- Online Text
- 1. Introduction
- 2. Microstates, Macrostates, and Entropy
- 3. The Entropy of Energy Quanta
- 4. Entropy and States of Matter
- 5. Spontaneity and Gibbs Free Energy
- 6. Coupling Reactions
- 7. Equilibrium
- 8. The Equilibrium Constant Expression
- 9. Le Chatelier's Principle
- 10. Temperature and Equilibrium
- 11. Conclusion
- 12. Further Reading
- Unit Guide (PDF)
Section 3: The Entropy of Energy Quanta
In the previous section, we saw how the random movement of gas particles leads to an even distribution of those particles inside a container. The particles will spontaneously spread out simply because the "spread out" macrostate is the most likely. In other words, the spread-out macrostate has the most entropy.
Figure 9-4. Energy Quanta
Like particles of gas, energy quanta also distribute themselves according to statistical mechanics.
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A similar analysis explains why heat flows from hot objects to cold objects. As discussed in Unit 3, energy is quantized; it exists in discrete packets called "quanta." These quanta move randomly between particles as they bump into each other. When two objects of different temperature are brought into contact, the quanta of energy distribute themselves uniformly throughout just like gas particles spreading throughout their container. (Figure 9-4)
Just as the most probable macrostate for the gas particles was 2:2, the most probable macrostate for the energy quanta is 2:2. Boltzmann's statistics not only explain why gas particles spontaneously spread out, but also why energy quanta spontaneously spread out.
As noted in the introduction to this unit, exothermic reactions are often (but not always) spontaneous. The underlying reason for this is that exothermic reactions increase entropy by releasing quanta of energy. The quanta spread out, and entropy increases. Thus, exothermic reactions tend to be spontaneous.
Energy quanta can spread by transferring from one particle to another throughout an object, but they can also spread out in a different sense. Not only can a quantum jump between particles, but it can also cause the particle to move in different ways. (Figure 9-5) A quantum of energy might make a particle move through space faster; this is called "translational energy." It also might cause a molecule to rotate in place; this is called "rotational energy." Finally, a quantum of energy might cause the bonds of a molecule to vibrate. This vibrational energy causes chemical bonds to stretch and contract, or to bend and straighten.
Figure 9-5. Energies
Energy can cause a molecule to move in different ways: vibration of its bonds, rotation of the molecule as a whole, or translation (movement through space).
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The more ways a molecule can move, the more ways quanta of energy can be distributed. The water molecules in an ice cube can only vibrate in place. Quanta of energy are restricted to vibrational energy, and therefore ice has a low entropy value. In liquid water, the quanta can spread out to cause vibration and rotation; liquid water has higher entropy. Gaseous water (steam) has the highest amount of entropy because the molecules possess vibrational, rotational, and translational energies.