For the just coagultion of 250 mL of `Fe(OH)_(3)` sol, 2 mL of `1 M Na_(2)SO_(4)` electrolyte is required. What is the coagulating value of `Na_(2)SO_(4)` electrolyte.

Answer

To find the coagulating value of `Na2SO4` electrolyte required for the coagulation of `Fe(OH)3` sol, we can follow these steps:

### Step 1: Understand the Concept of Coagulating Value
The coagulating value is defined as the minimum concentration of an electrolyte required to cause coagulation of a colloidal solution. It is typically expressed in millimoles per liter (mmol/L).

### Step 2: Determine the Amount of `Na2SO4` Used
In the problem, we are given that for the coagulation of 250 mL of `Fe(OH)3` sol, 2 mL of 1 M `Na2SO4` is required.

### Step 3: Calculate the Number of Millimoles of `Na2SO4`
To find the number of millimoles of `Na2SO4` used, we can use the formula:
\[ \text{Number of moles} = \text{Molarity} \times \text{Volume} \]
Since the volume is given in mL, we need to convert it to liters for the calculation. However, since we are looking for millimoles, we can directly calculate:
\[ \text{Millimoles of } Na2SO4 = \text{Molarity} \times \text{Volume (in mL)} \]
Substituting the values:
\[ \text{Millimoles of } Na2SO4 = 1 \, \text{mol/L} \times 2 \, \text{mL} = 2 \, \text{mmol} \]

### Step 4: Scale Up to 1 Liter
Now, we need to find out how many millimoles of `Na2SO4` would be required for 1000 mL (1 L) of `Fe(OH)3` sol. Since 250 mL requires 2 mmol, we can set up a proportion:
\[ \text{Millimoles for 1000 mL} = \left(\frac{2 \, \text{mmol}}{250 \, \text{mL}}\right) \times 1000 \, \text{mL} \]
Calculating this gives:
\[ \text{Millimoles for 1000 mL} = \frac{2 \times 1000}{250} = 8 \, \text{mmol} \]

### Step 5: Conclusion
Thus, the coagulating value of `Na2SO4` electrolyte is 8 millimoles per liter.

### Final Answer:
The coagulating value of `Na2SO4` is **8 mmol/L**.

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