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# Entropy

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Entropy

What will it look like?

When the pieces of a jigsaw puzzle are dumped from the box, the pieces naturally hit the table in a very random pattern. In order to put the puzzle together, a great deal of work must be done to overcome the natural disorder of the pieces. The pieces need to be turned right-side up, then sorted by color or edge (some people like to put the border together first). Then comes the challenge of finding the exact spot of each piece of the puzzle in order to get the final organized picture.

### Entropy

There is a tendency in nature for systems to proceed toward a state of greater disorder or randomness. Entropy is a measure of the degree of randomness or disorder of a system. Entropy is an easy concept to understand when thinking about everyday situations. The entropy of a room that has been recently cleaned and organized is low. As time goes by, it likely will become more disordered and thus its entropy will increase (see Figure below ). The natural tendency of a system is for its entropy to increase.

The messy room on the right has more entropy than the highly ordered room on the left.

Chemical reactions also tend to proceed in such a way as to increase the total entropy of the system. How can you tell if a certain reaction shows an increase or a decrease in entropy? The molecular state of the reactants and products provide certain clues. The general cases below illustrate entropy at the molecular level.

1. For a given substance, the entropy of the liquid state is greater than the entropy of the solid state. Likewise, the entropy of the gas is greater than the entropy of the liquid. Therefore, entropy increases in processes in which solid or liquid reactants form gaseous products. Entropy also increases when solid reactants form liquid products.
2. Entropy increases when a substance is broken up into multiple parts. The process of dissolving increases entropy because the solute particles become separated from one another when a solution is formed.
3. Entropy increases as temperature increases. An increase in temperature means that the particles of the substance have greater kinetic energy. The faster moving particles have more disorder than particles that are moving more slowly at a lower temperature.
4. Entropy generally increases in reactions in which the total number of product molecules is greater than the total number of reactant molecules. An exception to this rule is when a gas is being produced from nongaseous reactants.

The examples below will serve to illustrate how the entropy change in a reaction can be predicted.

$\text{Cl}_2(g) \rightarrow \text{Cl}_2(l)$

The entropy is decreasing because a gas is becoming a liquid.

$\text{CaCO}_3(s) \rightarrow \text{CaO}(s)+\text{CO}_ 2(g)$

The entropy is increasing because a gas is being produced and the number of molecules is increasing.

$\text{N}_2(g)+3\text{H}_2(g) \rightarrow 2\text{NH}_3(g)$

The entropy is decreasing because four total reactant molecules are forming two total product molecules. All are gases.

$\text{AgNO}_3(aq)+\text{NaCl}(aq) \rightarrow \text{NaNO}_3(aq)+\text{AgCl}(s)$

The entropy is decreasing because a solid is formed from aqueous reactants.

$\text{H}_2 (g)+\text{Cl}_2(g) \rightarrow 2\text{HCl}(g)$

The entropy change is unknown (but likely not zero), because there are equal numbers of molecules on both sides of the equation and all are gases.

#### Summary

• Entropy is defined.
• Situations involving entropy changes are described.

#### Review

Indicate whether entropy increases or decreases in each of the following situations:

1. The jigsaw puzzle is taken apart and put back in the box.
2. Clothes are folded and put away.
3. ice  $\rightarrow$ steam.
4. $\text{Pb(NO}_3)_2(aq)+2\text{KI}(aq) \rightarrow \text{PbI}_2(s)+2 \text{KNO}_3$ .