Stretch a rubber band while holding it gently to your lips. Then slowly let it relax while still in contact with your lips. a. What happens to the temperature of the rubber band on stretching? b. Is the stretching an exothermic or endothermic process? c. Explain the above result in terms of intermolecular forces. d. What is the sign of \(\Delta S\) and \(\Delta G\) for stretching the rubber band? e. Give the molecular explanation for the sign of \(\Delta S\) for stretching.

Short Answer

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When stretching the rubber band, its temperature increases due to an exothermic process that releases heat energy as the work done on the band is converted into thermal energy. This is caused by the work required to overcome intermolecular forces holding the coiled polymer chains together. As the rubber band becomes more ordered when stretched, ΔS (change in entropy) is negative. Gibbs Free Energy, ΔG, is positive in this case as the action is non-spontaneous. The negative sign of ΔS is due to the decrease in disorder while stretching the rubber band.

Step by step solution

01

Part a: Observation of temperature change

When stretching the rubber band, you might notice that the band feels warm, indicating that temperature of the rubber band increases when it is stretched.
02

Part b: Identification of the Thermodynamic Process

The process of stretching the rubber band and the subsequent increase in temperature is identified as an exothermic process. Exothermic processes are chemical reactions that release heat energy to the surroundings. In this case, the work done on the rubber band (where work is a form of energy) converts into thermal energy, which is experienced as heat when the rubber band is placed near the lips.
03

Part c: Explanation in Terms of Intermolecular Forces

When a rubber band is stretched, the long polymer chains that make up the band are straightened out. Initially, these chains are coiled and entangled. Pulling the chain straight requires work (energy) which overcomes intermolecular forces holding the polymer chains in a coiled and entangled state. This energy is then dissipated as heat, causing the rubber band to warm up.
04

Part d: Determining Sign of ΔS and ΔG

Delta S (ΔS) represents the change in entropy or disorder of the system. On stretching the rubber band, the disordered, coiled polymer chains are made more ordered; hence ΔS is negative. Meanwhile, Gibbs Free Energy ΔG is described as ΔG = ΔH - TΔS (where ΔH represents enthalpy, T represents temperature). Considering this equation, for an exothermic process ΔH is negative, while for ΔS is negative by reasoning above. Thus there could be situations where ΔG could be positive or negative depending on the temperature. But in this case, as the action is non-spontaneous, at room temperature ΔG would be positive.
05

Part e: Molecular Explanation for the sign of ΔS

ΔS is negative because whilst stretching, the long polymer chains constituting the rubber band are straightened and ordered, leading to a decrease in disorder, or a negative change in entropy. In a natural, unstretched state, the rubber chains have random, coiled configurations which are significantly more disordered. Therefore, when the chains are forced into a more ordered arrangement (as in stretching), the entropy decreases.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Entropy Change () and Exothermic Processes
When a rubber band is stretched, it may not be immediately apparent, but a significant thermodynamic process is taking place—one that involves entropy change and heat energy. Entropy, denoted as ), is a measure of the disorder within a system. As a rubber band stretches, it experiences a change in entropy, typically a decrease, signifying an increase in order within the system.

Simultaneously, this process is exothermic, meaning heat is released into the surroundings. This release is sensible as warmth when the rubber band is held close to the lips. In exothermic processes, like the stretching of a rubber band, the energy needed to change the rubber's shape is less than the energy released upon rearranging the rubber's internal molecular structure, leading to an overall release of excess energy as heat.

In terms of rubber elasticity, this occurs because the stretched rubber becomes more ordered as its polymer chains align. The system goes from a higher entropy state (unstretched, entangled) to a lower entropy state (stretched, aligned), with the excess energy given off as heat. The decrease in entropy is represented with a negative ) value, confirming the transition to a more ordered state.
Intermolecular Forces and Rubber Elasticity
Intermolecular forces play a pivotal role in the elasticity of rubber. These forces are the interactions that occur between molecules, including van der Waals forces, dipole-dipole interactions, and hydrogen bonds. Rubber is composed of long polymer chains; in their natural state, these chains are coiled and randomly entangled.

Stretching a rubber band means straightening out these entangled polymer chains. To do this, one must apply a force to overcome the intermolecular forces maintaining the coiled state. As these chains are elongated, the intermolecular forces resist the stretching, storing potential energy within the stretched band.

When the band is released, that energy is then used to return the polymer chains to their original, disordered state, hence the band retracts. Essentially, the intermolecular forces that hold the rubber molecules together allow the rubber to be both stretched and to return to its shape, which is a distinctive characteristic of rubber's elasticity.
Gibbs Free Energy () in Rubber Elasticity
Gibbs Free Energy, symbolized by ), represents the capacity of a system to perform work when temperature and pressure are constant. Concerning the thermodynamics of stretching a rubber band, ) can determine whether a process is spontaneous or non-spontaneous. The change in Gibbs Free Energy () for a system is given by the equation: ) = ) - * ), where ) is change in enthalpy (total heat content) and ) is the absolute temperature in Kelvin.

During the stretching of a rubber band, the process is non-spontaneous at room temperature, indicated by a positive ) value. This positivity denotes that energy must be supplied (through stretching) to proceed with the action. Although the system becomes more ordered (negative entropy change), the exothermic nature of the process (negative enthalpy change) complicates the spontaneity. In essence, the stretching of a rubber band at room temperature requires external influence, hence why ) is positive, signifying non-spontaneous behavior.

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