Question

Unit of surface tension is (a) dyne \(\mathrm{cm}\) (b) dyne \(\mathrm{cm}^{-1}\) (c) dyne \(\mathrm{cm}^{-2}\) (d) none

Short answer

The correct answer is (b) dyne \(\mathrm{cm}^{-1}\).

Step-by-step solution

Recall the definition of surface tension

Surface tension is the tendency of liquid surfaces to shrink into the minimum surface area possible. It can be mathematically defined as the force acting at right angles to the line of unit length on the liquid surface. Thus, unit of surface tension is force per unit length.

Identify the unit from the given options

Looking at the given options, dyne is a unit of force and \(\mathrm{cm}\), \(\mathrm{cm}^{-1}\), \(\mathrm{cm}^{-2}\) are all different expressions of length. So we are looking for a combination that would result in force per unit length.

Choose the correct option

The option that matches with the unit of surface tension, which is force per unit length, is dyne \(\mathrm{cm}^{-1}\). So the correct answer is option (b).

Confirmation

Therefore, we have confirmed that the unit of surface tension is dyne \(\mathrm{cm}^{-1}\).

Key concepts

Surface Tension

Surface tension is a remarkable physical phenomenon that is commonly observed in our daily lives, from water beads on a waxed car to the ability of some insects to walk on water. It arises from the cohesive forces between liquid molecules at the liquid's surface. These molecules are attracted to each other and to the molecules beneath them, but there is no attraction from air above, causing the molecules on the surface to be pulled inward. This inward force causes the liquid to contract and minimize its surface area, leading to the formation of droplets or allowing objects denser than water, such as a carefully placed needle, to stay afloat if the surface is not disrupted.

When learning about surface tension in physical chemistry, it is essential to recognize that it is not merely a force but a force per unit length. This means that surface tension tries to make a liquid occupy the smallest possible surface area for a given volume. It's like a stretched elastic membrane, and this is the reason why droplets form into spherical shapes, as spheres have the smallest possible surface area for a given volume. Understanding these fundamental principles helps comprehend behaviors of liquids in various situations, including biological membranes, industrial processes, and even in art like marbling.

Physical Chemistry

Physical chemistry is the branch of chemistry concerned with the underlying principles that govern the physical properties of molecules, the forces between them, and the resulting structures and reactions. Surface tension, as a concept, sits squarely within the remit of physical chemistry, manifesting the delicate balance between intermolecular forces at play within a liquid.

In physical chemistry, one often studies phenomena such as surface tension in the context of thermodynamics, quantum chemistry, and kinetics. In thermodynamics, surface tension is considered as an expression of the system's free energy—more specifically, the surface free energy. Surface tension is related to the potential energy and can even affect the boiling and melting points of liquids. By studying surface tension, chemists can gain insights into molecular interactions, develop new materials, and understand natural processes like the formation of cells and the behavior of water in plants.

Unit Conversion

Unit conversion is a vital skill not only in chemistry but in all fields of science and engineering. It allows for the quantification and comparison of various physical quantities in terms consistent and comprehensible across different systems of units. In the context of surface tension, the correct unit communicates the amount of force exerted per unit length of the liquid's surface.

The SI unit for surface tension is the newton per meter (N/m), but in the cgs (centimeter-gram-second) system, the dyne per centimeter (dyn/cm) is used. 1 dyne is equivalent to 10^-5 newtons, and since the two measurements are force per unit length, they can be converted from one to another with the appropriate conversion factors. For instance, students and professionals dealing with surface tension must be comfortable converting between these units to interpret experimental data correctly or to apply the information in real-world situations. Developing proficiency in unit conversion ensures clear and effective communication of scientific measurements.