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Unit 9: Equilibrium and Advanced Thermodynamics—Balance in Chemical Reactions

Section 4: Entropy and States of Matter

In the previous sections, we saw that high entropy is associated with two things: a wide distribution of particles and a wide distribution of energy quanta. The more particles and energy quanta can spread out, the more entropy there is. (Figure 9-6)

Bearing this in mind, it should make sense that a substance in the solid phase would have relatively low entropy. In a solid, the particles are locked in place and highly ordered, the clear opposite of disorder or entropy. The atoms can hardly move around in a solid's rigid structure and so their opportunities for spreading out are minimal. The quanta of energy in a solid are restricted mainly to vibration, so the distribution of quanta is also minimized.

Entropy and the States of Matter

Figure 9-6. Entropy and the States of Matter

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Entropy and the States of Matter

Figure 9-6. Entropy and the States of Matter

Entropy increases as temperature increases and as a substance changes from solid to liquid to gas.

The entropy of the liquid phase is higher. The particles are no longer locked in place. Because they are now free to move, they can distribute themselves in more ways. The energy quanta can distribute themselves in a greater variety of ways as well. Like a solid, the molecules can vibrate; but because they have more freedom of movement, molecules have rotational and some translational energy, too.

Gases have the highest entropy values because they have the greatest freedom of movement. Gas particles are separate and distribute themselves throughout their container (see Section 2: Microstates, Macrostates, and Matter). And, gases also possess all three types of energy: translational, rotational, and vibrational.

Finally, a substance that is dissolved in a liquid also has a high level of entropy for reasons similar to gases. Dissolved particles are free to not only move throughout the volume of the liquid, but also to move in all three ways. Generally speaking, the entropy value of a dissolved substance is higher than pure liquids but less than gases. To summarize, the entropy of the phases of matter are:

Solid < Liquid < Dissolved < Gas

Using this information, we can make an educated guess about whether entropy is increasing or decreasing when a chemical reaction occurs. Consider the following reaction in which solid table salt dissolves in water:

NaCl(s) → Na+(aq) + Cl-(aq)

In this case, a solid (low entropy) is turning into two aqueous ions (higher entropy). We can reasonably assume that entropy increases. When entropy increases, the change in entropy, ΔS, is positive. As we know, this reaction is spontaneous; salt dissolves in water. Consider another spontaneous process, the sublimation of dry ice (solid CO2):

CO2(s) → CO2(g)

Here, a solid (low entropy) turns into a gas (high entropy). Again, ΔS is positive.

Both of the above reactions are spontaneous, and both produce products with higher entropy than the reactants. It may be tempting, then, to assume that all such reactions are spontaneous. But consider the burning of hydrogen gas:

2H2(g) + O2(g) → 2H2O(l)

In this reaction, gases (high entropy) change into liquid (low entropy); ΔS is negative. Yet, the reaction is spontaneous; hydrogen is highly flammable.


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