Q.Explain why

Here are the explanations for each point:

(a) Concept: Balance of cohesive and adhesive forces.

1. The angle of contact ($\theta$) is determined by the relative strengths of adhesive forces ($F_a$) between the liquid and solid, and cohesive forces ($F_c$) within the liquid.
2. For water and glass, $F_a$ (water-glass) is stronger than $F_c$ (water-water), causing water to spread and $\theta < 90^\circ$.
3. For mercury and glass, $F_c$ (mercury-mercury) is much stronger than $F_a$ (mercury-glass), causing mercury to contract and $\theta > 90^\circ$.

(b) Concept: Wetting and spreading based on the angle of contact.

1. Wetting occurs when the liquid spreads over the solid, which happens when the angle of contact ($\theta$) is acute.
2. For water on glass, adhesive forces are stronger than cohesive forces, leading to an acute angle of contact ($\theta < 90^\circ$), allowing water to wet the glass and spread.
3. For mercury on glass, cohesive forces are stronger than adhesive forces, resulting in an obtuse angle of contact ($\theta > 90^\circ$), causing mercury to minimize contact and form drops.

(c) Concept: Surface tension as an intensive property.

1. Surface tension ($\sigma$) is defined as the force per unit length acting perpendicular to a line on the liquid surface, or as the surface energy per unit area.
2. It arises from the net inward cohesive forces experienced by molecules at the liquid-air interface.
3. This property depends only on the nature of the liquid, its temperature, and any impurities present, not on the total surface area.

(d) Concept: Effect of surfactants (detergents) on surface tension and wetting.

1. Detergents are surfactants that significantly reduce the surface tension of water.
2. A reduction in surface tension implies a weakening of the cohesive forces within the liquid.
3. With relatively weaker cohesive forces, the adhesive forces between the water-detergent solution and the solid surface become more dominant.
4. This dominance of adhesive forces leads to better wetting and a smaller (more acute) angle of contact.

(e) Concept: Minimization of surface energy.

1. Liquid molecules at the surface possess higher potential energy due to surface tension.
2. Any system in equilibrium tends to achieve a state of minimum potential energy.
3. For a given volume, a sphere is the geometric shape that has the minimum surface area.
4. Therefore, to minimize its total surface energy, a liquid drop free from external forces (like gravity) naturally assumes a spherical shape.

(a) The angle of contact of mercury with glass is obtuse, while that of water with glass is acute.

1. Understanding Angle of Contact: The angle of contact ($\theta$) is the angle formed inside the liquid between the tangent to the liquid surface at the point of contact with the solid and the solid surface itself. It's a measure of how much a liquid wets a solid surface.

2. Role of Intermolecular Forces: The shape of the liquid meniscus and thus the angle of contact is determined by the competition between two types of intermolecular forces:

   • Cohesive forces ($F_c$): Attractive forces between molecules of the same liquid.
   • Adhesive forces ($F_a$): Attractive forces between liquid molecules and solid molecules.

3. Case of Water with Glass (Acute Angle):

   • For water and clean glass, the adhesive forces between water molecules and glass molecules ($F_a$) are significantly stronger than the cohesive forces between water molecules ($F_c$).
   • This strong attraction to the glass surface pulls the water molecules upwards along the glass, causing the liquid to spread and form a concave meniscus.
   • When $F_a > F_c$, the liquid tends to wet the solid, and the angle of contact is acute ($0^\circ < \theta < 90^\circ$).

4. Case of Mercury with Glass (Obtuse Angle):

   • For mercury and glass, the cohesive forces between mercury molecules ($F_c$) are much stronger than the adhesive forces between mercury molecules and glass molecules ($F_a$).
   • The mercury molecules are more attracted to each other than to the glass. This causes the liquid to pull away from the glass surface, forming a convex meniscus.
   • When $F_c > F_a$, the liquid tends not to wet the solid, and the angle of contact is obtuse ($90^\circ < \theta < 180^\circ$).

(b) Water on a clean glass surface tends to spread out while mercury on the same surface tends to form drops.

1. Direct Consequence of Angle of Contact: This phenomenon is a direct result of the angle of contact discussed in part (a) and the relative strengths of adhesive and cohesive forces.

2. Water Spreading on Glass (Wetting):

   • As established, water has an acute angle of contact with clean glass. This means the adhesive forces between water and glass are stronger than the cohesive forces within water.
   • To maximize the favorable interaction (adhesion) with the glass surface, water molecules spread out, increasing the contact area with the glass. This is known as "wetting" the surface.
   • The spreading minimizes the overall surface energy of the system by maximizing the lower energy solid-liquid interface at the expense of the higher energy liquid-gas interface.

3. Mercury Forming Drops on Glass (Non-Wetting):

   • Mercury has an obtuse angle of contact with glass. This indicates that the cohesive forces within mercury are much stronger than the adhesive forces between mercury and glass.
   • To minimize the unfavorable interaction (adhesion) with the glass surface, mercury molecules pull together, minimizing the contact area with the glass. This results in the formation of distinct spherical or semi-spherical drops. This is known as "non-wetting" the surface.
   • The dropping minimizes the overall surface energy by minimizing the higher energy solid-liquid interface and maximizing the lower energy liquid-gas interface.

