One gram of a protective colloid 'X' is to be added to 200ml of gold sol to prevent coagulation of it when `1 ml of 10% NaCl is added. Calculate the gold number of protective colloid 'X'.

Answer

To calculate the gold number of protective colloid 'X', we will follow these steps:

### Step 1: Understand the Definition of Gold Number
The gold number is defined as the amount of protective colloid (in milligrams) required to prevent the coagulation of 10 ml of gold sol when 1 ml of a 10% NaCl solution is added.

### Step 2: Identify the Given Data
- Amount of protective colloid 'X' = 1 gram
- Volume of gold sol = 200 ml
- Volume of NaCl solution added = 1 ml
- Concentration of NaCl solution = 10%

### Step 3: Convert the Amount of Protective Colloid to Milligrams
1 gram = 1000 milligrams. Therefore, 1 gram of protective colloid 'X' is equal to 1000 mg.

### Step 4: Calculate the Amount of Protective Colloid Required for 1 ml of Gold Sol
Since 1 gram (1000 mg) of protective colloid is required for 200 ml of gold sol, we can find out how much is needed for 1 ml:
\[ \text{Amount for 1 ml} = \frac{1000 \text{ mg}}{200 \text{ ml}} = 5 \text{ mg} \]

### Step 5: Calculate the Amount of Protective Colloid Required for 10 ml of Gold Sol
Now, we need to find out how much protective colloid is required for 10 ml of gold sol:
\[ \text{Amount for 10 ml} = 5 \text{ mg/ml} \times 10 \text{ ml} = 50 \text{ mg} \]

### Step 6: Conclusion
The gold number of protective colloid 'X' is 50 mg. This means that 50 mg of protective colloid 'X' is required to prevent the coagulation of 10 ml of gold sol upon the addition of 1 ml of 10% NaCl solution.

### Final Answer
The gold number of protective colloid 'X' is **50 mg**.

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