Question

Gold number of a protective colloid A is x. A mixture is prepared by adding 50 mL of 10% NaCl solution to 500 mL gold sol. What minimum mass of A is needed to prevent coagulation?

• A. \(50x\)
• B. \(500x\)
• C. \(5x\)
• D. \(0.5x\)

Hint:

Gold number definition is based on 10 mL gold sol protected against 1 mL of 10% NaCl. Scale proportionally in numerical questions.

Answer 1

The Correct Option is C

Concept: Gold number is defined as: The minimum mass in milligrams of protective colloid required to prevent coagulation of 10 mL standard gold sol when 1 mL of 10% NaCl solution is added. Mathematically: \[ Gold\;Number=x \] means \[ x\;mg \] protects \[ 10mL\;gold\;sol \] against \[ 1mL\;10%\;NaCl \]

Step 1: Compare amount of gold sol. Standard gold sol: \[ 10mL \] Given gold sol: \[ 500mL \] Ratio: \[ \frac{500}{10}=50 \]

Step 2: Compare sodium chloride amount. Standard NaCl amount: \[ 1mL \] Given: \[ 50mL \] Ratio: \[ \frac{50}{1}=50 \]

Step 3: Determine scaling factor. Overall protective requirement scales proportionally. Required colloid: \[ x\times\frac{50}{10} \] or direct formula \[ =5x \] Thus minimum mass becomes \[ \boxed{5x} \]