(c) Surface tension of a liquid is independent of the area of the surface.

1. Definition of Surface Tension: Surface tension ($\sigma$) is defined as the force acting per unit length on the surface of a liquid, perpendicular to a line drawn on the surface and tangential to the surface. Alternatively, it can be defined as the surface energy per unit area.

2. Origin of Surface Tension: Surface tension arises from the unbalanced cohesive forces experienced by molecules at the liquid-gas interface.

   • Molecules in the bulk of the liquid are surrounded by other liquid molecules, experiencing attractive forces in all directions, resulting in a net zero force.
   • Molecules at the surface, however, are only attracted by molecules below and to their sides, not by molecules above (as there are fewer or no liquid molecules above them). This results in a net inward attractive force, pulling surface molecules into the bulk.

3. Intrinsic Property: This net inward force creates a tension in the surface layer, making it behave like a stretched elastic membrane. This tension is an intrinsic property of the liquid, dependent only on the nature of the liquid, its temperature, and the surrounding medium.

4. Analogy: Consider a rubber band. The tension in the rubber band depends on the material of the rubber and how much it's stretched, not on the total surface area of the rubber band itself. Similarly, surface tension is a measure of the "tightness" or "strength" of the surface layer, which is uniform throughout the surface for a given liquid and conditions.

5. Why Area Doesn't Matter: If surface tension depended on the area, a larger surface would imply a different surface tension, which contradicts its definition as a force per unit length or energy per unit area. The force per unit length (or energy per unit area) remains constant regardless of how large or small the surface is, as long as the liquid's properties and conditions (like temperature) are unchanged.

(d) Water with detergent dissolved in it should have small angles of contact.

1. Role of Detergents (Surfactants): Detergents are surface-active agents (surfactants). Their primary function is to reduce the surface tension of water. They achieve this by positioning themselves at the water-air interface, disrupting the strong cohesive forces between water molecules.

2. Effect on Surface Tension: When detergent is dissolved in water, the detergent molecules (which have both hydrophilic and hydrophobic parts) migrate to the surface. The hydrophobic tails orient towards the air, and the hydrophilic heads remain in the water. This arrangement weakens the cohesive forces between water molecules at the surface, thereby significantly reducing the surface tension ($\sigma_{lg}$) of the water.

3. Impact on Angle of Contact (Wetting):

   • Recall Young's equation: $\cos \theta = \frac{\sigma_{sg} - \sigma_{sl}}{\sigma_{lg}}$.
   • When detergent is added, $\sigma_{lg}$ (surface tension of the liquid-gas interface) decreases.
   • For $\cos \theta$ to increase (which means $\theta$ decreases, becoming more acute), the denominator $\sigma_{lg}$ must decrease, assuming $\sigma_{sg} - \sigma_{sl}$ remains relatively constant or changes less significantly.
   • A smaller angle of contact means the liquid wets the surface more effectively.

4. Practical Implication (Cleaning):

   • In cleaning, water needs to penetrate small crevices and spread over dirty surfaces.
   • Pure water often has a relatively high surface tension and may not wet certain surfaces well (e.g., oily fabrics).
   • By reducing the surface tension, detergents allow water to spread out more easily, penetrate pores, and make better contact with dirt particles. This enhanced wetting ability is crucial for effective cleaning.

(e) A drop of liquid under no external forces is always spherical in shape.

1. Surface Tension and Energy Minimization: Every system in nature tends towards a state of minimum potential energy. For a liquid, the surface molecules possess higher potential energy compared to molecules in the bulk due to the unbalanced cohesive forces they experience.

2. Minimizing Surface Area: To minimize this surface potential energy, a liquid will naturally try to minimize its surface area. The surface tension acts as a force that pulls the surface inwards, striving to achieve the smallest possible surface area for a given volume.

3. The Sphere as the Optimal Shape: Among all possible three-dimensional shapes that can enclose a given volume, a sphere has the smallest surface area.

4. Absence of External Forces: In the absence of external forces such as gravity, air resistance, or contact with solid surfaces, there are no other forces to counteract the inward pull of surface tension. Therefore, the liquid drop is free to assume the shape that minimizes its surface energy, which is a perfect sphere.

5. Real-World Observation: On Earth, gravity distorts the shape of larger drops, flattening them. However, in microgravity environments (like space), where the effect of gravity is negligible, liquid drops and bubbles are observed to be perfectly spherical.

Young's equation cos(theta)=(sigma_sg-sigma_sl)/sigma_lg. (a)/(b) water-glass: adhesion wins, acute angle, spreads (wets). mercury-glass: cohesion wins, obtuse angle, beads. (c) surface tension = force per unit length, an intrinsic property independent of total area. (d) detergent lowers sigma_lg, raising cos(theta) -- smaller contact angle, better wetting/cleaning. (e) liquid minimizes surface area for given volume with no external force -- sphere has least surface area per volume.