Problem 152 - A Complete Resource Book in Chemistry for JEE Main

Question

The coagulation of \(100 \mathrm{ml}\) of colloidal solution of gold is completely prevented by addition of \(0.25 \mathrm{~g}\) of a substance " \(X\) "to it before addition of \(10 \mathrm{ml}\) of \(10 \% \mathrm{NaCl}\) solution. The gold number of " \(\mathrm{X}\) " is (a) 25 (b) 250 (c) \(2.5\) (d) \(0.25\)

Step-by-Step Solution

Answer

The gold number of 'X' is 25.

Step 1: Understand the Gold Number Concept

The gold number is defined as the minimum amount (in milligrams) of a lyophilic substance needed to prevent the coagulation of 10 ml of gold sol by the addition of 1 ml of 10% NaCl solution. It's a measure of the protective power of the colloid.

Step 2: Know the Problem Parameters

You have 100 ml of colloidal gold solution and a protective substance 'X' weighing 0.25 g. 100 ml of this solution is equivalent to 10 times the typical standard, as it fits into 10 ml conversion frames, since 100 ml equates to 10 such volumes.

Step 3: Calculate Amount of Substance Per Standard Volume

To calculate the gold number, we first need to find the amount of substance X required for the standard volume (i.e., for 10 ml of solution with 1 ml of the precipitating NaCl). The given substance weight is 0.25 g which is 250 mg. Therefore, for 10 ml of the solution, the weight of substance X would be (250/10) mg = 25 mg.

Step 4: Conclude the Gold Number

The gold number is the amount (in mg) of the substance X required per 10 ml of the gold sol to prevent coagulation by 1 ml of 10% NaCl. From the above calculation, this amount is 25 mg.

Key Concepts

Colloidal Solution

Colloidal solutions, or colloids, are a type of mixture where one substance (dispersed phase) is microscopically dispersed evenly throughout another substance (continuous phase). Unlike solutions, the particles in a colloidal solution do not settle out upon standing and are typically in the range of 1 to 1000 nanometers in size. An everyday example of a colloidal solution is milk, where fat droplets are dispersed in water.
Colloidal gold is an example used in chemistry experiments, where gold particles are distributed in a liquid medium. This makes the gold practically invisible to the naked eye, yet the solution may appear colored due to scattering of light by the particles. This size and suspended state allow certain optical properties, leading to vivid colors often seen in colloids.

Coagulation Prevention

Coagulation prevention is the process in which the prevention of the clumping of particles is achieved. In colloidal solutions, it is essential to maintain the stability of dispersed particles, preventing them from aggregating and settling. This is often done using stabilizing agents like lyophilic substances. These substances enhance the stability by rendering the colloidal particles resistant to coagulation induced by external factors, such as the addition of electrolytes.
In our exercise, the substance 'X' plays the role of a stabilizer. By adding this before introducing NaCl, it ensures that the gold particles remain well-dispersed, thus preventing coagulation or clumping. This prevention is crucial, especially in industrial processes or when using colloids in research and product development.

Lyophilic Substance

Lyophilic substances are materials having a strong affinity for the dispersion medium (usually water). These substances naturally stabilize colloidal solutions due to their attraction to the solvent, creating a protective layer around colloidal particles. This layer prevents aggregation and ensures that particles do not come together to form larger clusters.
Such substances are crucial when formulating a stable colloidal solution. They not only contribute to the stability but also increase the colloid's durability against coagulating agents. In our scenario, approximately 0.25 g of lyophilic substance 'X' helps to maintain the gold particles in solution even after the addition of NaCl, ensuring a consistent, non-coagulated suspension.

Protective Power of Colloids

The protective power of colloids refers to their ability to safeguard specific particles in suspension from coagulating when an electrolyte is added. This is quantified by the gold number, which reflects how effective a lyophilic substance is at stabilizing colloidal particles. A lower gold number indicates a more effective colloid that requires less substance to achieve stabilization, highlighting its high protective power.
In the given exercise, the gold number is derived by determining how much substance 'X' is needed per standard testing condition to ensure that the colloidal gold does not coagulate. With a calculated gold number of 25 mg, it underscores that the protective power can be significantly affected by the choice and amount of lyophilic substance used.