For the coagulation of 40ml of ferric hydroxide sol, 10ml of 0.4 M KCI is required. Then, coagulation value of KCI is

Options

A. 10
B. 50
C. 100
D. 40

Answer

To find the coagulation value of KCl for the coagulation of 40 ml of ferric hydroxide sol, we can follow these steps:

### Step 1: Understand the concept of coagulation value
The coagulation value is defined as the number of millimoles of a substance required to coagulate a certain volume of a colloidal solution.

### Step 2: Identify the given data
- Volume of ferric hydroxide sol (V_ferric hydroxide) = 40 ml
- Volume of KCl solution (V_KCl) = 10 ml
- Molarity of KCl (M_KCl) = 0.4 M

### Step 3: Calculate the number of millimoles of KCl used
To find the number of millimoles of KCl used, we can use the formula:

\[ \text{Millimoles of KCl} = \text{Molarity} \times \text{Volume (in liters)} \]

First, convert the volume of KCl from ml to liters:

\[ V_{KCl} = 10 \, \text{ml} = 0.010 \, \text{liters} \]

Now, calculate the millimoles:

\[ \text{Millimoles of KCl} = 0.4 \, \text{mol/L} \times 0.010 \, \text{L} = 0.004 \, \text{mol} \]

Since 1 mol = 1000 millimoles:

\[ \text{Millimoles of KCl} = 0.004 \, \text{mol} \times 1000 = 4 \, \text{millimoles} \]

### Step 4: Calculate the coagulation value
Now, we need to find out how many millimoles of KCl are required to coagulate 40 ml of ferric hydroxide sol. Since we used 4 millimoles of KCl for 10 ml, we can find the coagulation value for 40 ml using the ratio:

\[ \text{Coagulation value} = \frac{\text{Millimoles of KCl}}{\text{Volume of ferric hydroxide sol (in ml)}} \times 1000 \]

Thus, for 40 ml of ferric hydroxide sol:

\[ \text{Coagulation value} = \frac{4 \, \text{millimoles}}{10 \, \text{ml}} \times 40 = 16 \, \text{millimoles} \]

### Final Answer
The coagulation value of KCl for the coagulation of 40 ml of ferric hydroxide sol is **16 millimoles**.

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