Problem 48 - Master Resource Book in JEE Main Physics

Question

The angle of contact at the interface of water-glass is \(0^{\circ}\) Ethylalcohol-glass is \(0^{\circ}\), Mercury-glass is \(140^{\circ}\) and Methyliodide-glass is \(30^{\circ} .\) A glass capillary is put in a trough containing one of these four liquids. It is observed that the meniscus is convex. The liquid in the trough is (NCFRT Exemplar] (a) water (b) ethylalcohol (c) mercury (d) methyliodide

Step-by-Step Solution

Answer

The liquid in the trough is mercury.

Step 1: Understanding the Problem

We're given four different liquids in contact with glass: water with a contact angle of \(0^{\circ}\), ethylalcohol with \(0^{\circ}\), mercury with \(140^{\circ}\), and methyliodide with \(30^{\circ}\). We need to determine which liquid results in a convex meniscus inside a glass capillary.

Step 2: Recap of Meniscus Shapes

The shape of the meniscus depends on the contact angle: if the contact angle is less than \(90^{\circ}\), the meniscus is concave. If it's greater than \(90^{\circ}\), the meniscus is convex. A contact angle of exactly \(0^{\circ}\) also results in a concave meniscus as the liquid wets the surface.

Step 3: Analyzing Contact Angles

For water and ethylalcohol, both have a contact angle of \(0^{\circ}\), leading to a concave meniscus. Methyliodide has a contact angle of \(30^{\circ}\), which is also less than \(90^{\circ}\), so it will be concave. Mercury, with a contact angle of \(140^{\circ}\), is the only liquid with an angle greater than \(90^{\circ}\), resulting in a convex meniscus.

Step 4: Conclusion

Since the meniscus observed is convex, the liquid in the trough must be mercury, as it is the only one with a contact angle greater than \(90^{\circ}\).

Key Concepts

Contact Angle

The contact angle is crucial in understanding how a liquid interacts with a solid surface. It is the angle formed between the tangent to the liquid surface and the solid surface at the point of contact. This angle helps us determine whether a liquid will spread out on a surface or form droplets.
If a liquid completely wets a surface, the contact angle is less than or equal to 90 degrees, often leading to a concave meniscus. This is because the cohesive forces within the liquid are less than the adhesive forces between the liquid and solid. For example:

• Water and glass have a contact angle of 0 degrees, indicating full wetting and a concave meniscus.
• Ethyl alcohol also has a contact angle of 0 degrees with glass, behaving similarly to water.

On the other hand, when the contact angle is greater than 90 degrees, the liquid does not wet the surface well, resulting in a convex meniscus. This occurs due to stronger cohesive forces within the liquid compared to adhesive forces. Mercury and glass exhibit a contact angle of 140 degrees, demonstrating this behavior.

Capillary Action

Capillary action is the movement of a liquid within the narrow spaces of a porous material. This occurs against the force of gravity, due to the intermolecular forces at play. When a capillary tube is placed in a liquid, the liquid either rises or falls in the tube, depending on the forces involved.
If the adhesive (attraction between the liquid and solid surface) forces are stronger than the cohesive (attraction between liquid molecules) forces, the liquid will rise. This is typical in a scenario where the contact angle is less than 90 degrees, resulting in a concave meniscus. Examples include:

• Water climbing up a thin tube due to its desire to wet the surface.
• Similar action seen in ethyl alcohol with glass, due to its full wetting behavior.

Conversely, if the cohesive forces dominate, the liquid will drop lower in the capillary tube, leading to a convex meniscus. With mercury having a contact angle greater than 90 degrees with glass, it does not rise in a capillary tube, instead, it forms a convex meniscus.

Surface Tension

Surface tension is the tendency of a liquid surface to shrink into the minimal surface area possible. It arises from the intermolecular forces at play. In a liquid, molecules at the surface are pulled inward and tend to stick together, creating a 'tightened' surface.
This phenomenon plays a significant role in creating the shape of a meniscus in capillary action. The balance between cohesive forces within the liquid and adhesive forces between the liquid and tube determines the surface shape.

• A strong surface tension in liquids like water results in a concave meniscus when in contact with glass.
• Mercury, despite having a high surface tension, forms a convex meniscus due to its much stronger cohesive forces compared to its adhesive forces with glass.

Understanding surface tension is key to predicting how different liquids interact with surfaces, influencing their effective use in various applications, from biological cells to industrial processes.