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# The spontaneity of reactions

## Problem Nobody ignores that a steam engine is not driven by water. However the reaction $2H_2O(l)$ $\rightarrow$ $2H_2(g)$ $+$ $O_2(g)$ would theoretically produce enough hydrogen $H_2$ gas to drive the train! Unfortunately this reaction does not happen in nature, it is not spontaneous. What are the general criteria which allow to decide whether a reaction is spontaneous or not?

## Criteria

### First criterium: The minimum of energy

- A baby lacking of balance on his little feet falls down. - The electrons in an atom tend to occupy the lowest energy level. - An oven looses heat. - All combustions have a negative $\Delta H$ , that means that enthalpy, the form of energy which is particularly important in chemistry , decreases!

Systems tend to transform spontaneously into a state with less energy.

But the matter is not that simple: - Ice in a lemonade glass transforms spontaneously into water absorbing heat during this transformation. - If our clothes are wet, we feel cold. That is because water absorbs spontaneaously heat during vaporization and deprieves our body of that heat. - Ammonium chloride($NH_4Cl$) dissolves spontaneously in water while cooling it, that means deprieving it from its heat! These observations show that minimising energy, in chemistry loosing heat cannot be the only criterium for spontaneity of a reaction!

### Second criterium: Temperature

Consider the following transformations: $H_2O(s)$ $\rightarrow$ $H_2O(l)$ $(1)$ Fusion of ice $H_2O(l)$ $\rightarrow$ $H_2O(s)$ $(2)$ Freezing of water At $20^oC$, (1) is spontaneous, whereas (2) is not. At $-20^oC$, (2) is spontaneous, whereas (1) is not. Thinking about reactions (1) and (2) we see that a rise of temperature favorises the reaction (1) where the system absorbs heat, a drop in temperature favorises the reaction (2) where the system looses heat.

At high temperature the endothermic reactions tend to be spontaneous, at low temperature the exothermic.

But the matter is not that simple: - Combustions are exothermic and proceed even at high temperatures - The endothermic dissolution of ammonium chloride proceeds even at low temperatures These observations show that temperature cannot be the only criterium for the spontaneity of reactions !

### Third criterium: The statistical probability

Example 1  A photograph takes snapshots after a group of visitors has entered an exposition. Guess which snapshot has been taken half an hour after the opening of the exhibition ! Answer: The one at the bottom, the one at the top has probably been made immediately after the opening. Why? Although some persons must make the effort to climb up to the mezzanine ($\Delta H>0$), which would be an argument against the snapshot at the bottom, there are quite simply more possibilities for persons to stand in front of 5 pictures than 2. The snapshot at the bottom is statistically more probable. We see a tendency to the increase of "disorder" in an isolated system. This tendency is in this case stronger than the law of the least effort (Minimum energy)

Example 2: The diffusion At the top, we can see the molecules of a gas. The wall is taken off. What happens? Answer: The gas diffuses into the empty compartment. Why? There are much more possible configurations of the molecules, if they occupy the whole volume. Picture 3 is statistically more probable.

Example 3: The explosion

Ammonium nitrate is an explosive which is very much favoured by terrorists (you can buy it as fertilizer!) $2NH_4NO_3(s)$ $\rightarrow$ $2N_2(g)$ $+$ $4H_2O(g)$ $+$ $O_2(g)$ The reason for the explosion is the very fast production of gases which happens spontaneously. Why spontaneously ? The products of this reaction are very small gaseous molecules for which there exist much more possible configurations due to the big volume and their diversity compared to the solid at the left side, where the $NH_4^+$ and $NO_3^-$ ions are in a fixed position inside the cristal lattice. The "disorder" increases from left to right.

Systems tend to a maximum of disorder.

The probability of a system state (the "disorder") is defined by a state function called →   Entropy , symbol $S$ .