration, let's compare the given electrolytes:

a) NaCl
b) MgSO4
c) Al2(SO4)3
d) K4[Fe(CN)6]

Factors Affecting Coagulation:
To understand why option 'C' (Al2(SO4)3) is the correct answer, we need to consider the factors affecting coagulation. These factors include:

1. Valency of the ions: Higher valency ions have a stronger charge and can cause faster coagulation.
2. Concentration of the electrolyte: Higher concentrations of electrolytes lead to faster coagulation.
3. Nature of the electrolyte: Some electrolytes have stronger charges or specific interactions with the gold particles, leading to faster coagulation.

Analysis:
Let's analyze each option based on the above factors:

a) NaCl:
- Valency: Na+ and Cl- ions have a valency of 1.
- Concentration: Not mentioned.
- Nature: Na+ and Cl- ions do not have a strong charge or specific interactions with gold particles.

b) MgSO4:
- Valency: Mg2+ and SO42- ions have a valency of 2.
- Concentration: Not mentioned.
- Nature: Mg2+ ions have a higher charge than Na+ ions, but still not as strong as some other options.

c) Al2(SO4)3:
- Valency: Al3+ and SO42- ions have a valency of 3.
- Concentration: Not mentioned.
- Nature: Al3+ ions have a higher charge than Mg2+ or Na+ ions, making them more effective in coagulation.

d) K4[Fe(CN)6]:
- Valency: K+ and [Fe(CN)6]4- ions have a valency of 1 and 4, respectively.
- Concentration: Not mentioned.
- Nature: While [Fe(CN)6]4- ions have a higher charge, they may not have specific interactions with gold particles.

Conclusion:
Based on the analysis, option 'C' (Al2(SO4)3) is the correct answer. The Al3+ ions in Al2(SO4)3 have a higher valency and can cause faster coagulation of the gold sol. However, it is important to note that the concentration of the electrolyte also plays a crucial role in determining the rate of coagulation.