Let us recap where we are: starting with the most basic units of matter, atoms (at least from a chemistry perspective) we have seen that:

• Atoms interact electrostatically with each other in a variety of ways, from transient interactions that result in weak (that is, easy to break) attractions to strong (bonding) interactions that are much more difficult to break.
• When atoms interact to form more stable systems, the potential energy of the system decreases, but the total energy of the system remains constant. The energy of the interacting atoms can decrease if is transferred to the surroundings. This generally involves collisions with other molecules, but the emission of a photon is also possible.
• Whether weak or strong, all types of interaction require energy to break - typically this energy is derived from interactions with surrounding molecules, although absorption of a photon is also possible.
  

The ways that atoms interact depends upon the arrangements of the electrons within them. Different types of atoms have different “internal” arrangements of electrons.

When atoms bond to form new materials (compounds), the properties of those compounds are emergent - that is they are quite different from the properties of the isolated component atoms.
The macroscopic properties of materials depend upon the types of bonds present and their spatial organization, which influences molecular shape, the distribution of charges within the molecule, and intermolecular interactions. Some materials are continuous (diamond, metals) while others are composed of discrete molecular units (water, methane, lipids, proteins).

The temperature at which a material changes from solid to liquid, liquid to gas, and visa versa (phase changes) enables you to make predictions about how much energy is required to overcome the interactions between the particles that make up the material.

Now we are ready to draw all these ideas together and make connections between the macroscopic and molecular levels. We will consider the factors that allow us to predict how and when chemical changes will occur - the heart of chemistry.

Temperature

Up to now the major type of change we have considered are phase changes, that is changing from a solid to liquid, or liquid to gas, and vice versa. In order to think about the details of what happens during a phase change, there are a number of ideas that we need to explore more thoroughly. The first of these is temperature. If you look up the definition of temperature you will often find something like ‘temperature is a measure of the “hotness” of an object’. You may have even thought to yourself - well that’s not very illuminating is it? However, it is actually quite difficult to give a simple definition of temperature, typically abbreviated as T. Temperature is a physical concept (that is, something you should be taught about in physics courses), but perhaps you weren’t, so you will have to bear with us (a chemist and a cell and molecular biologist) as we work our way through it.

A useful macroscopic way of thinking about temperature is that it tells you in which direction thermal energy (often called heat) will move - energy always moves from a hotter object (higher temperature) to a cooler (lower temperature) object. While this seems such an obvious statement it captures a very important aspect of how the world behaves. And even though it is “obvious”, do you really know why it must be the case? Why doesn’t heat flow from cooler to warmer? And how does a refrigerator or an air conditioner work, exactly? Do they violate some “law of the universe”? (we will be coming back to these questions later on).

Temperature and thermal energy are often confused, and before we go on we need to have a good grasp of the difference between them. The temperature of an object is independent of the size of the object, at least until we get down to the atomic/molecular level where temperature begins to lose its meaning as a concept. The temperature of a drop of boiling water is the same as the temperature of a pan (or an ocean) of boiling water, it is 100°C. At the same time, the total amount of thermal energy in a drop of water is much less than that in a large pot of water - which (we hope) makes sense - a drop of boiling water may sting for a moment if it lands on you - but a pan of boiling water will cause serious damage if it splashed over you. Why? - even though the two are at the same temperature, one has relatively little thermal energy while the other has a lot - the amount of energy is related to the size of the system. In addition, the amount of thermal energy also depends on the type/composition of the material. Different amounts of different substances can have different amounts of thermal energy, even if they are at the same temperature (now that is weird).

Kinetic energy

Another way of thinking about temperature is that it is related to the energy of the particles in the sample – the faster the particles are moving the higher the temperature. It may well take different amounts of energy to get particles moving at the same average kinetic energy. For a simple monoatomic gas, like helium or neon, the only motion that the atoms can do is to move from one place to another - in a straight line - until they bump into something else, i.e. another atom or molecule. This kind of motion is called translational motion and is directly linked to the kinetic energy of the atom or molecule through the relationship E_K(bar) = 1/2 mv(bar)², where v(bar) is the average velocity of all of the molecules in the population, and m is the mass. In any given sample of moving atoms, there are collisions, but any individual collision does not alter the total energy of the system (that is what conserved means), but the relative kinetic energies of the two (or more) colliding atoms can change - if one slows down, the other will speed up (remember, we are now talking only about monoatomic species, things get more complicated with more complex molecules).

A single atom/molecule has kinetic energy, but not a temperature. This is an important distinction. While populations of molecules have a temperature, related to their average velocity,
individual molecules within the population can differ dramatically from one another in the amount of kinetic energy they have. When it comes to chemical reactions, it is individual kinetic energies that will be critical (we consider this point in detail in chapter 7).

Thinking about populations of molecules

Within a population of atoms/molecules the many collisions that occur per second will lead to a range of speeds and directions (that is, velocities) of the atoms/molecules. When large numbers of particles are involved in a phenomenon, their individual actions are not important (although they are when individual molecules collide). We treat large numbers of molecules as a population; a population characterized in terms of a distribution, that is the number or probability of molecules moving with various velocities. This makes it possible to use statistical methods to characterize the behavior of the population. While any particular molecule will behave differently from one moment to the next, depending upon whether it collides with other molecules or not, the behavior of the population is quite predictable. This is an example of how the random behavior of individuals can give rise to lawful (that is predictable) behaviors of populations. From this population perspective, it is the distribution of kinetic energies of atoms or molecules that depends upon the temperature of the system, and as we will see, the molecular composition of the material. We will not concern ourselves with deriving the equations that describe these relationships, but rather focus on a general description of the behavior of the motions of atoms and ?molecules in various states of matter. We think you will find this quite comprehensible.

Let us think about a population of molecules at a particular temperature, in the gas phase. Because of their constant collisions with one another, the population of molecules will have a distribution of speeds. We can calculate the probability of a particular molecule moving at a particular speed. This relationship is known as the Maxwell-Boltzmann distribution. Its shape is a function of the temperature of the system; typically it rises fairly steeply from zero (all of the curves begin at zero) to a maximum, which then decreases and tails off at higher velocities (or kinetic energies).

Question to answer:

• What happens to the average speed as the temperature increases?
• When molecules collide, why don’t they always stick together?
• What do you think happens to the average speed as the molecular weight increases (assuming the temperature stays the same)?
• Imagine a system composed of two different types of molecules, one relatively light and one relatively heavy. At a particular temperature, how do their average kinetic energies compare?
• Which, on average, is moving faster?
  

Questions to ponder:

• If one consider’s the uncertainty principle, what is the slowest velocity a molecule can move at?
• You place a thermometer into a solution - why does it take time for the reading on the thermometer to correspond to the temperature of the solution