50 ml of a colloidal solution is completely precipitated by addition of 0.5 ml of 1 M NaCl solution. What will be the coagulation value.

Answer

To solve the problem of determining the coagulation value of the colloidal solution, we will follow these steps:

### Step 1: Calculate the number of millimoles of NaCl added
The formula to calculate the number of millimoles is:
\[ \text{Number of millimoles} = \text{Molarity} \times \text{Volume (in liters)} \]
Given:
- Molarity of NaCl = 1 M
- Volume of NaCl = 0.5 ml = 0.5/1000 L = 0.0005 L

Now, substituting the values:
\[ \text{Number of millimoles of NaCl} = 1 \, \text{mol/L} \times 0.0005 \, \text{L} = 0.0005 \, \text{mol} = 0.5 \, \text{mmol} \]

### Step 2: Convert the volume of the colloidal solution to liters
The volume of the colloidal solution is given as 50 ml. To convert this to liters:
\[ \text{Volume in liters} = \frac{50 \, \text{ml}}{1000} = 0.05 \, \text{L} \]

### Step 3: Calculate the coagulation value
The coagulation value is calculated using the formula:
\[ \text{Coagulation value} = \frac{\text{Number of millimoles of electrolyte}}{\text{Volume of colloidal solution (in liters)}} \]
Substituting the values we have:
\[ \text{Coagulation value} = \frac{0.5 \, \text{mmol}}{0.05 \, \text{L}} = 10 \, \text{mmol/L} \]

### Final Answer
The coagulation value of the colloidal solution is **10 mmol/L**.

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