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Spontaneous processes

Spontaneous processes

Key concepts for this section

• A spontaneous process is a process that occurs in a system without any input of energy from the surroundings.

• A spontaneous process is also called an irreversible process, since to reverse the process requires the input of external energy.

• Energy conservation (see the first law of thermodynamics) alone does not allow us to predict spontaneity.

The first law says nothing about the direction that a process obeying it will operate in. A process in which two bodies initially at the same temperature and in physical contact transfer heat between them in such a way that one body becomes warmer while the other becomes colder does not violate the first law. But we all know that this does not occur. In fact, the opposite process occurs spontaneously. Two bodies in contact and initially at different temperatures will come to thermal equilibrium, exchanging heat between them until both are at the same temperature.
  This is our first example of a spontaneous process: two bodies at different temperatures T(1) and T(2) will spontaneously exchange heat in such a way to establish thermal equilibrium at some intermediate temperature. Note that if we treat the two objects together as an isolated system (the boundary separating the two objects from the rest of the universe is a good insulator, whereas heat is freely conducted across the area of contact between the two objects), this process occurs without exchange of heat with the surroundings (q = 0) and with no change in volume, so no P-V work is done (w = 0). Therefore, by the first law, ΔU = 0 for the system. But then ΔU = 0 for the reverse process, and yet this is never observed. Clearly, more is needed to predict spontaneity - at least in this example involving just transfer of heat energy between two bodies. What about other spontaneous physical and chemical changes?

Other examples of spontaneous processes.

Conversion of gravitational potential energy into kinetic energy. Any object - a bowling ball for example - will fall from a high place, such as the ledge of a building, to the ground. In this case, the potential energy of a mass - given by the relation V = mgh - is converted into kinetic energy as it falls.

Change of state with temperature. Water freezes spontaneously at temperatures below 0° C, and ice melts spontaneously at temperatures above 0° C.

Approach to chemical equilibrium. In chemical reactions, the approach to equilibrium is spontaneous. For example, in the reaction between hydrogen gas and iodine gas to form gaseous hydrogen iodide, if we start with a mixture of hydrogen and iodine at 440°C, it will spontaneously begin to react, forming HI(g).

This process continues until the concentrations of the three gases satisfy the equilibrium condition. This reaction can be illustrated by a progress curve (shown below right). At the start of the reaction, the concentrations of the reactants do not satisfy the equilibrium condition.

Therefore, all concentrations change spontaneously with time until the equilibrium condition is met. Once the reaction has progressed to equilibrium, the concentrations of reactants and products are constant with time (flat portions of the progress curves).

If instead we start with 100% hydrogen iodide a reaction also spontaneously occurs, in which some of the HI is converted into hydrogen and iodine. Again, the process occurs because the initial state is not in equilibrium.

What makes a process spontaneous?

Many processes that we know of as spontaneous also release energy. In chemical reactions for example, the formation of chemical bonds between individual, nonbonded atoms is spontaneous and accompanied by the release of heat. This is the case for the formation of a molecule of H2 from two hydrogen atoms. In most chemical reactions, however, some bonds are broken while others are formed. When the bonds that form in the products of a reaction are stronger, or greater in number than those that exist in the reactants, heat is released in the reaction. Hydrogen and oxygen react spontaneously to form water. When two moles of water form by the reaction of two moles of of H2 and one mole of O2 a great deal of heat is released. In fact, the presence of significant amounts of these gases together is quite dangerous, since this reaction readily occurs explosively.

Enthalpy change does not tell the whole story, however. A spontaneous process is not necessarily exothermic, as shown by the example of the dissolving in water of many ionic solids (e.g. ammonium nitrate). When such solids dissolve in water, a spontaneous process, the solution becomes noticeably colder. The system loses heat, meaning this process is endothermic despite its spontaneous character.

This example actually provides an important clue about the nature of another factor in determining whether a system undergoes a spontaneous process. The initial state of the system is characterized by the presence of two separate phases: pure liquid water and the highly ordered ionic solid - which is in the form of a crystal. In the final state of the system, reached by a spontaneous process, the component ions of the previously localized and ordered crystal are now uniformly distributed throughout the solution.

There are apparently two factors that together determine whether a physical or chemical process will occur spontaneously within a given system - the release of energy and a "spreading out" and increased mixing of the matter composing the system. Often, this more broadly distributed and mixed system can be qualitatively identified with increase in randomness or disorder. The ions of the crystal have lose their highly ordered arrangement and end up distributed randomly throughout the whole volume of the solution. In trying to understand and quantify the contribution of this factor to spontaneity, we give it a name - entropy - and shortly we will see how it can be precisely defined.

Next: Entropy
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