For coagulation of 20ml of a negative sol Xml of 1M `NaCl , Y ml of 1M BaCl_2 and Z ml` of `AlCl_3` are required separately . What is the correct order of X.Y and Z, values ?

Answer

To determine the correct order of X, Y, and Z for the coagulation of a negative sol using different electrolytes, we can follow these steps:

### Step 1: Understand the nature of the sol
The sol in question is a negatively charged sol. To coagulate a negative sol, we need to add cations, which are positively charged ions.

### Step 2: Identify the cations from the given electrolytes
The electrolytes provided are:
- 1M NaCl (which provides Na⁺ cations)
- 1M BaCl₂ (which provides Ba²⁺ cations)
- 1M AlCl₃ (which provides Al³⁺ cations)

### Step 3: Apply the Schulze-Hardy rule
According to the Schulze-Hardy rule, the coagulation power of an electrolyte increases with the charge of the cation. Therefore, we can rank the cations based on their charge:
- Na⁺ (charge = +1)
- Ba²⁺ (charge = +2)
- Al³⁺ (charge = +3)

### Step 4: Determine the order of coagulation power
Since the coagulation ability increases with the charge of the cation, the order of coagulation power for the cations is:
- Al³⁺ > Ba²⁺ > Na⁺

### Step 5: Relate coagulation power to volume required
Given that all the electrolytes are at the same concentration (1M), a higher coagulation power means that a smaller volume of that electrolyte is needed to achieve coagulation. Therefore, the relationship between the volumes required (X, Y, Z) will be the reverse of the coagulation power:
- Al³⁺ (Z) will require the least volume,
- Ba²⁺ (Y) will require a moderate volume,
- Na⁺ (X) will require the most volume.

### Conclusion
Thus, the order of volumes required for coagulation is:
X > Y > Z

### Final Answer
X > Y > Z

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